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3.75k
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stringclasses 2
values | latex
sequencelengths 1
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HW | [
"$\\displaystyle P(x)=(x+3) Q(x)+4$"
] |
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HW | [
"$\\displaystyle Q(x)=(x-2) Q^{\\prime}(x)+5$"
] |
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HW | [
"$\\displaystyle P(2)=5 \\times Q(2)+4$"
] |
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HW | [
"$\\displaystyle P(2)=5 \\times Q(2)+4$"
] |
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"$\\displaystyle -4$"
] |
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HW | [
"$\\displaystyle -4$"
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HW | [
"$\\displaystyle x^{2}+x+y^{2}+y-15=0$"
] |
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HW | [
"$\\displaystyle x^{2}+x+y^{2}+y-15=0$"
] |
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HW | [
"$\\displaystyle x^{2}-15+y^{2}=0, \\quad x^{2}+y^{2}=15$"
] |
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HW | [
"$\\displaystyle -2 x y=15, \\quad \\therefore x y=-\\frac{15}{2}$"
] |
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HW | [
"$\\displaystyle \\frac{-15}{2}$"
] |
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HW | [
"$\\displaystyle \\frac{-15}{2}$"
] |
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HW | [
"perfect!!"
] |
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HW | [
"perfect!!"
] |
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HW | [
"$\\left(3 P(x)-4 Q(x)\\right) \\div (x-8) = 3 P(8)-4 Q(8)=24 -8 =16 \\therefore 16 $"
] |
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HW | [
"$\\left(3 P(x)-4 Q(x)\\right) \\div (x-8) = 3 P(8)-4 Q(8)=24 -8 =16 \\therefore 16 $"
] |
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HW | [
"$\\displaystyle 16$"
] |
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HW | [
"$\\displaystyle 16$"
] |
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HW | [
"$\\displaystyle P(x)=(x-2)(4 x+2)+4$"
] |
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HW | [
"$\\displaystyle =4 x^{2}-6 x=(x+2) Q(x)+R$"
] |
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HW | [
"$\\displaystyle =4 x^{2}-6 x=(x+2) Q(x)+R$"
] |
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HW | [
"28"
] |
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HW | [
"$\\displaystyle 1+(k-2)+(k+2) m+n+5=0$"
] |
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"$\\displaystyle m=-1$"
] |
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HW | [
"$\\displaystyle m=-1$"
] |
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HW | [
"$\\displaystyle -2+n+4=0$"
] |
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HW | [
"$\\displaystyle -2+n+4=0$"
] |
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HW | [
"$\\displaystyle n=-2$"
] |
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HW | [
"2"
] |
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HW | [
"522"
] |
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HW | [
"522"
] |
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HW | [
"$\\displaystyle P(x+4)=(x+3) Q(x)+R$"
] |
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HW | [
"$\\displaystyle P(x+4)=(x+3) Q(x)+R$"
] |
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HW | [
"$\\displaystyle P(1)=9$"
] |
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HW | [
"$\\displaystyle P(1)=9$"
] |
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HW | [
"$\\displaystyle (a-1) x+(b+3) y+c+5=-x+y+7$"
] |
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HW | [
"$\\displaystyle (a-1) x+(b+3) y+c+5=-x+y+7$"
] |
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HW | [
"$\\displaystyle a=0, b=-2, c=2 \\Rightarrow a+b+c=0$"
] |
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HW | [
"$\\displaystyle a=0, b=-2, c=2 \\Rightarrow a+b+c=0$"
] |
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HW | [
"$\\displaystyle 0$"
] |
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HW | [
"$\\displaystyle 0$"
] |
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HW | [
"$\\displaystyle (1+m) k+2 m+n=0$"
] |
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HW | [
"$\\displaystyle 1+m=0, m=-1$"
] |
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HW | [
"$\\displaystyle 2 m+n=0,-2+n=0 \\quad n=2$"
] |
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HW | [
"$\\displaystyle P(x)=(x+2)(x-1) Q(x)+x+5$"
] |
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HW | [
"$\\displaystyle P(x+6)=(x+5) Q^{\\prime}(x)+R$"
] |
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HW | [
"$\\displaystyle x P(x)+x^{2}=x^{3}-9 x^{2}-4 x+36 .$"
] |
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HW | [
"$\\displaystyle x P(x)=x^{3}-10 x^{2}-4 x+36$."
] |
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HW | [
"$\\displaystyle x P(x)=x^{3}-10 x^{2}-4 x+36$."
] |
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HW | [
"$\\displaystyle p(1)=1-10-4+36$"
] |
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HW | [
"$\\displaystyle p(1)=1-10-4+36$"
] |
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HW | [
"$\\displaystyle =13 .$"
] |
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HW | [
"$\\displaystyle =13 .$"
] |
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HW | [
"$\\displaystyle x^{2}+2 x+1=(x-1)(x+3)+4$"
] |
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HW | [
"$\\displaystyle x^{2}+2 x+1=(x-1)(x+3)+4$"
] |
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HW | [
"$\\displaystyle Q(x)=x+3$"
] |
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HW | [
"$\\displaystyle 2$"
] |
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HW | [
"$\\displaystyle 2$"
] |
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HW | [
"$\\displaystyle a+b=1 \\quad \\rightarrow \\quad a-5=1 \\rightarrow a=6$"
] |
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HW | [
"$\\displaystyle a+b=1 \\quad \\rightarrow \\quad a-5=1 \\rightarrow a=6$"
] |
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HW | [
"$\\displaystyle b+5=0 \\rightarrow b=-5$"
] |
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HW | [
"$\\displaystyle b+5=0 \\rightarrow b=-5$"
] |
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HW | [
"$\\displaystyle c-4=4 \\rightarrow c=8$"
] |
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HW | [
"$\\displaystyle a-b+c=6+5+8=19$"
] |
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HW | [
"$\\displaystyle P(x)=(x-1)(3 x+1)+4$"
] |
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HW | [
"$\\displaystyle =3 x^{2}-2 x -1+4$"
] |
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HW | [
"$\\displaystyle =3 x^{2}-2 x+3$"
] |
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HW | [
"$\\displaystyle =3 x^{2}-2 x+3$"
] |
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HW | [
"$\\displaystyle x=1,(1-3+2)^{2}=a_{6}+a_{5}+\\cdots+a_{0}=0$"
] |
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HW | [
"$\\displaystyle a_{6}+a_{5}+\\cdots+a_{0}+a_{6}-a_{5}+\\cdots+a_{0}$"
] |
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HW | [
"$\\displaystyle a_{6}+a_{5}+\\cdots+a_{0}+a_{6}-a_{5}+\\cdots+a_{0}$"
] |
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HW | [
"$\\displaystyle 8=a_{10}+a_{9}+a_{8}+ \\cdots +a_{1}+a_{0}$ - ①"
] |
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HW | [
"$\\displaystyle 8=a_{10}+a_{9}+a_{8}+ \\cdots +a_{1}+a_{0}$ - ①"
] |
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HW | [
"$\\displaystyle {2}^{10}+8 = a_{10}-a_{9}+a_{8}- \\cdots -a_{1}+a_{0}$ - ②"
] |
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HW | [
"$\\displaystyle {2}^{10}+8 = a_{10}-a_{9}+a_{8}- \\cdots -a_{1}+a_{0}$ - ②"
] |
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HW | [
"$\\displaystyle 2^{10}+16=2\\left(a_{10}+a_{8}+\\cdots+a_{0}\\right)$"
] |
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HW | [
"$\\displaystyle 2^{10}+16=2\\left(a_{10}+a_{8}+\\cdots+a_{0}\\right)$"
] |
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HW | [
"$\\displaystyle a_{10}+a_{8}+\\cdots+a_{0}=2^{9}+8$"
] |
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HW | [
"$\\displaystyle =520$"
] |
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HW | [
"$\\displaystyle =520$"
] |
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HW | [
"520"
] |
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HW | [
"520"
] |
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HW | [
"$\\displaystyle a=3, b=-1, c=6 .$"
] |
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HW | [
"$\\displaystyle 3 b-\\frac{8}{5}=5 . \\quad b=\\frac{11}{5}$."
] |
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HW | [
"$\\displaystyle a+b+2 c=1+\\frac{11}{5}+\\frac{8}{5}=\\frac{24}{5}$"
] |
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HW | [
"$\\displaystyle a+b+2 c=1+\\frac{11}{5}+\\frac{8}{5}=\\frac{24}{5}$"
] |
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HW | [
"$\\displaystyle a+6=-25, a=-31, b=-28$"
] |
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HW | [
"$\\displaystyle a+6=-25, a=-31, b=-28$"
] |
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HW | [
"$\\displaystyle \\therefore -59$"
] |
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HW | [
"$\\displaystyle \\therefore -59$"
] |
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HW | [
"$\\displaystyle 1+(k-2)+(k+4) m+n+1=0$"
] |
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HW | [
"$\\displaystyle k(1+m)+1-2+4 m+n+1$"
] |
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HW | [
"$\\displaystyle k(1+m)+1-2+4 m+n+1$"
] |
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HW | [
"$\\displaystyle =k(1+m)+4 m+n=0$"
] |
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HW | [
"$\\displaystyle =k(1+m)+4 m+n=0$"
] |
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HW | [
"$\\displaystyle m=-1$"
] |
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HW | [
"$\\displaystyle m=-1$"
] |
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HW | [
"$\\displaystyle - 4+n=0$"
] |
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HW | [
"$\\displaystyle n=4$"
] |
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HW | [
"$\\displaystyle m \\times n=-1 \\times 4=-4$"
] |
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