5272道题目5525 条题源记录 · 相同内容已合并
多项式・因式与余式挑战
Exactly how many x-intercepts does the graph of \( f\left(x\right)=x\left(x-10\right)^2\left(x-11\right)^3 \) have in the xy-plane, where \( y=f\left(x\right) \)?
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多项式・因式与余式进阶
The graph of the polynomial function \( f \) in the xy-plane, where \( y=f\left(x\right) \), has x-intercepts of \( \left(-2,\ 0\right) \) and \( \left(8,\ 0\right) \). Which of the following must be true?
原库参考解析
多项式・因式与余式进阶
\( \left(x-20\right)\left(x-18\right)\left(x+9\right)\left(x+17\right)=0 \)
What is a positive solution to the given equation?
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多项式・因式与余式进阶
\( -5\left(v-8\right)\left(v-2\right)\left(v+9\right)=0 \)
What value of v is a solution to the given equation?
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多项式・因式与余式挑战
The function h is defined by \( h\left(x\right)=\left(x+p\right)\left(x-4\right)\left(2x-6\right) \), where p is a constant. In the xy-plane, the graph of \( y=h\left(x\right) \) passes through the point \( \left(-6,\ 0\right) \). What is the value of \( h\left(0\right) \)?
原库参考解析
多项式・因式与余式进阶
\( \left(x-16\right)\left(x-12\right)\left(x+7\right)\left(x+13\right)=0 \)
What is a positive solution to the given equation?
原库参考解析
多项式・因式与余式挑战
One of the factors of \( 5x^3+105x^2+540x \)is x+b, where b is a positive constant. What is the smallest possible value of b?
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多项式・因式与余式进阶
Which of the following could be the equation of the graph shown in the xy-plane?
原库参考解析
多项式・因式与余式挑战
One of the factors of x3 + 2x2 − 23x − 60 is x + k, where k is a constant. What is the smallest possible value of k ?
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多项式・因式与余式挑战
Which of the following expressions has a factor of x ＋ 2b, where b is a positive integer constant?
原库参考解析
多项式・因式与余式进阶
f(x) = x + 4
g(x) =3x2 - rx + 48
The functions f and g are given. In function g, r is a constant. If f(x) · g(x) = 3x3+192, what is the value of r ?
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多项式・因式与余式进阶
34z14 + bz7 + 70
In the given expression, b is a positive integer. If qz7 + r is a factor of the expression, where q and r are positive integers, what is the greatest possible value of b?
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