5272道题目5525 条题源记录 · 相同内容已合并
多项式・因式与余式进阶
\( f(x)=x+3 \)
\( g(x)=7x^2-rx+63 \)
The function \( f \) and g are given. In function g, r is a constant. If \( f(x)·g(x)=7x^{3}+189 \), what is the value of r?
原库参考解析
多项式・因式与余式挑战
One of the factors of \( 8x^4+50x^2+63 \) is \( ax^2+b \), where a and b are positive constants. Which of the following is a possible value of ab?
原库参考解析
多项式・因式与余式进阶
What is an x-intercept of the graph of the equation \( y=(x+3)(x-11)(x+12) \) in the xy-plane?
原库参考解析
多项式・因式与余式基础
\( p(x)=x^3+4x^2+9x+12 \)
When the given function p is graphed in the xy-plane, where \( y=p(x) \), the y-intercept of the graph is \( (0,\ y) \). What is the value of y?
原库参考解析
多项式・因式与余式挑战
For the polynomial function \( f \), the graph of \( y=f(x) \) in the xy-plane passes through the points (-5, 0), (3, 0), and (7, 0). Which of the following must be a factor of \( f(x) \) ?
原库参考解析
多项式・因式与余式挑战
When the polynomial function g is graphed in the xy-plane such that \( y=g(x) \), it passes through the points (4, 0), (7, 0), and (0, 18). Which of the following must be true?
I. When \( g(x) \) is divided by \( (x−4) \), the remainder is 0.
II. The point (7,0) is an x-intercept of the graph of \( y=g(x) \).
III. When \( g(x) \) is divided by \( (x−18) \), the remainder is 0.
原库参考解析
多项式・因式与余式挑战
Which expression is NOT a factor of \( 1,120x^4-43,750 \)?
原库参考解析
多项式・因式与余式挑战
One of the factors of \( 8x^4+26x^2+21 \) is \( ax^2+b \), where a and b are positive constants. Which of the following is a possible value of ab?
参考答案
多项式・因式与余式进阶
The table shows several values of x and their corresponding values of \( f(x) \) for the polynomial function \( f \). Which of the following could define \( f \)?
参考答案
多项式・因式与余式进阶
\( f(x)=11x^{10}+2x^8 \)
\( g(x)=−14x^7+9x^5 \)
The polynomial \( p(x) \) is defined as the product of the given polynomials, \( f(x) \) and \( g(x) \). What is the coefficient of \( x^{15} \) in \( p(x) \)?
参考答案
多项式・因式与余式进阶
When the polynomial function g is graphed in the xy-plane such that \( y=g(x) \), it passes through the points (6, 0), (7, 0), and (0, 13). Which of the following must be true?
I. When \( g(x) \) is divided by (x − 6), the remainder is 0.
II. The point (7, 0) is an x-intercept of the graph of \( y=g(x) \).
III. When \( g(x) \) is divided by (x − 13), the remainder is 0.
参考答案
多项式・因式与余式挑战
Which expression is a factor of \( y^2(x−8)−16(x−8)^3 \)?
参考答案
