Polynomials

\(\text{Which expression is equivalent to }60y+90y?\)

\(\text{Which expression is equivalent to 12}x^3-5x^3?\)

\(\text{Which expression is equivalent to }(2x^{2}+x-9)+(x^{2}+6x+1)?\)

\(\text{Which expression is equivalent to }\left(9x^2+9\right)-\left(2x^2\right)?\)

\(\text{Which expression is equivalent to }(9x^{3}+5x+7)+(6x^{3}+5x^{2}-5)?\)

\(\text{Which expression is equivalent to }(7x^{3}+7x)-(6x^{3}-3x)?\)

\(\text{Which expression is equivalent to }(9nr^{2}+3nr)+(6n^{2}r+5nr)?\)

\(\text{Which expression is equivalent to }(9c+8)-(4c^3-6)?\)

\(\text{Which expression is equivalent to }(5a^{2}-3ab+7b^{2})-(4a^{2}+ab-2b^{2})?\)

\(\text{Which expression is equivalent to }(6t^4-3t^2+3t-6)-(2t^4-4t^3+6t^2-6)?\)

\(\begin{aligned}\text{If }a=3k+4r\text{ and }b=9k-12r+6,\text{which expression is equivalent to }a-b?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(5x^3-2)-(-6x^3+3)\\
&\text{The given expression is equivalent to }bx^3-5\text{ where }b\text{ is a constant. What is the value of }b?\end{aligned}\)

\(\text{Which expression is equivalent to }16(x+15) ?\)

\(\text{Which expression is equivalent to }13(x^2-7)?\)

\(\text{Which of the following is equivalent to }2(x^2-x)+3(x^2-x)?\)

\(\text{Which expression is equivalent to }2(xy^2+x^2y)-8(xy^2-4x^2y)?\)

\(\text{Whic expression is equivalent to }(x^3+6x^2-8x)+8(x^2+4)?\)

\(\text{Which expression is equivalent to }(w+7)(3w-10)?\)

\(\begin{aligned}
&\text{The expression }(9x-28)(15x+4)\text{ is equivalent to the expression }ax^{2}+bx+c,\text{ where }a,~b,\\
&\text{and }c\text{ are constants. What is the value of }b?\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~f(x)=11x^{10}+3x^{8}\\
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~g(x)=-17x^7+9x^5\\
&\text{The polynomial }p(x)\text{ is defined as the product of the given polynomials, }f(x)\text{ and }g(x).\\
&\text{What is the coefficient of }x^{15}\text{ in }p(x)?\end{aligned}\)

\(\text{Which expression is equivalent to }(3x^3-x^2+4)(5x^2+8x)?\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~3(2x+1)(4x+1)\\&\text{Which of the following is equivalent to the expression above?}\end{aligned}\)

\(\text{Which expression is equivalent to }2\left(x-\frac{3}{2}\right)\left(x+14\right)?\)

\(\text{Which expression is equivalent to }2\left(x-\frac{9}{2}\right)(x+8)?\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(4x+10)(2x+1)-(2x-14)\\
&\text{For all values of }x\text{ the given expression is equivalent to which of the following?}\\
&~~~~\text{ I. }~~8x^2+22x+24\\&~~~~~\text{II. }~8x^2+24x+10-2x-14\end{aligned}\)

\(\text{Which of the following is equivalent to }\left(a+\frac{b}{2}\right)^2?\)

\(\text{Which of the following expressions is equivalent to }\left(\frac{a}{4}+\frac{b}{3}\right)^{2}?\)

\(\text{Which expression is equivalent to }\left(x^{2}+11\right)^{2}+\left(x-5\right)\left(x+5\right)?\)

\(\text{Which expression is equivalent to }(x^{2}+11)^{2}+(x-8)(x+8)?\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-16(5x-3)^2+4(5x-4)^2\\&\text{The given expression can be rewritten as }\frac{a}{6}x^2+\frac{b}{6}x+\frac{c}{6},\text{where }a,~b,\text{ and }c\text{ are constants. What }\\&\text{is the value of }a+b+c?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-16(5x-3)^2+4(5x-2)^2\\&\text{The given expression can be rewritten as }\frac{a}{4}x^2+\frac{b}{4}x+\frac{c}{4},\text{where }a,~b,\text{ and }c\text{ are constants. What }\\&\text{is the value of }a+b+c?\end{aligned}\)

\(\begin{aligned}
&\text{Exactly how many }x\text{-intercepts does the graph of }f(x)=x(x-8)^{2}(x-13)^{3}\text{ have in the}\\
&xy\text{-plane, where }y=f(x)?\end{aligned}\)

\(\begin{aligned}
&\text{What is an }x\text{-coordinate of an }x\text{-intercept of the graph of }y=3(x-14)(x+5)(x+4)\text{ in the }\\&xy\text{-plane?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~(x-16)(x-10)(x+7)(x+17)=0\\&\text{What is a positive solution to the given equation?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x(x-13)(x+9)(x-5)^2=0\\&\text{What is the greatest solution to the given equation?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~-3(4v-1)(v+6)^{2}-(v+6)^{2}=0\\
&\text{What is the positive solution to the given equation?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x^{3}(x^{2}-5)=-4x\\&\text{If } x > 0,\text{what is one possible solution to the equation above?}\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~7x^{2}(4x-13)(4x-u)=0\\
&\text{In the given equation, }u\text{ is a positive constant. The sum of the solutions to the equations is 9.}\\
&\text{What is the value of }u?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\frac{4}{7}(4x+7)(x+\sqrt{4k+7})(x-\sqrt{4k+7})=0\\
&\text{In the given equation, }k\text{ is a positive constant. The product of the solutions to the equation is 77.}\\&\text{What is the value of }k?\end{aligned}\)

\(\begin{aligned}
&\text{The function }g\text{ is defined by }g(x)=x(x-2)(x+6)^{2}.\text{ The value of }g(7-w)\text{ is }0,\text{ where }w\text{ }\\
&\text{is a constant. What is the sum of all possible values of }w?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~f(x)=3(x-a)(x-b)(x-c)\\
&\text{The function }f\text{ is defined by the given equation, where }a,b,\text{and }c\text{ are distinct constants.}\\
&\text{When }a < x < b\text{, the value of }f(x)\text{ is positive. The graph of }y=f(x)\text{ in the }xy\text{-plane}\\
&\text{contains the point }(r,s)\text{, where }r\text{ and }s\text{ are constants. If }s=8,\text{which of the following}\\
&\text{could be true?}\\
&~~~~~~\text{I. }~~~r < a\\
&~~~~~\text{II. }~~b < r <c\\
&~~~~\text{III. }~~r > c\\
\end{aligned}\)