Polynomial Operations

What is the product of the following expression?

 $\left(2x\ -\ 6\right)\left(3x\ -\ 5\right)$  

•  $5x\ -\ 11$  

•  $6x^2\ -\ 28x\ +\ 30$  

•  $10x\ -\ 22$  

•  $6x^2\ -\ 6x\ -\ 11$  

Answer explanation

What is the Greatest Common Factor of the following?

 $3m^2n\ +\ 12mn^2$  

•  $3n$  

•  $3m$  

•  $3mn$  

•  $3mn^2$  

Answer explanation

What is the product of the following expression?

 $\left(x^2\ -\ 3y\right)\left(x^2\ +\ 3y\right)$  

•  $x^4\ -6y\ -9y^2$  

•  $x^4\ -\ 9y^2$  

•  $x^4\ +\ 9y^2$  

•  $x^4\ +6y\ -9y^2$  

Answer explanation

What is the product of the following expressions?

 $2x\ +3\ \ \ \ \ \ and\ \ \ \ \ \ \ \ 4x^2\ -5x\ +6$  

•  $8x^3-2x^2+3x+18$  

•  $8x^3-2x^2-3x+18$  

•  $8x^3+2x^2-3x+18$  

•  $8x^3+2x^2+3x+18$  

Answer explanation

Which trinomial is equivalent to the following expression?

 $3\left(x-3\right)^2\ -\ 4\left(x-1\right)$  

•  $3x^2-2x-23$  

•  $3x^2-2x-31$  

•  $3x^2-22x+23$  

•  $3x^2-22x+31$  

Answer explanation

When multiplying polynomials for a math test, Patrick found the product to be the following expression. He had to state the lead coefficient of this polynomial. Patrick wrote -5. 

Do you agree or disagree with Patrick?

 $-5x\ +\ 2x^3\ +\ 8x^2\ -\ 15$  

• I Agree with Patrick. The lead coefficient it the first numerical value being multiplied by a variable in an expression. -5x comes first in the expression, -5 is the lead coefficient.

• I Disagree, -5 is not the lead coefficient. is the lead coefficient. The lead coefficient is the entire first term we see in an expression, -5x is the lead coefficient.

• I Disagree, -5 is not the lead coefficient. The lead coefficient is the entire term with the highest exponent in it.

• I Disagree, the lead coefficient is the amount being multiplied by the highest exponential term. That would be the first term in the expression if it were written in standard form.

Answer explanation

 $\left(3x^2\ -\ 2x\ +5\right)\ -\ \left(x^2\ +\ 3x\ -\ 2\right)\ \ \ \ multiplied\ by\ \ \ \ \ \frac{1}{2}x^2$  

What is the Simplest form of the operations and instructions given above?

•  $x^4\ -\ 5x\ +\ 7$  

•  $2x^2\ -\ 5x\ +\ 7$  

•  $x^4\ -\ 2.5x^3\ +\ 3.5x^2$  

Answer explanation

 $2x^2\ +\ 7x\ -\ 10\ \ \ \ \ \ AND\ \ \ \ \ \ x\ \ +\ \ 5$  

Express the product of the two polynomials above in standard form.

•  $2x^3\ +\ 17x^2\ \ +25x\ -\ 50$  

•  $2x^2\ +\ 8x\ -\ 5$  

•  $19x^2\ +\ 25x\ -\ 50$  

Answer explanation

 $g\left(x\right)\ =\ 2\left[f\left(x\right)\right]^2\ -\ 1$  

If f(x) = 2x + 1, and g(x) is the result of substituting f(x)'s expression in place of f(x) in the relatioinhsip above, what is the simplest form of g(x) ?

•  $g\left(x\right)\ =\ 2\left(2x\ +\ 1\right)^2\ -\ 1$  

•  $g\left(x\right)\ =\ 2\left[\left(2x+1\right)\left(2x+1\right)\right]\ \ -\ 1$  

•  $g\left(x\right)\ =\ 8x^2\ +\ 8x\ +\ 2$  

•  $g\left(x\right)\ =\ 8x^2\ +\ 8x\ +\ 1$  

Answer explanation