Question 1

Polynomial Operation Assignment*all work/steps shown or describe in wordsI need help on these

Polynomial Operation Assignment*all work/steps shown or describe in wordsI need help-example-1

Question 2

In each case, use the distributive property to multiply the polynomials:

5)

$\begin{gathered} (2x+7)(x^2-4x+6)=(2x+7)(x^2)+(2x+7)(-4x)+(2x+7)(6) \\ =(2x)(x^2)+(7)(x^2)+(2x)(-4x)+(7)(-4x)+(2x)(6)+(7)(6) \\ =2x^3+7x^2-8x^2-28x+12x+42 \\ =2x^3-x^2+-16x+42 \end{gathered}$

Therefore:

6)

$\begin{gathered} (4x^2-2x+6)(x^2+5x-1)=(4x^2)(x^2+5x-1)+(-2x)(x^2+5x-1)+(6)(x^2+5x-1) \\ =(4x^2)(x^2)+(4x^2)(5x)+(4x^2)(-1)+(-2x)(x^2)+(-2x)(5x)+(-2x)(-1)+(6)(x^2)+(6)(5x)+(6)(-1) \\ =4x^4+20x^3-4x^2-2x^3-10x^2+2x+6x^2+30x-6 \\ =4x^4+18x^3-8x^2+32x-6 \end{gathered}$

Therefore:

$\mleft(4x^2-2x+6\mright)\mleft(x^2+5x-1\mright)=4x^4+18x^3-8x^2+32x-6$

7)

$\begin{gathered} (2x+7)^2=(2x+7)(2x+7) \\ =(2x)(2x+7)+(7)(2x+7) \\ =(2x)(2x)+(2x)(7)+(7)(2x)+(7)(7) \\ =4x^2+14x+14x+49 \\ =4x^2+28x+49 \end{gathered}$

Therefore:

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