Question

select all the expressions that are equivalent to the polynomial below. -15x^2 - 29x - 12 (-19x^2 - 4x - 7)+(4x^2 + 25x - 5) (5x^2 - 10x + 8)-(10x^2 + 19x + 20) (-7x^2 - 21x + 13)-(8x^2 + 8x + 25) -2(4x - 15)-3(5x^2 + 7x + 6) (-17x^2 + 2x - 3)+(2x^2 - 31x - 9) -2(7x + 1)-5(3x^2 + 3x + 2)

Explanation:

Step1: Combine like - terms for each option

Option 1: $(-19x^{2}-4x - 7)+(4x^{2}+25x - 5)$

\[

$$\begin{align*} &(-19x^{2}+4x^{2})+(-4x + 25x)+(-7-5)\\ =&-15x^{2}+21x - 12 \end{align*}$$

\]

Option 2: $(5x^{2}-10x + 8)-(10x^{2}+19x + 20)$

\[

$$\begin{align*} &5x^{2}-10x + 8-10x^{2}-19x - 20\\ =&(5x^{2}-10x^{2})+(-10x-19x)+(8 - 20)\\ =&-5x^{2}-29x - 12 \end{align*}$$

\]

Option 3: $(-7x^{2}-21x + 13)-(8x^{2}+8x + 25)$

\[

$$\begin{align*} &-7x^{2}-21x + 13-8x^{2}-8x - 25\\ =&(-7x^{2}-8x^{2})+(-21x-8x)+(13 - 25)\\ =&-15x^{2}-29x - 12 \end{align*}$$

\]

Option 4: $-2(4x - 15)-3(5x^{2}+7x + 6)$

\[

$$\begin{align*} &-8x + 30-15x^{2}-21x - 18\\ =&-15x^{2}+(-8x-21x)+(30 - 18)\\ =&-15x^{2}-29x + 12 \end{align*}$$

\]

Option 5: $(-17x^{2}+2x - 3)+(2x^{2}-31x - 9)$

\[

$$\begin{align*} &(-17x^{2}+2x^{2})+(2x-31x)+(-3-9)\\ =&-15x^{2}-29x - 12 \end{align*}$$

\]

Option 6: $-2(7x + 1)-5(3x^{2}+3x + 2)$

\[

$$\begin{align*} &-14x-2-15x^{2}-15x - 10\\ =&-15x^{2}+(-14x-15x)+(-2 - 10)\\ =&-15x^{2}-29x - 12 \end{align*}$$

\]

Answer:

$(-7x^{2}-21x + 13)-(8x^{2}+8x + 25)$, $(-17x^{2}+2x - 3)+(2x^{2}-31x - 9)$, $-2(7x + 1)-5(3x^{2}+3x + 2)$