Question

5
select all the correct answers.
select all the expressions that are equivalent to the polynomial below.
$-12x^2 - 19x - 5$
$\square \\ \\ 2(x - 1) - 3(4x^2 + 7x + 1)$
$\square \\ \\ (2x^2 - 11x - 9) - (14x^2 + 8x - 4)$
$\square \\ \\ (-16x^2 + 10x - 3) + (4x^2 - 29x - 2)$
$\square \\ \\ (4x^2 - 13x - 7) - (16x^2 + 9x - 5)$
$\square \\ \\ 3(x - 5) - 2(6x^2 + 9x + 5)$
$\square \\ \\ (-15x^2 + 9x - 10) + (3x^2 - 10x - 5)$

Explanation:

Step1: Simplify \(2(x - 1)-3(4x^{2}+7x + 1)\)

First, distribute the 2 and -3:
\(2x-2-12x^{2}-21x - 3\)
Then, combine like terms:
\(-12x^{2}+(2x - 21x)+(-2 - 3)=-12x^{2}-19x - 5\)

Step2: Simplify \((2x^{2}-11x - 9)-(14x^{2}+8x - 4)\)

Distribute the negative sign:
\(2x^{2}-11x - 9-14x^{2}-8x + 4\)
Combine like terms:
\((2x^{2}-14x^{2})+(-11x - 8x)+(-9 + 4)=-12x^{2}-19x - 5\)

Step3: Simplify \((-16x^{2}+10x - 3)+(4x^{2}-29x - 2)\)

Combine like terms:
\((-16x^{2}+4x^{2})+(10x - 29x)+(-3 - 2)=-12x^{2}-19x - 5\)

Step4: Simplify \((4x^{2}-13x - 7)-(16x^{2}+9x - 5)\)

Distribute the negative sign:
\(4x^{2}-13x - 7-16x^{2}-9x + 5\)
Combine like terms:
\((4x^{2}-16x^{2})+(-13x - 9x)+(-7 + 5)=-12x^{2}-22x - 2\) (not equivalent)

Step5: Simplify \(3(x - 5)-2(6x^{2}+9x + 5)\)

Distribute the 3 and -2:
\(3x-15-12x^{2}-18x - 10\)
Combine like terms:
\(-12x^{2}+(3x - 18x)+(-15 - 10)=-12x^{2}-15x - 25\) (not equivalent)

Step6: Simplify \((-15x^{2}+9x - 10)+(3x^{2}-10x - 5)\)

Combine like terms:
\((-15x^{2}+3x^{2})+(9x - 10x)+(-10 - 5)=-12x^{2}-x - 15\) (not equivalent)

Answer:

• \(2(x - 1)-3(4x^{2}+7x + 1)\)
• \((2x^{2}-11x - 9)-(14x^{2}+8x - 4)\)
• \((-16x^{2}+10x - 3)+(4x^{2}-29x - 2)\)