the polynomial \$6x^2 + x - 15\$ has a factor of \$2x - 3\$. what i…

QUESTION IMAGE

$the polynomial \$6x^2 + x - 15\$ has a factor of \$2x - 3\$. what i…$

Question

the polynomial \$6x^2 + x - 15\$ has a factor of \$2x - 3\$. what is the other factor?

\$3x - 5\$
\$3x + 5\$
\$4x - 5\$
\$4x + 5\$

Explanation:

Response

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Set up the factoring equation

\[
6x^2 + x - 15 = (2x - 3)(ax + b)
\]

Determine the coefficients

\[

\begin{aligned} 2a &= 6 \implies a = 3 \\ -3b &= -15 \implies b = 5 \end{aligned}

\]

Verify the middle term

\[
(2x - 3)(3x + 5) = 6x^2 + 10x - 9x - 15 = 6x^2 + x - 15
\]
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Answer: