Question

exponents and polynomials
factoring a quadratic with leading coefficient greater than 1

factor.

\\2y^2 + 13y + 15\\

Explanation:

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<reasoning>

Identify the coefficients

Using the Factoring Trinomials knowledge point
\[

$$\begin{aligned} &2y^2 + 13y + 15\\ &a = 2,\quad b = 13,\quad c = 15 \end{aligned}$$

\]

Find two numbers that multiply to ac and add to b

Using the AC Method knowledge point
\[

$$\begin{aligned} &a \cdot c = 2 \cdot 15 = 30\\ &p \cdot q = 30,\quad p + q = 13\\ &p = 10,\quad q = 3 \end{aligned}$$

\]

Rewrite the middle term and factor by grouping

Using the Factoring by Grouping knowledge point
\[

$$\begin{aligned} &2y^2 + 10y + 3y + 15\\ &2y(y + 5) + 3(y + 5)\\ &(2y + 3)(y + 5) \end{aligned}$$

\]
</reasoning>

<answer>
Factor.
\(2y^2 + 13y + 15 =\) <blank>\((2y + 3)(y + 5)\)</blank>
</answer>

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Answer:

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<reasoning>

Identify the coefficients

Using the Factoring Trinomials knowledge point
\[

$$\begin{aligned} &2y^2 + 13y + 15\\ &a = 2,\quad b = 13,\quad c = 15 \end{aligned}$$

\]

Find two numbers that multiply to ac and add to b

Using the AC Method knowledge point
\[

$$\begin{aligned} &a \cdot c = 2 \cdot 15 = 30\\ &p \cdot q = 30,\quad p + q = 13\\ &p = 10,\quad q = 3 \end{aligned}$$

\]

Rewrite the middle term and factor by grouping

Using the Factoring by Grouping knowledge point
\[

$$\begin{aligned} &2y^2 + 10y + 3y + 15\\ &2y(y + 5) + 3(y + 5)\\ &(2y + 3)(y + 5) \end{aligned}$$

\]
</reasoning>

<answer>
Factor.
\(2y^2 + 13y + 15 =\) <blank>\((2y + 3)(y + 5)\)</blank>
</answer>

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