Question

question 15
factor the following trinomial.
$20y^2 + 37y + 15$
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question 16
factor the following.
$x^2 - 4$
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Explanation:

Step1: Split middle term (Q15)

Find two numbers: $12$ and $25$, since $12+25=37$ and $12\times25=20\times15=300$.
$20y^2 + 12y + 25y + 15$

Step2: Group and factor (Q15)

Group terms and factor GCFs:
$4y(5y + 3) + 5(5y + 3)$

Step3: Factor common binomial (Q15)

Extract the shared binomial factor:
$(4y + 5)(5y + 3)$

Step4: Recognize difference of squares (Q16)

$x^2 - 4 = x^2 - 2^2$, use $a^2-b^2=(a-b)(a+b)$

Step5: Apply difference of squares (Q16)

$(x - 2)(x + 2)$

Answer:

1. $(4y + 5)(5y + 3)$
2. $(x - 2)(x + 2)$