Factor 4x^2+20x+16

Problem

$4x^2+20x+16$

Solution

1. Identify the greatest common factor (GCF) for all three terms, which is $4$

2. Factor out the GCF from the expression.

$4(x^2+5x+4)$

3. Find two numbers that multiply to the constant term $4$ and add to the linear coefficient $5$

4. Determine that the numbers are $4$ and $1$ since $4\cdot 1=4$ and $\mathrm{\$}4$ + 1 = 5$.

5. Rewrite the quadratic expression inside the parentheses as a product of two binomials using these numbers.

$4(x+4)(x+1)$

Final Answer

$4x^2+20x+16=4(x+4)(x+1)$

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