Question

question
factor the trinomial:
5x² + 27x + 28
answer

Explanation:

Step1: Multiply first and last coefficients

Multiply \(5\) and \(28\), we get \(5\times28 = 140\).

Step2: Find two numbers for \(140\)

Find two numbers that multiply to \(140\) and add up to \(27\). The numbers are \(20\) and \(7\) since \(20\times7=140\) and \(20 + 7=27\).

Step3: Rewrite the middle - term

Rewrite \(27x\) as \(20x+7x\). So the trinomial becomes \(5x^{2}+20x + 7x+28\).

Step4: Group the terms

Group the terms: \((5x^{2}+20x)+(7x + 28)\).

Step5: Factor out the GCF from each group

From the first group \(5x^{2}+20x\), the GCF is \(5x\), so \(5x(x + 4)\). From the second group \(7x+28\), the GCF is \(7\), so \(7(x + 4)\).

Step6: Factor out the common binomial factor

We have \(5x(x + 4)+7(x + 4)=(5x + 7)(x + 4)\).

Answer:

\((5x + 7)(x + 4)\)