Question

gcf of each set to
write the factored form o
1 ( 3x^2 + 19x + 20 )

Explanation:

Step1: Identify coefficients and constant

For quadratic \(3x^2 + 19x + 20\), \(a = 3\), \(b = 19\), \(c = 20\).

Step2: Find two numbers

Find two numbers that multiply to \(a\times c=3\times20 = 60\) and add to \(b = 19\). The numbers are \(15\) and \(4\) (since \(15\times4 = 60\), \(15 + 4 = 19\)).

Step3: Split the middle term

Rewrite the middle term: \(3x^2+15x + 4x + 20\).

Step4: Factor by grouping

Group terms: \((3x^2 + 15x)+(4x + 20)\). Factor out GCF from each group: \(3x(x + 5)+4(x + 5)\). Then factor out \((x + 5)\): \((3x + 4)(x + 5)\).

Answer:

\((3x + 4)(x + 5)\)