Question

1. $6x^2 + 19x + 10$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(6\times10 = 60\) and add up to \(19\). The numbers are \(15\) and \(4\) since \(15\times4 = 60\) and \(15 + 4=19\).

Step2: Rewrite the middle term

Rewrite \(19x\) as \(15x + 4x\) in the quadratic expression:
\(6x^{2}+15x + 4x+10\)

Step3: Group the terms

Group the first two terms and the last two terms:
\((6x^{2}+15x)+(4x + 10)\)

Step4: Factor out the GCF from each group

Factor out \(3x\) from the first group and \(2\) from the second group:
\(3x(2x + 5)+2(2x + 5)\)

Step5: Factor out the common binomial factor

Factor out \((2x + 5)\) from both terms:
\((3x + 2)(2x + 5)\)

Answer:

\((3x + 2)(2x + 5)\)