Question

1. factor the following: write your answer in the following form: (ax + b)(cx + d) (1 point) 6x² + 7x + 2

Explanation:

Step1: Multiply leading and constant terms

We have \(a = 6\), \(b=7\), \(c = 2\). Multiply \(a\times c=6\times2 = 12\). We need to find two numbers that multiply to 12 and add up to 7. The numbers are 3 and 4 since \(3\times4=12\) and \(3 + 4=7\).

Step2: Rewrite the middle - term

Rewrite \(7x\) as \(3x+4x\). So, \(6x^{2}+7x + 2=6x^{2}+3x+4x + 2\).

Step3: Group the terms

Group the terms: \((6x^{2}+3x)+(4x + 2)\).

Step4: Factor out the greatest common factor from each group

From the first group \(6x^{2}+3x\), the GCF is \(3x\), so \(6x^{2}+3x=3x(2x + 1)\). From the second group \(4x + 2\), the GCF is 2, so \(4x + 2=2(2x+1)\).

Step5: Factor out the common binomial factor

We have \(3x(2x + 1)+2(2x + 1)=(2x + 1)(3x+2)\).

Answer:

\((2x + 1)(3x+2)\)