Question

unit 7 review assignment
topic 3: factoring polynomials

1. $3x^2 + 10x + 7$

Explanation:

Step1: Identify factoring method

For quadratic \(ax^2 + bx + c\) (\(a = 3\), \(b = 10\), \(c = 7\)), use AC method. Find \(ac = 3\times7 = 21\).

Step2: Find factors of 21

Find two numbers that multiply to 21 and add to 10. Numbers are 3 and 7 (since \(3 + 7 = 10\), \(3\times7 = 21\)).

Step3: Rewrite middle term

Rewrite \(10x\) as \(3x + 7x\): \(3x^2 + 3x + 7x + 7\).

Step4: Group and factor

Group first two and last two terms: \((3x^2 + 3x) + (7x + 7)\). Factor out GCF from each group: \(3x(x + 1) + 7(x + 1)\).

Step5: Factor out common binomial

Factor out \((x + 1)\): \((3x + 7)(x + 1)\).

Answer:

\((3x + 7)(x + 1)\)