Question

factor the given polynomial completely. if the polynomial cannot be factored, say that it is pr
3x² +14x -5
select the correct choice below and fill in any answer boxes within your choice.
a. 3x² +14x -5 =
b. the polynomial is prime.

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(3\times(-5) = -15\) and add up to \(14\). The numbers are \(15\) and \(-1\) since \(15\times(-1)=-15\) and \(15 + (-1)=14\).

Step2: Split the middle term

Rewrite the middle term \(14x\) using \(15x\) and \(-x\): \(3x^{2}+15x - x - 5\).

Step3: Group and factor

Group the first two terms and the last two terms: \((3x^{2}+15x)+(-x - 5)\). Factor out the GCF from each group: \(3x(x + 5)-1(x + 5)\).

Step4: Factor out the common binomial

Factor out \((x + 5)\) from both terms: \((3x - 1)(x + 5)\).

Answer:

A. \(3x^{2}+14x - 5=(3x - 1)(x + 5)\)