Question

factor.
14x² + 9x - 5

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(14\times(-5)= -70\) and add up to \(9\). The numbers are \(14\) and \(-5\) since \(14\times(-5)=-70\) and \(14 + (-5)=9\).

Step2: Rewrite the middle term

Rewrite \(9x\) as \(14x-5x\) in the expression \(14x^{2}+9x - 5\):

$$14x^{2}+14x-5x - 5$$

Step3: Group and factor

Group the first two terms and the last two terms:
\((14x^{2}+14x)-(5x + 5)\)
Factor out the greatest common factor from each group:
\(14x(x + 1)-5(x + 1)\)

Step4: Factor out the common binomial

Now, factor out the common binomial \((x + 1)\):
\((14x-5)(x + 1)\)

Answer:

\((14x - 5)(x + 1)\)