Question

factor.
14y² - 3y - 5

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(14\times(-5)= -70\) and add up to \(-3\). The numbers are \(-10\) and \(7\) since \(-10\times7 = -70\) and \(-10 + 7=-3\).

Step2: Rewrite the middle term

Rewrite \(-3y\) as \(-10y + 7y\) in the expression \(14y^{2}-3y - 5\):

$$14y^{2}-10y + 7y-5$$

Step3: Group and factor

Group the first two terms and the last two terms:
\((14y^{2}-10y)+(7y - 5)\)
Factor out the greatest common factor from each group:
\(2y(7y - 5)+1(7y - 5)\)

Step4: Factor out the common binomial

Now, factor out the common binomial \((7y - 5)\):
\((2y + 1)(7y - 5)\)

Answer:

\((2y + 1)(7y - 5)\)