Question

which of the following expressions is a factor of the polynomial below?
$6y^2 - 11y - 10$
a) $(3y + 2)$ hollywood

Explanation:

Step1: Factor the quadratic polynomial

We use the method of factoring by grouping for the quadratic polynomial \(6y^2 - 11y - 10\). First, we need to find two numbers that multiply to \(6\times(-10)= - 60\) and add up to \(-11\). The numbers are \(-15\) and \(4\) since \(-15\times4=-60\) and \(-15 + 4=-11\).

We rewrite the middle term using these two numbers:
\(6y^2-15y + 4y-10\)

Step2: Group and factor

Group the first two terms and the last two terms:
\((6y^2 - 15y)+(4y - 10)\)

Factor out the greatest common factor from each group:
\(3y(2y - 5)+2(2y - 5)\)

Now, we can factor out the common binomial factor \((2y - 5)\):
\((3y + 2)(2y - 5)\)

Answer:

A) \((3y + 2)\)