Question

1 which of the following expressions is a factor of the polynomial below? $2x^2 - 11x + 15$ a) $(2x - 3)$ mrs. wilson b) $(x + 3)$ ms. schmidt c) $(2x - 5)$ mrs. brewer d) $(2x + 5)$ mr. avery e) $(2x - 1)$ mrs. hillman

Explanation:

Step1: Factor the quadratic polynomial

We have the quadratic polynomial \(2x^2 - 11x + 15\). To factor it, we need to find two numbers that multiply to \(2\times15 = 30\) and add up to \(-11\). The numbers are \(-5\) and \(-6\) since \((-5)\times(-6)=30\) and \(-5 + (-6)=-11\).

Rewrite the middle term using these numbers:
\(2x^2 - 6x - 5x + 15\)

Step2: Group and factor

Group the first two terms and the last two terms:
\((2x^2 - 6x) + (-5x + 15)\)

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

Now, factor out the common binomial factor \((x - 3)\):
\((2x - 5)(x - 3)\)

So the factors of \(2x^2 - 11x + 15\) are \((2x - 5)\) and \((x - 3)\).

Answer:

C. \((2x - 5)\)