Question

3 which of the following expressions is a factor of the polynomial below? $3a^2 + 22a - 45$ a) $(3a - 1)$ parasailing b) $(a - 15)$ playing kickball c) $(3a + 5)$ making pizzas d) $(a + 9)$ riding go - karts e) $(a - 9)$ raking leaves

Explanation:

Step1: Factor the quadratic polynomial

We have the quadratic polynomial \(3a^2 + 22a - 45\). We need to find two numbers that multiply to \(3\times(-45)=-135\) and add up to \(22\). The numbers are \(27\) and \(- 5\) since \(27\times(-5)=-135\) and \(27+( - 5)=22\).

Rewrite the middle term:
\(3a^2+27a - 5a - 45\)

Step2: Group and factor

Group the first two terms and the last two terms:
\((3a^2 + 27a)+(-5a - 45)\)

Factor out the greatest common factor from each group:
\(3a(a + 9)-5(a + 9)\)

Now, factor out the common binomial factor \((a + 9)\):
\((3a - 5)(a + 9)\)

Answer:

D. \((a + 9)\) riding go - karts