Question

Use the quadratic expression 15x2+14x−16 to answer the questions.

A: Which statement describes the correct method to factor the quadratic expression?
B: What are the factors of the quadratic expression?
Select one answer for question A, and select two answers for question B.
A: This quadratic expression can be factored by using the difference of squares pattern.
A: This quadratic expression can be factored by finding the correct pair of binomial factors.
A: This quadratic expression can be factored by using the perfect square trinomial pattern.
B: (3x+4)
B: (3x−2)
B: (5x+8)
B: (5x+4)
B: (5x−4)
B: (3x+4)

Answer 1

A: second one or middle choice

B: (5x + 8)(3x - 2)

Explanation:

First question (A)

It is a trinomial. You can't use the difference of squares on it. The difference of squares have two terms as an answer.

It is not a perfect square. 15 is not a perfect square and c would have to be positive not minus to even think about using a perfect square.

So the A answer is the second one. You need two different binomials to factor this.

Second Question

You could try all the possible pairings and solve them by brute force.

The are five choices the go with the first one (3x + 4). Eventually you would get the answer, you would have to try 5 + 4 + 3 + 2 + 1 = 15 attempts.

There must be a shorter way.

14 means that the expressions are fairly far apart. This was just luck on my part. There is no logic. 8 and 2 for 16 are fairly far apart.

(5x + 8)(3x - 2)

The middle term is 8*3x - 2*5x = 14x and that looks like the answer.