Factor completely. Then select the correct factors from the options below. (You will select two factors). $$ 4 x^{2}-5 x-6 $$

Question

UpStudy AI · Accepted Answer

We start with the quadratic:

4x² – 5x – 6

To factor, we look for two numbers that multiply to (a × c) = 4 × (–6) = –24 and add to b = –5.

The numbers –8 and 3 work since (–8) + 3 = –5 and (–8) × 3 = –24.

Now, rewrite the middle term using these numbers:

4x² – 8x + 3x – 6

Next, group the terms:

(4x² – 8x) + (3x – 6)

Factor each group separately:

4x² – 8x = 4x(x – 2)
  3x – 6  = 3(x – 2)

Now, factor out the common binomial (x – 2):

= (x – 2)(4x + 3)

Thus, the completely factored form is:

(4x + 3)(x – 2)

So, the two factors you should select are: (4x + 3) and (x – 2).
The factors are (4x + 3) and (x – 2).

Factor completely. Then select the correct factors from the options below. (You will select two factors). \( 4 x^{2}-5 x-6 \)