Question

Select the correct answer from each drop-down menu.

What is the factored form of this expression?
6x² + 5x - 6 = ( , )

Answer 1

`6x^2+5x-6=(3x-2)(2x+3)`

Explanation:

Given expression:

`6x^2+5x-6`

To factor a quadratic in the form
`ax^2+bx+c`, first find two numbers that multiply to
`ac` and sum to
`b`:

`\implies ac=6 \cdot -6=-36`

`\implies b=5`

Two numbers that multiply to -36 and sum to 5 are: 9 and -4

Rewrite b as the sum of these two numbers:

`\implies 6x^2+9x-4x-6`

Factorize the first two terms and the last two terms separately:

`\implies 3x(2x+3)-2(2x+3)`

Factor out the common term (2x + 3):

`\implies (3x-2)(2x+3)`

Therefore:

`6x^2+5x-6=(3x-2)(2x+3)`

Answer 2

Explanation:

Equation

y = 6x^2 + 5x - 6

Solution

This will factor, but it will take a bit of doing.

First we can try some factors using just 2s and 3s and see what happens.

(3x 2)(2x 3) This looks promising. We must get 5 as the middle term.

6x^2 9x 4x 6 The 9 and 4 must have opposite signs and come to 5.

Since it is plus 5x in the middle, the 9x must be plus and 4x is minus. When put together, they will get 5x.

(3x - 2)(2x + 3)

that works. So the

answer is y = (3x - 2)(2x + 3)