Question

Factor completely. 4x^2– 13x + 9

Answer 1

(x-1)(4x-9)

Explanation:

Answer 2

`\boxed {\boxed {\sf (4x-9)(x-1)}}`

Explanation:

There are many ways to factor a trinomial like the one given, but I am going to use the AC Method.

`4x^2 -13x+9`

This trinomial is in standard form, with the highest exponent listed first or (ax² +bx +c). If we match the value in the trinomial with the corresponding variable we see that:

• a= 4
• b= -13
• c= 9

First, we find the product of a and c.

• a * c = 4 *9 = 36

Next, we find what numbers multiply to 36 or (a*c) and add to b or -13. Remember that 2 negative numbers multiply to be a positive number. We will use -4 and -9.

• -4 * -9 = 36
• -4 + -9 = -13

Break up the second term of the trinomial into the 2 new numbers.

`4x^2 -4x -9x+9`

Create 2 binomials.

`(4x^2-4x) + (-9x+9)`

Factor the greatest common factor out of both binomials. For the first, the GCF is 4x. For the second, the GCF is -9.

`4x(x-1) + (-9x+9)`

`4x(x-1)+ -9 (x-1)`

Both terms contain the binomial (x-1), so we can factor it out.

`(4x-9)(x-1)`

The trinomial 4x²-13x+9 is (4x-9)(x-1) when factored completely.