Question

Talia grouped the terms and factored out the GCF of the groups of the polynomial 15x2 – 3x – 20x + 4. Her work is shown below. (15x2 – 3x) + (–20x + 4) 3x(5x – 1) + 4(–5x + 1) Talia noticed that she does not have a common factor. What should she do?

Answer 1

Factor out a -1 from one of the terms so they are the same

Explanation:

15x^2 – 3x – 20x + 4

(15x2 – 3x) + (–20x + 4)

3x(5x – 1) + 4(–5x + 1)

Talia should notice that the terms in the parentheses are opposites of each other and factor out a -1 out of the second term

3x(5x-1) +4 (-1) (5x-1)

Now the terms have a common factor

(5x-1) (3x+(-1)4)

(5x-1) (3x-4)

Answer 2

Talia needs to factor out a negative from one of the groups so the binomials will be the same.

Explanation:

`15x^2 - 3x - 20x + 4`

Group first two terms and last two terms to factor it

`(15x^2 - 3x)+(- 20x + 4)`

Now we factor out GCF

GCF of 15x^2-3x is 3x

GCF of -20x+4 is -4 because first term should be positive

`(15x^2 - 3x)+(- 20x + 4)`

`3x(5x- 1)-4(5x-1)`

Talia needs to factor out negative so that the binomials will be same (5x-1)