In order to factor x ^ 2 – 2x – 8 we must break up the “bx” term into two terms whose coefficients…
add to-2 and multiply to -8.
add to & and multiply to 2.
add to 1 and multiply to -8.
odd to 1 and multiply to 2
The correct answer and explanation is:
To factor the quadratic expression x2−2x−8x^2 – 2x – 8, we need to break up the middle term −2x-2x into two terms whose coefficients both add up to -2 and multiply to give the product of the constant term (-8).
Let’s start by identifying the factors of -8 that sum up to -2. The pairs of numbers that multiply to -8 are:
- 1 and -8
- -1 and 8
- 2 and -4
- -2 and 4
Now, let’s check the sums of these pairs:
- 1+(−8)=−71 + (-8) = -7
- −1+8=7-1 + 8 = 7
- 2+(−4)=−22 + (-4) = -2 (This is the pair we want!)
- −2+4=2-2 + 4 = 2
The pair that adds up to -2 is 22 and −4-4, so we will break up the middle term −2x-2x into 2x2x and −4x-4x. The expression then becomes: x2+2x−4x−8x^2 + 2x – 4x – 8
Now, group the terms in pairs: (x2+2x)−(4x+8)(x^2 + 2x) – (4x + 8)
Factor out the greatest common factor (GCF) from each group: x(x+2)−4(x+2)x(x + 2) – 4(x + 2)
Notice that both terms contain (x+2)(x + 2), so factor this common binomial out: (x−4)(x+2)(x – 4)(x + 2)
Thus, the factored form of x2−2x−8x^2 – 2x – 8 is (x−4)(x+2)(x – 4)(x + 2).
In summary, by identifying the correct pair of numbers that multiply to -8 and add to -2, we can break up the middle term and factor the quadratic expression into two binomials. This technique is known as factoring by grouping.