Question

Factor 2x^2 - 10x + 8 completely.

2(x + 2)(x - 2)
2(x - 1)(x - 4)
2(x - 2)(x + 4)

Answer 1

To factor \[2x^2-10x+8\]are there any numbers that can be factored out of each term? Hopefully your answer is "yes, all of the terms have coefficients that are multiples of 2" (and looking at the answer choices, it should be obvious as well!). If we factor out that 2, we have
\[2x^2-10x+8 = 2(x^2-5x+4)\]Now our task is to find 2 numbers that when multiplied together = 4, but when added together = -5

The factors of 4 are:
1*4
2*2
-1*-4
-2*-2

Looks like -1,-4 is our pick because -1*-4 = 4 and -1+-4=-5

When we multiply two binomials together, such as \((x-a)(x-b)\) the following happens:
\[(x+a)(x+b) = x(x+b) + a(x+b) = x*x + b*x +a*x +a*b = \]\[=x^2+bx+ax+ab = \]\[x^2+(a+b)x +ab\]If we compare that with our equation to be factored (after the 2 is taken out):\[x^2-5x+4\] we can see the reason why we want the two numbers that sum to -5 and multiply to 4 — we are just making the matching parts equal. Because we have figured out that a = -1 and b = -4, we can deduce that the factors must be \((x+(-1))(x+(-4))\) or \((x-1)(x-4)\). Combine that with the 2 we previously factored out, and the answer should be apparent.

Which answer is correct?

Answer 2

woah. thats a lot to grasp but it helped tremendously!~!!!!!

medal for you

Answer 3

Glad it helped!

Of course, given that this is a multiple-guess question, you could have approached this by just multiplying out all of the answers until you found that matched. But, you will eventually need to know how to factor, so I didn't go with that approach. Not a bad idea, however, to multiply out your answer when factoring to make sure that you did it correctly!

Answer 4

ya. definitely will do that. im just getting used to this stuff. im doing a algebra class this summer to get ahead and am having a few problems. thanks that helped.