Factor the following problems SHOW YOUR WORK 1. x^2+16x+24 2. x^2-10a+25

1 answer:

8 0

<span>x^2+16x+24: Think: What are the integer factors of 24? I'd list 1, 2, 3, 4, 6, 8, 12 and 24. Next: Look for a pair of factors from that list that:

(1)ADD up to 16 AND (2) whose product is 24. Unfortunately there seems to be no such pair from the above list.

So: Use the quadratic formula to find the roots of </span>x^2+16x+24:

-16 plus or minus sqrt[ 256-4(1)(24) ]
x = --------------------------------------------------
2
-16 plus or minus sqrt(160) -16 plus or minus 4 sqrt(10)
= --------------------------------------- = ----------------------------------------
2 2
2(-8 plus or minus 2 sqrt(10) )
= ------------------------------------------- = -8 plus or minus 2sqrt(10)
2

If c is a root, (x-c) is a factor. Thus, if -8 plus 2sqrt(10) is a root,

(x+8-2sqrt(10) is a factor. Can you find the other factor?

x^2-10a+25 is much easier to factor. The sqrt of 25 is 5, so try x= -5 as a root. Dividing x-5 into <span>x^2-10a+25, we get x-5. Therefore, the factors are

(x-5) and (x-5).</span>

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