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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The algebra tiles represent the perfect square trinomial x2 10x c. what is the value of c? c =

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The value of c for which the considered trinomial becomes perfect square trinomial is: 20 or -20

<h3>What are perfect squares trinomials?</h3>

They are those expressions which are found by squaring binomial expressions.

Since the given trinomials are with degree 2, thus, if they are perfect square, the binomial which was used to make them must be linear.

Let the binomial term was ax + b(a linear expression is always writable in this form where a and b are constants and m is a variable), then we will obtain:

$(ax + b)^2 = a^2x^2 + b^2 + 2abx$