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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

2. Complex Numbers

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Exercise 86 Page 184

To factor a perfect square trinomial, the first and last terms have to be perfect squares.

Yes.

Practice makes perfect

Let's consider the given trinomial.

x^2+16x+64

To determine if an expression is a perfect square trinomial, we need to ask ourselves three questions.

Is the first term a perfect square?	x^2=( x)^2 ✓
Is the last term a perfect square?	64= 8^2 ✓
Is the middle term twice the product of 8 and x?	16x=2* 8* x ✓

As we can see, the answer to all three questions is yes! Therefore, we have a perfect square trinomial.

Checking Our Answer

Check your answer ✓

We can write the trinomial as the square of a binomial. Note there is an addition sign in the middle. x^2+16x+64 ⇔ ( x+ 8)^2 Let's un-factor the square of the binomial and compare it with the given expression.

(x + 8)^2

ExpandPosPerfectSquare

(a+b)^2=a^2+2ab+b^2

x^2+16x+64

After expanding and simplifying, the result is the same as the given expression. Therefore, we can be sure our solution is correct!

Subchapter links

Exercises p.182-184