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McGraw Hill Integrated II, 2012
MH
McGraw Hill Integrated II, 2012 View details
1. Graphing Quadratic Functions
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Exercise 80 Page 103

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

yes; (2x-5)^2

Practice makes perfect

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

Is the first term a perfect square? 4x^2= 2^2x^2=( 2x)^2 ✓
Is the last term a perfect square? 25= 5^2 ✓
Is the middle term twice the product of 25 and 4x? 20x= 2* 25* 4x ✓

As we can see, the answer to the three questions above is yes! Therefore, we can write the trinomial as the square of a binomial. Note there is a subtraction sign in the middle. 4x^2-20x+25 ⇔ ( 2x- 5)^2

Checking Our Answer

 Check your answer ✓
Let's un-factor our answer and compare it with the given expression.

(2x - 5 )^2
ExpandNegPerfectSquare

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

4x^2 - 20x + 25

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

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