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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 79 Page 103

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

yes; (2x+1)^2

Practice makes perfect

To determine if an expression 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? 1= 1^2 ✓
Is the middle term twice the product of 1 and 2x? 4x= 2* 1* 2x ✓

As we can see, the answer to all three questions is yes! Therefore, we can write the trinomial as the square of a binomial. Note there is an addition sign in the middle. 4x^2+4x+1 ⇔ ( 2x+ 1)^2

Checking Our Answer

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

(2 x + 1)^2
ExpandPosPerfectSquare

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

4 x^2 + 4 x + 1

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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