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McGraw Hill Integrated II, 2012 View details

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Exercise 74 Page 84

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

(x+6)^2

Practice makes perfect

We want to factor a perfect square trinomial. x^2+12x+36How do we know that the expression is a perfect square trinomial? Well, let's ask a few questions.

Is the first term a perfect square?	x^2= x^2 ✓
Is the last term a perfect square?	36= 6^2 ✓
Is the middle term twice the product of 6 and x?	12x=2* 6* x ✓

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 an addition sign in the middle. x^2+12x+36 ⇔ ( x+ 6)^2

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Check your answer ✓

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

(x+6)^2

ExpandPosPerfectSquare

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

x^2+12x+36

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

Subchapter links

1 Adding and Subtracting Polynomials p.81

2 Multiplying a Polynomial by a Monomial p.81

3 Multiplying Polynomials p.81

4 Special Products p.82

5 Using the Distributive Property p.82

6 Solving x^2+bx+c=0 p.83

7 Solving ax^2+bx+c=0 p.83

8 Differences of Squares p.84

9 Perfect Squares p.84

10 Roots and Zeros p.85

Exercise 74 Page 84

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