Lesson 5 Ex5

4-26 Honors Algebra Warm-upA square with side length x is cut from a right triangle shown at the right. What value of x will result in a figure that is 3/4 of the area of the original triangle? Show how you arrived at your answer.

There are multiple ways to get the answer, check with a partner to make sure your way is reasonable.

Answer: x = 4 units

HW: p.451 #11-31odd, 32, 34

Check odds in the back of the book.

32.Sample: 8(2n +3) cm by (n – 1) cm

34. 3in x 12in x 2in

FOIL

(3x + 4)(3x – 4)=

(3x + 4)2 =

(3x – 4)2 =

= 9x2 – 16Difference of Two Squares= 9x2 + 24x + 16Perfect Square Trinomial= 9x2 – 24x + 16Perfect Square Trinonmial

Method 6: Factoring Perfect Square Trinomials

1. Check the trinomial to see if it is of the form

a2 + 2ab + b2 or a2 - 2ab + b2

3 conditions

• The first term must be a perfect square (a2)

• The last term must be a perfect square (b)2

• The middle term must be twice the product of the square roots of the first and last terms 2(a)(b).

2. If a2 + 2ab + b2, write as (a + b)2

If a2 - 2ab + b2, write as (a - b)2

Factor Perfect Square Trinomials

A. Determine whether 25x2 – 30x + 9 is a perfect square trinomial. If so, factor it.

1. Is the first term a perfect square? Yes, 25x2 = (5x)2.

2. Is the last term a perfect square? Yes, 9 = 32.

3. Is the middle term equal to 2(5x)(3)? Yes, 30x = 2(5x)(3).

Answer: Yes, (5x – 3)2 Factor using the

pattern.

Factor Perfect Square Trinomials

B. Determine whether 49y2 + 42y + 36 is a perfect square trinomial. If so, factor it.

1. Is the first term a perfect square? Yes, 49y2 = (7y)2.

2. Is the last term a perfect square? Yes, 36 = 62.

3. Is the middle term equal to 2(7y)(6)? No, 42y ≠ 2(7y)(6).

Answer: 49y2 + 42y + 36 is not a perfect square trinomial.

Factor Completely

First check for GCF, then check for perfect square trinomial.

Since 16y2+ 8y – 15 is not a perfect square trinomial,

= 16y2 + 20y – 12y – 15 m = 20 and n = –12

= (16y2 + 20y) + (–12y – 15) Group

= 4y(4y + 5) – 3(4y + 5) Factor out the GCF

Answer: (4y + 5)(4y – 3)

use ax2 + bx + c.

Factor 16y2 + 8y – 15.

Solve Equations with Repeated Factors

Solve 4x2 + 36x + 81 = 0.

(2x + 9)2 = 0 Factor the perfect square trinomial.

2x + 9 = 0 Set the repeated factor equal to zero.

2x = –9

Solve for x.

A. Solve (b – 7)2 = 36.

Answer: {1, 13}

Use the Square Root Property to Solve Equations

Square Root Property

b = 7 ± 6 Add 7 to each side.

b = 7 + 6 or b = 7 – 6 Separate into two equations.

= 13 = 1 Simplify.

b – 7 = ±6

A. A

B. B

C. C

D. D

A. {–1, 9}

B. {–1}

C. {9}

D. {0, 9}

B. Solve the equation (x – 4)2 = 25. Check your solution.