Download presentation

Published byGyles Fleming Modified over 5 years ago

1
**Perfect Square Trinomials and Difference of Perfect Squares**

Factoring Perfect Square Trinomials and Difference of Perfect Squares

2
**Factor with special patterns**

STANDARD 4.0 Factor with special patterns Factor the expression. a. x2 – 49 = x2 – 72 Difference of two squares = (x + 7)(x – 7) b. d d + 36 = d 2 + 2(d)(6) + 62 Perfect square trinomial = (d + 6)2 c. z2 – 26z + 169 = z2 – 2(z) (13) + 132 Perfect square trinomial = (z – 13)2

3
GUIDED PRACTICE for Example 2 Factor the expression. 4. x2 – 9 ANSWER (x – 3)(x + 3) 5. q2 – 100 ANSWER (q – 10)(q + 10) 6. y2 + 16y + 64 ANSWER (y + 8)2

4
GUIDED PRACTICE for Example 2 7. w2 – 18w + 81 (w – 9)2

5
**Factor out monomials first**

STANDARD 4.0 Factor out monomials first Factor the expression. a. 5x2 – 45 = 5(x2 – 9) = 5(x + 3)(x – 3) b. 6q2 – 14q + 8 = 2(3q2 – 7q + 4) = 2(3q – 4)(q – 1) c. –5z2 + 20z = –5z(z – 4) d. 12p2 – 21p + 3 = 3(4p2 – 7p + 1)

6
GUIDED PRACTICE GUIDED PRACTICE for Example 4 Factor the expression. s2 – 24 ANSWER 3(s2 – 8) t2 + 38t – 10 ANSWER 2(4t – 1) (t + 5) x2 + 24x + 15 ANSWER 3(2x2 + 8x + 5) x2 – 28x – 24 ANSWER 4(3x + 2)(x – 3) –16n2 + 12n ANSWER –4n(4n – 3)

7
GUIDED PRACTICE GUIDED PRACTICE for Example 4 z2 + 33z + 36 ANSWER 3(2z + 3)(z + 4)

8
**Factor the polynomial x3 – 3x2 – 16x + 48 completely.**

STANDARD 4.0 Factor by grouping Factor the polynomial x3 – 3x2 – 16x + 48 completely. x3 – 3x2 – 16x + 48 = x2(x – 3) – 16(x – 3) Factor by grouping. = (x2 – 16)(x – 3) Distributive property = (x + 4)(x – 4)(x – 3) Difference of two squares

9
**Factor polynomials in quadratic form**

Factor completely: (a) 16x4 – 81 and (b) 2p8 + 10p5 + 12p2. a x4 – 81 = (4x2)2 – 92 Write as difference of two squares. = (4x2 + 9)(4x2 – 9) Difference of two squares = (4x2 + 9)(2x + 3)(2x – 3) Difference of two squares Factor common monomial. b. 2p8 + 10p5 + 12p2 = 2p2(p6 + 5p3 + 6) Factor trinomial in quadratic form. = 2p2(p3 + 3)(p3 + 2)

10
GUIDED PRACTICE for Examples 3 and 4 Factor the polynomial completely. x3 + 7x2 – 9x – 63 ANSWER (x + 3)(x – 3)(x + 7) g4 – 625 (4g2 + 25)(2g + 5)(2g – 5) ANSWER t6 – 20t4 + 24t2 4t2(t2 – 3)(t2 – 2 ) ANSWER

11
**Find a common monomial factor**

EXAMPLE 1 Find a common monomial factor Factor the polynomial completely. a. x3 + 2x2 – 15x = x(x2 + 2x – 15) Factor common monomial. = x(x + 5)(x – 3) Factor trinomial. b. 2y5 – 18y3 = 2y3(y2 – 9) Factor common monomial. = 2y3(y + 3)(y – 3) Difference of two squares c. 4z4 – 16z3 + 16z2 = 4z2(z2 – 4z + 4) Factor common monomial. = 4z2(z – 2)2 Perfect square trinomial

12
**Factor the sum or difference of two cubes**

EXAMPLE 2 Factor the sum or difference of two cubes Factor the polynomial completely. a. x3 + 64 = x3 + 43 Sum of two cubes = (x + 4)(x2 – 4x + 16) b z5 – 250z2 = 2z2(8z3 – 125) Factor common monomial. = 2z2 (2z)3 – 53 Difference of two cubes = 2z2(2z – 5)(4z2 + 10z + 25)

13
GUIDED PRACTICE for Examples 1 and 2 Factor the polynomial completely. x3 – 7x2 + 10x ANSWER x( x – 5 )( x – 2 ) y5 – 75y3 ANSWER 3y3(y – 5)(y + 5 ) b b2 ANSWER 2b2(2b + 7)(4b2 –14b + 49) 4. w3 – 27 ANSWER (w – 3)(w2 + 3w + 9)

Similar presentations

© 2021 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google