Check: Factoring packet

Algebra 2Lesson 5.4

WARM-UP

Warm-up 5.4 &

Daily HW Quiz

Objective

Factor and solve polynomial equations.

Algebra 2

Notes 5.4More Factoring

How do you factor a trinomial whose leading coefficient is not 1?

(3x + 1)(x + 4)

Example: Factor 3x2 + 13x + 4We will make a T to determine the coefficients of the factors...

Write factors ofthe first term inthis column.

3

1

Write factors ofthe last term inthis column.

2

2

Multiple diagonally and add.See if the sum matches themiddle term...

2 + 6 ≠ 13

…if not, try another combination of factors...

3

1

1

4

1 + 12 = 13

( )

( )

These are thecoefficients ofthe factors...

Example: Factor 6d2 + 33d – 63Remember, look for the GCF first...

GCF: 3

3(2d2 + 11d – 21)

Now, factor the trinomial (using a T)

3(2d – 3)(d + 7)

–3 + 14

1

2 –3

7

= 11

Ex 1 Factor the polynomial completely

a) y3-4y2-12y

b) 3x3+30x2+75x

c) 5g5-80g3

EX1 (d) Factor a2 + 4ab – 9x2 + 4b2

This has a perfect square trinomial hidden in it.

a2+ 4ab + 4b2– 9x2

(a + 2b)2 – 9x2

Now, this is the difference of 2 squares (a + 2b + 3x)(a + 2b – 3x)

EX 2 Factoring Sum or Difference of Cubes

Sum Formula: a3+b3=(a+b)(a2-ab+b2)

a) x3+8

Difference formula: a3-b3=(a-b)(a2+ab+b2)

b) 125x3-1

c) 54x3-128

Ex 3 Factor polynomials in quadratic form

a) 10x4-10

b) 3m12+54m7+51m2

Classwork

P. 354 # 1-7

EX 4 Find the real number solutions for each.

a) 16x3-44x2-42x=0

b) 2x5=12x3-16x

Classwork

P. 355 # 8-10

Homework

p. 357 #11-37 odd, 51 (15 pts)

Closurex2 + 6x – 25y2 + 9

HINT: This has a perfect square trinomial hidden in it.

(x+3-5y)(x+3+5y)