Bell Ringer

Factor the following:81x3 – 192

a) 3(3x - 4)(9x2 + 4x + 16)b) (3x- 4)(9x2 + 4x + 16)c) 3(3x - 4)(9x2 + 12x + 16)d) (9x - 4)(9x2 + 4x + 16)

Students will be able to factor polynomial equations.

Page 356#18-29,

32-40 (even)

Today’s Lesson

Goal: Factor by Grouping & Factor Polynomials into Quadratic Form

• Factor by Grouping - factors out common terms, and then groups them.

• For polynomials raised to higher powers, such as to the fourth power, we can factor into two quadratics.

Factor by Grouping

Pattern:

ra + rb +sa +sb = r(a + b) + s(a + b)

=(r + s)(a + b)

Factor by Grouping

• Example 1:

x3 – 3x2 –16x + 48

x2 (x-3) – 16(x – 3)

(x2 – 16)(x-3)

Factor by Grouping Exercisesx3 + 2x2 + 3x + 6 m3 – 2m2 + 4m – 8

Factor into Quadratic Form• Recall a quadratic is of the form:

ax2 + bx2 + c

• Sometimes with higher powers, we factor our polynomial into quadratic form.

• Example: x4 – 81

Think of rewriting x4 as (x2)2

= (x2 + 9)(x2 – 9)

= (x2 + 9)(x + 3)(x – 3)

Factor into Quadratic Form16x4 – 81 6y6 – 5y3 – 4

Factor into Quadratic Form

• Example 2:

2x8 + 10x5 + 12x2 Factor common monomial

= 2x2(x6 + 5x3 + 6)Factor our trinomial

= 2x2(x3 + 3)(x3 + 2)

Challenge Problem

• The dimensions of a jewelry box are: length 4x, width (x-1), and height (x-2). If the volume of the box is 24 cubic inches, find the dimensions of the box.

• Hint: Remember V=lwh. Multiply this out, and then try factoring by grouping to solve.

• State the new dimensions, and show all of your work.

Challenge Problemvolume 24 in3, length 4x, width (x-1), height (x-2)

Minute Paper

1) What was the most important topic you learned today?

2) What did you like/dislike about the lesson?

3) How could I improve it?

Homework

Page 356

#18-29; 32-40 (even)

Factor by Grouping

Factoring into Quadratics

Solve by Factoring