
A2H Unit 9: Factoring Polynomials
Presentation
•
Mathematics
•
10th Grade
•
Medium
+1
Standards-aligned
Hannah Wiley
Used 3+ times
FREE Resource
6 Slides • 24 Questions
1
Unit 9: Polynomials
Topic #1: Factoring Quadratics Review
trinomial where a = 1
trinomial where a > 1 (grouping)
difference of squares
Topic #2: Factoring Cubic Expressions
grouping
difference of cubes
sum of cubes
2
Soon, we are going to be analyzing the graphs of polynomial functions and looking for specific features.
Factoring specifically shows us the "zeros" of the functions.
What are we going to use this for?
3
This video covers the following types of factoring:
GCF
trinomials when a = 1
trinomials when a > 1
difference of squares
grouping w./ cubics
4
Multiple Choice
16x2 - 20xy
4 (4x2 - 5xy)
4x (4x - 5y)
4x2 (4 - 5y)
2(duck)
5
Multiple Choice
x³+7x²-2x-14
(x²-2)(x-7)
(x²+2)(x-7)
(x²+2)(x+7)
(x²-2)(x+7)
6
Multiple Choice
Write x3 + 9x2 + 18x in factored form
x(x + 6)(x + 3)
x(x + 9)(x + 2)
x(x + 6)
x(x - 6)(x - 3)
7
Multiple Select
Using factoring, select all zeros of: (x2−1)(x2 +x−12) HINT: Factor both of the polynomials
1
-1
-4
3
-3
8
Multiple Choice
Which expression is a factor of 121x2−36 ?
11x+6
11x+12
11x-36
121x-6
9
Math Response
What are the factors of x2−49 ? (put each factor in parentheses with no spaces)
10
Multiple Choice
Find the factors of
x2 + x - 6
(x - 6)(x - 9)
(x + 3)(x + 2)
(x + 3)(x - 2)
(x + 2)(x + 4)
11
Multiple Choice
Find the factors of
x2 - 5x - 36
(x + 4)(x - 9)
(x - 4)(x + 9)
(x - 9)(x + 6)
(x + 4)(x + 9)
12
Multiple Choice
Find the factors of
5m2 - 45m + 90
3(m + 1)(m + 8)
5(m - 3)(m - 6)
2(m - 7)(m + 3)
5(m - 5)(m + 3)
13
Multiple Choice
8x3 - 18x
2x(4x2-9)
(4x2+3)(2x-3)
2x(2x+3)(2x-3)
PRIME
14
Multiple Choice
3x3-x2+6x-2
(x2+2)(3x+1)
(x2+2)(3x-1)
(3x3+6x)(x2-2)
none of the aboe
15
Multiple Choice
Prime
( 2x - 32y) (2 x + 32y)
( 2x - 8y) (2 x - 8y)
( 2x - 8y) (2 x + 8y)
16
Multiple Choice
4b5+4b3+16b2
4b3(b4+b2+4b)
4b3(b4+4b+5)
4(b5+b3+4b2)
4b2(b3+b+4)
17
Multiple Choice
What are the remaining factors for
(x3 +x2 -17x +15) if (x -1) is a factor? (use synthetic division)
(x-1) (x+5) (x-3)
(x-1) (x+5) (x + 3)
(x+1) (x+5) (x-3)
(x+1) (x-5) (x-3)
18
This video covers more factoring of cubic expressions. If you struggled with any of the previous questions, this video might help you understand the connection between synthetic division and factoring more.
19
Multiple Choice
Yes, (x-2) is a factor. There is a remainder.
No, (x-2) is not a factor. The remainder is zero.
Yes, (x-2) is a factor. The remainder is zero.
No, (x-2) is not a factor. There is a remainder.
20
Multiple Choice
One of the factors of the polynomial below is x-4. Write the polynomial in its fully factored form.
f(x)=2x3+7x2−53x−28
f(x)=(x−4)(2x+1)(x+7)
f(x)=(x−4)(2x2+15x+7)
f(x)=2x2+15x+7
f(x)=(2x+1)(x+7)
21
This video covers sums and differences of cubic expressions. On the next slide, I'll have the formulas that he shows on his whiteboard.
22
Factoring a Sum or Difference of Cubes
23
Multiple Choice
a³-b³=
(a-b)(a²+ab+b²)
(a+b)(a²-ab+b²)
(a-b)(a²-ab+b²)
(a+b)(a²+ab+b²)
24
Multiple Choice
Complete the formula
a³+b³=
(a-b)(a²+ab+b²)
(a+b)(a²-ab+b²)
(a-b)(a²-ab+b²)
(a+b)(a²+ab+b²)
25
Multiple Choice
(x + 1)3
(x+1)(x2 - x + 1)
(x - 1) (x2 + x - 1)
(x + 1)(x2 - 2x + 1)
26
Multiple Choice
(2x - 1)(4x2 + 2x + 1)
(2x + 1)(4x2 - 2x + 1)
(2x - 1)(4x2 - 2x - 1)
(2x + 1)(4x2 +2x + 1)
27
Multiple Choice
27x³-64
(3x-4)(9x²+12x+16)
(3x-4)(9x²-12x+16)
(3x+4)(9x²-12x+16)
(3x+4)(9x²+12x+16)
28
Multiple Choice
8x3-27
(2x+3)(4x2-6x+9)
(2x-3)(4x2+6x+9)
(2x-3)(4x2+6x-9)
(2x-3)(2x2+6x+9)
29
Multiple Choice
Which number is both a perfect square and a perfect cube?
64
27
81
16
30
Multiple Choice
Identify if the expression can be factored as sum or difference of cubes:
3x3 + 24
No
Yes
Yes, getting GCF first
It is a sum of squares
Unit 9: Polynomials
Topic #1: Factoring Quadratics Review
trinomial where a = 1
trinomial where a > 1 (grouping)
difference of squares
Topic #2: Factoring Cubic Expressions
grouping
difference of cubes
sum of cubes
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