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Math Polynomials & Factoring (Mod 14/15) Review
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Terms in this set (38)
Define monomial.
1 term
[14.1]
Define binomial.
2 terms
[14.1]
Define trinomial.
3 terms
[14.1]
If a expression has 4 or more terms, what would you call it?
polynomial
Define linear.
highest degree of 1
Define quadratic.
highest degree of 2
Define cubic.
highest degree of 3
If an expression's highest degree is 4 or more, what do you call it?
[#] degree
- 4th degree, 9th degree, 7th degree...
[14.1]
What is a term?
each number in the problem
- 4x² + 16x ; 2 terms and is classified as a binomial
[14.1]
What is a degree?
greatest sum of all exponents in a term
- 4x + 3x² ; degree is 2 and is classified as a quadratic
[14.1]
Find the degree:
4xy² + 3x²y²
4th degree:
add degrees up when there are multiple variables in a term; x¹y² would have 3 and x²y² would have 4 (larger than 3)
[14.1]
Simplify:
7x³y² + 3xy² + 6x - 9x³y² + 2xy² + 5x - 1
- 2x³y² + 5xy² + 11x - 1
[14.1]
Simplify:
(3x² - 6x + 2) - (8x + 6 - 5x²)
8x² - 14x - 4
[14.2]
Simplify:
(3a²b - 6ab² + 2a) + (4ab² - 3b - 2a²b)
a²b - 2ab² + 2a - 3b
[14.2]
Find the product:
12x⁵(5x⁴)
60x⁹
[14.3]
Find the product:
-2u(4u³ + 5u²s² + 6s)
-8u⁴ - 10u³s² - 12us
[14.3]
Find the product:
(x - 5)(x² + 4x - 6)
x³ - x² - 26x + 30
[14.4]
Find the product:
(5c + 7)(5c - 7)
25c² - 49
[14.4]
Find the product:
(6y² - 3y)²
36y⁴ - 36y³ + 9y
[14.4]
Find the product:
(9p² - 3q)(4p³ - 5)
36p⁵ - 45p² - 12p³q + 15q
[14.4]
What is the GCF of 5x² + 30x⁴?
5x²
[15.1 GCF]
Factor:
5k³ + 20k² - 15
5(k³ + 4k² - 3)
[15.1 GCF]
Factor:
2x³ - 12x² + 18 - 3x
(2x² - 3)(x - 6)
[15.1 grouping]
Factor:
uv - u - u² + v
(v - u)(u + 1)
[15.1 grouping; rearranged terms]
Factor:
n² + 13n + 36
(n + 9)(n + 4)
[15.2]
Factor:
4k² + 12k + 8
4(k + 1)(k + 2)
[bottom of 15.2 with GCF]
Factor:
3n² - 26n + 35
(n - 7)(3n - 5)
[slip-n-slide]
Factor:
6y² + 11y + 4
(3y + 4)(2y + 1)
[slip-n-slide; remember to reduce fractions!]
Factor:
-4x² - 10x - 6
-2(2x + 3)(x + 1)
[slip-n-slide with GCF first]
Factor and determine if this is a perfect-square trinomial or a difference of two squares:
4x² - 12x + 9
perfect-square trinomial
(2x - 3)²
[15.4]
Factor and determine if this is a perfect-square trinomial or a difference of two squares:
36n² + 24n + 4
perfect-square trinomial
4(3n + 1)²
[15.4 with GCF first]
Factor and determine if this is a perfect-square trinomial or a difference of two squares:
4x² + 24x + 36
perfect-square trinomial
4(x + 3)²
[15.4 with GCF first]
Factor and determine if this is a perfect-square trinomial or a difference of two squares:
16x⁴ - 24x² + 9
perfect-square trinomial
(4x² - 3)²
Factor and determine if this is a perfect-square trinomial or a difference of two squares:
4b⁴ - 49b²
difference of two squares
b²(2b + 7)(2b - 7)
[15.4 with GCF first]
Factor and determine if this is a perfect-square trinomial or a difference of two squares:
400x⁴ - 484x²
difference of two squares
4x²(10x + 11)(10x - 11)
[15.4 with GCF first]
Factor and determine if this is a perfect-square trinomial or a difference of two squares:
s² - 16
difference of two squares
(s + 4)(s - 4)
[15.4]
Factor and determine if this is a perfect-square trinomial or a difference of two squares:
x⁸ - 49
difference of two squares
(x⁴ + 7)(x⁴ - 7)
[15.4]
What should you ALWAYS do before factoring?
check if there is a GCF to the problem in both variables and numbers
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