GCF
What is the greatest common factor of
-9y^4+18y^2-6y
-3y
when the leading term in the problem is negative we must factor out a negative.
Write the factored form of
y^2 + 11y + 28.
(y+4)(y+7)
Factor the trinomial
4x^4-12x^3+8x^2
STEP 1: 4x^2(x^2-3x+2) FACTOR-GCF
STEP 2: 4x^2(x-1)(x-2) FACTOR-X^2-bX+c
Factor the perfect square trinomial
25x^2 – 60x + 36.
(5x-6)^2
A rectangle has an area of
x^2+7x+12.
What are the possible dimensions of the rectangle?
(x+3)(x+4)
Factor out the GCF from the terms of the polynomial
6x^4+10x^3+4x^2
2x^2(3x^2+5x+2)
When asked to factor out the GCF you are dividing the polynomial by the GCF.
What is the factored form of
x^2 − 9x + 20?
(x-5)(x-4)
Factor by grouping
6x^2 + 17x + 5
No GCF
6*5=30
6x^2+2x+15x+5
(6x^2+2x)+(15x+5)
2x(3x+1)+5(3x+1)
(2x+5)(3x+1)
Factor the expression
25x^2 − 36.
(5x-6)(5x+6)
A rectangle has an area of
14y^3 − 63y.
a. What are expressions for the length and width where one dimension is the GCF?
b. Does a rectangle exist with the given dimensions if y = 2? Explain
7y(2y^2-9)
Factor out the GCF from the terms of the polynomial
3x^3-14x^2+15
This polynomial does not have a GCF to factor out.
What is the factored form of
y^2 + 6y – 16?
(y+8)(y-2)
Factor by grouping
8x^2-14x-15
(2x-5)(4x+3)
Factor and state what type of trinomial it is:
y^2 + 8y + 16.
(y+4)^2
A perfect square trinomial
The area, in square feet, of a rectangular patio is
3x^2 + 17x + 20
What are the dimensions of the patio?
(x+4)(3x+5)
Factor out the GCF from the terms of the polynomial
-4y^5 + 6y^3 + 8y^2 – 2y
-2y(2y^4-3y^2-4y+1)
What is the factored form of
x^2 + 4xy − 21y^2?
(x+7y)(x-3y)
Factor by grouping
-24x^2+20x+100
-4(2x-5)(3x+5)
Factor the binomial completely.
27x^2-3
3(3x-1)(3x+1)
A pools area, in square yards, is represented by the polynomial
4x^2-49
What are the possible dimensions of the pool?
Double points: What shape would the pool be?
(2x-7)(2x+7)
The pool would be a rectangular shape since the length and width would be different lengths when given x.