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Transcript of Factoring Polynomials
Trinomial with a Leading Coefficient of 1
Since the leading coefficient is 1, the factored form will be of the form: (x )(x )
Find two numbers that multiply to be the constant of the polynomial and add to be the coefficient of x
Fill in the blank spots of each set of parentheses with the two numbers you found
Difference of Two Squares
Check if a GCF can be factored out.
If a polynomial has two terms and uses subtraction, check to see if it is the difference of two squares
Is the first term a monomial times itself?
Is the second term a monomial times itself?
If the polynomial is of the form a - b , factor it in the following way: (a + b)(a - b)
If possible, factor out any GCF
Group the first two terms and last two terms
From each group, factor out the GCF. The remaining binomials should be the same. If not, regroup and try again.
Factor out this common binomial term and write your answer.
Trinomial with a Leading Coefficient Other than 1
Check if a GCF can be factored out
Multiply the leading coefficient and the constant
Find factors of this product that add together to be the coefficient of x
Split the middle term of the original polynomial with the factors
Group the first and last two terms
Factor the GCF out of each group and write final factored form
Check to see if the polynomial has common factors in each of its terms
Factor out the greatest common factor from each term
The polynomial that is left after the GCF has been divided out of each term will be placed in parentheses to be multiplied by the GCF
4y(xy + 4x-2)
x + 7x + 10
(5)(2)=10 and 5 + 2 =7
(x + 2)(x + 5)
6x - x - 2
(6)(-2) = -12
Factors of -12 that add to -1: -4 and 3
6x - 4x + 3x - 2
2x(3x - 2) + 1(3x - 2)
(2x + 3)(4x - 1)
8x - 2x + 12x - 3
2x (4x - 1) + 3(4x - 1)
(x + 3)(x - 3)
x - 9
x = (x)(x)
9 = (3)(3)
What if it cannot be factored?
A polynomial that cannot be factored is called "prime."
Good luck factoring!