Factoring
Factor: Change an addition expression into a multiplication expression.
1. Always look for a common factor
a. immediately take it out to the front of the expression, take out all common factors
b. show what’s left inside ONE set of parenthesis
c. if you factor out the entire term, leave a 1 in its place
2x2 – 10
3x3 + 5x2 + 7x
8x2 + 4x
a2b + a4b2 – 3a3b
Factor: Change an addition expression into a multiplication expression.
1. Always look for a common factor
a. immediately take it out to the front of the expression, take out all common factors
b. show what’s left inside ONE set of parenthesis
2. Identify the number of terms. If there was a common factor, then look at the number of terms
left inside the parenthesis. We will be factoring expressions with 2, 3 or 4 terms.
3. If there are only two terms, see if it is the difference squares
a. a2 – b2 = (a + b)(a – b)
Factor.
w2 – 16
50v2 – 2z2
y3 – 9y
x2 – 64
1. Always look for a common factor
a. immediately take it out to the front of the expression, take out all common factors
b. show what’s left inside ONE set of parenthesis
2. Identify the number of terms. If there was a common factor, then look at the number of terms
left inside the parenthesis. We will be factoring expressions with 2, 3 or 4 terms.
3. If there are four terms:
a.
first try splitting the expression into two parts, right down the middle
i. factor out what’s common to the first two terms
ii. factor out what’s common to the second two terms
iii. if what’s left in the parenthesis is the same, write down that factor
iv. show what’s left in a new set of parentheses.
b. Move the first term to the end then split the expression down the middle
i. factor out what’s common to the first two terms
ii. factor out what’s common to the second two terms
iii. if what’s left in the parenthesis is the same, write down that factor
iv. show what’s left in a new set of parentheses.
Factor Completely.
ax – 3x + 2a – 6
x2 – y2 + 10y – 25
2x + 4y – 3x2 – 6xy
c3 – c2u – 25c + 25u
If subtraction is written backwards, factor out a negative.
When you factor out the negative sign, you write the subtraction switched around.
Beware of “backwards” subtraction.
C(x – y) + (y – x)
d(3 – x) – f(x – 3)
C(x – y) – (x – y): not factored, still subtraction
d(3 – x) + f(3 – x)
(x – y)(C – 1)
(3 – x)(d + f)
Factor Completely.
y(x – 3) – (3 – x)
7x(y – 1) + 4(1 – y)
4x + 6y – 2ax – 3ay
xw – yw – 5x + 5y
1. Always look for a common factor
b. immediately take it out to the front of the expression, take out all common factors
c. show what’s left inside ONE set of parenthesis
2. Identify the number of terms. If there was a common factor, then look at the number of terms
left inside the parenthesis. We will be factoring expressions with 2, 3 or 4 terms.
3. If there are three terms, and the leading coefficient is positive: Trial and Error Method
a. find all the factors of the first term
b. find all the factors of the last term
c. Within 2 sets of parentheses,
i. place the factors from the first term in the front of the parentheses
ii. place the factors from the last term in the back of the parentheses
d. NEVER put common factors together in one parenthesis.
e. check the last sign,
i. if the sign is plus: use the SAME signs, the 1 in front of the 2nd term
ii. if the sign is minus: use different signs, one plus and one minus
f. “smile” to make sure you get the middle term
i. multiply the inner most terms together
ii. multiply the outer most terms together
iii. add the two products together.
Factor Completely.
6x2 – 13x + 6
8x2 + 10x – 25
2d2 + 13d + 20
10x2 – 24x – 18
4. Always look for a common factor
d. immediately take it out to the front of the expression, take out all common factors
e. show what’s left inside ONE set of parenthesis
5. Identify the number of terms. If there was a common factor, then look at the number of terms
left inside the parenthesis. We will be factoring expressions with 2, 3 or 4 terms.
6. If there are three terms, and the leading coefficient is positive: AC Method
a. Multiply the first term to the last term (make sure you have descending order)
b. find all the factors of the produce
c. find the two factors that add to the middle term
d. now rewrite the expression replacing the middle term with the two factors
e. factor by grouping: first two term and then the last two terms
Factor Completely.
2t2 + 5t – 12
2yz3 + 17yz2 + 8yz
4x2 + 6x + 2
16x2 – 16x – 12
Factor Completely.
7x3 – 14x2
6x2y + 3xy – 9xy2
24p3 + 33p2 – 8p – 11
5z2 – 45w2
15t2 – 20t – 50
2x4y3 – 5x3y3 – 18x2y3
Factor: Change an addition expression into a multiplication expression.
1. Always look for a common factor
a. immediately take it out to the front of the expression, take out all common factors
b. show what’s left inside ONE set of parenthesis
2. Identify the number of terms. If there was a common factor, then look at the number of terms
left inside the parenthesis. We will be factoring expressions with 2, 3 or 4 terms.
3. If there are only two terms, see if it is the sum or difference of perfect cubes
a. a3 – b3 = (a – b)(a2 + ab + b2)
b. a3 + b3 = (a + b)(a2 – ab + b2)
Factor Completely.
w3 – 27
y3 + 8
250 + 2z3
x3 – 64w3