FACTORING
An
ALGEBRAIC Adventure
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Factoring-a way of life in
MATH
Begin the journey for success in
FACTORING
Go
for
it…
How do you factor a Monomial
term.
Always check for a common factor.
Check all NUMBERS first and then all
VARIABLES.
8X3 + 2X2 – 10X
The common NUMBER (Factor) is 2
The common VARIABLE (Factor) is X
Divide each term by 2X
So…….2X(4X2 + X – 5) is the factored form.
Remember: To factor you look for
a common number and/or variable
to “divide” out of each “term”.
4X5 + 8X4 – 12X3 + 16X2
There are FOUR “terms” in this algebraic expression. A
“term” is separated by a “+” or “-” sign.
4 is the “common” numeric factor and the largest power
the variables have in “common” is a “2”.
So, let’s “divide” by 4 and subtract 2 from each exponent of
“X”.
4X2( X3 + 2X2 – 3X1 + 4)
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Factoring Monomial terms
#1.
X2 + 2X
Answer: X(X + 2)
#2.
4Y3 - 12Y2
Answer: 4Y2(Y – 3)
#3.
Divided by “X”
Divided by “4Y2”
12W4 + 9W2 – 6W
Answer: 3W(4W3 + 3W -2) Divided by “3W”
(Remember to SUBTRACT Powers when dividing
Variables)
Now try these: (Factor)
1. 10X2 -5X
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See Answer
5X (2X – 1)
2. 13Y3+26Y2 -39Y
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See Answer
13Y (Y2 + 2Y - 3)
3. 16U4 - 28U3 + 4U2
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See Answer
4U2 (4U2 -7U+1)
Let’s try some more:
1. 100Y5 – 50Y4 + 25Y3
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See Answer
25Y3( 4Y2 – 2Y + 1)
2. 16M2 + 32M3 – 40M5
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See Answer
8M2( 2 + 4M – 5M3)
Factoring TRINOMIALS (3)
First, let’s multiply two “binomials” (2 terms)
(X + 4)(X + 6)=
X2 + 10X + 24
How does this work?
“FOIL”-First Outer Inner Last
(FO + IL)(FI+ OL)
So, follow the steps: F’s multiplied, then
O’s next, then I’s, then finally, L’s, then
simplify all terms…….
Now try to multiply these
Binomials:
(X – 6)(X + 8)
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See Answer
X2 + 2X - 48
(X – 7)(X – 4)
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See Answer
X2 – 11X + 28
How to Factor TRINOMIALS??
X2 + 10X + 24
First, look at the sign of the last term, in this case
it’s positive (+).
Next, look at the sign of the middle term, in this
case a positive (+), SO both signs in your
factors will be positive (+).
Now, find ALL factors of the last term (24).
1 * 24; 2 * 12; 3 * 8; 4 * 6----now, since the last
term has a + in front of it, which factors will
ADD up to the middle term of 10.
So, now we have:
(X + 6) (X + 4)
Now let’s factor:
X2 + 2X – 48
Now we must look again at the sign of the last
term ( - ). It is negative, so the factors of 48
now must subtract to render a + 2 in the middle
term:
1 * 48; 2 * 24; 3 * 16; 4 * 12; 6 * 8----the factors
that multiply to give 48 and subtract to give us
a 2 are 6 and 8. The larger factor, in this case
8, will get the + and the 6 will get the -. SO:
(X + 8)(X – 6)
Now YOU try Factoring
TRInomials
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See Answer