Divide (2x3 - 12x2+ 16x)/
(x-2)(x-4)
Answers
Answer:
2x • (x - 4)2
Step-by-step explanation:
Step by Step Solution
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Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2". 1 more similar replacement(s).
STEP
1
:
Equation at the end of step 1
(((2•(x3))-(22•3x2))+16x)
—————————————————————————•(x-4)
(x-2)
STEP
2
:
Equation at the end of step
2
:
((2x3 - (22•3x2)) + 16x)
———————————————————————— • (x - 4)
(x - 2)
STEP
3
:
2x3 - 12x2 + 16x
Simplify ————————————————
x - 2
STEP
4
:
Pulling out like terms
4.1 Pull out like factors :
2x3 - 12x2 + 16x = 2x • (x2 - 6x + 8)
Trying to factor by splitting the middle term
4.2 Factoring x2 - 6x + 8
The first term is, x2 its coefficient is 1 .
The middle term is, -6x its coefficient is -6 .
The last term, "the constant", is +8
Step-1 : Multiply the coefficient of the first term by the constant 1 • 8 = 8
Step-2 : Find two factors of 8 whose sum equals the coefficient of the middle term, which is -6 .
-8 + -1 = -9
-4 + -2 = -6 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and -2
x2 - 4x - 2x - 8
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-4)
Add up the last 2 terms, pulling out common factors :
2 • (x-4)
Step-5 : Add up the four terms of step 4 :
(x-2) • (x-4)
Which is the desired factorization
Canceling Out :
4.3 Cancel out (x-2) which appears on both sides of the fraction line.
Equation at the end of step
4
:
2x • (x - 4) • (x - 4)
STEP
5
:
Multiplying Exponential Expressions:
5.1 Multiply (x-4) by (x-4)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (x-4) and the exponents are :
1 , as (x-4) is the same number as (x-4)1
and 1 , as (x-4) is the same number as (x-4)1
The product is therefore, (x-4)(1+1) = (x-4)2
Final result :
2x • (x - 4)2
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