Add (6a²-6a+10) to the quotient of (3a³+13a²+2a-8) ÷ (a+4)
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Step-by-step explanation:
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We think you wrote:
(6a^(2)-30a)/(a-2)(a^(2)+2a-8)/(2a^(3)-10a^(2))
This deals with power equations.
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1 result(s) found
a
3⋅(a+4)
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Step by Step Solution:
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STEP
1
:
Equation at the end of step 1
((6•(a2))-30a) (((a2)+2a)-8)
——————————————•——————————————————
(a-2) ((2•(a3))-(2•5a2))
STEP
2
:
Equation at the end of step
2
:
((6•(a2))-30a) (((a2)+2a)-8)
——————————————•—————————————
(a-2) (2a3-(2•5a2))
STEP
3
:
a2 + 2a - 8
Simplify ———————————
2a3 - 10a2
STEP
4
:
Pulling out like terms
4.1 Pull out like factors :
2a3 - 10a2 = 2a2 • (a - 5)
Trying to factor by splitting the middle term
4.2 Factoring a2 + 2a - 8
The first term is, a2 its coefficient is 1 .
The middle term is, +2a its coefficient is 2 .
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 2 .
-8 + 1 = -7
-4 + 2 = -2
-2 + 4 = 2 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -2 and 4
a2 - 2a + 4a - 8
Step-4 : Add up the first 2 terms, pulling out like factors :
a • (a-2)
Add up the last 2 terms, pulling out common factors :
4 • (a-2)
Step-5 : Add up the four terms of step 4 :
(a+4) • (a-2)
Which is the desired factorization
Equation at the end of step
4
:
((6•(a2))-30a) (a+4)•(a-2)
——————————————•———————————
(a-2) 2a2•(a-5)
STEP
5
:
Equation at the end of step
5
:
((2•3a2) - 30a) (a + 4) • (a - 2)
——————————————— • —————————————————
(a - 2) 2a2 • (a - 5)
STEP
6
:
6a2 - 30a
Simplify —————————
a - 2
STEP
7
:
Pulling out like terms
7.1 Pull out like factors :
6a2 - 30a = 6a • (a - 5)
Polynomial Long Division :
7.2 Polynomial Long Division
Dividing : a - 5
("Dividend")
By : a - 2 ("Divisor")
dividend a - 5
- divisor * a0 a - 2
remainder - 3
Quotient : 1
Remainder : -3
Equation at the end of step
7
:
6a • (a - 5) (a + 4) • (a - 2)
———————————— • —————————————————
a - 2 2a2 • (a - 5)
STEP
8
:
Canceling Out
8.1 Cancel out (a-5) which appears on both sides of the fraction line.
Canceling Out :
8.2 Cancel out (a-2) which appears on both sides of the fraction line.
Dividing exponential expressions :
8.3 a1 divided by a2 = a(1 - 2) = a(-1) = 1/a1 = 1/a
Final result :
3 • (a + 4)
———————————
a
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