Factorise b^3+22b^2-48b
Answers
Answer:
Step-by-step explanation:
Equation at the end of step 1
((b3) - 2b2) - 48b
STEP
2
:
STEP
3
:
Pulling out like terms
3.1 Pull out like factors :
b3 - 2b2 - 48b = b • (b2 - 2b - 48)
Trying to factor by splitting the middle term
3.2 Factoring b2 - 2b - 48
The first term is, b2 its coefficient is 1 .
The middle term is, -2b its coefficient is -2 .
The last term, "the constant", is -48
Step-1 : Multiply the coefficient of the first term by the constant 1 • -48 = -48
Step-2 : Find two factors of -48 whose sum equals the coefficient of the middle term, which is -2 .
-48 + 1 = -47
-24 + 2 = -22
-16 + 3 = -13
-12 + 4 = -8
-8 + 6 = -2 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -8 and 6
b2 - 8b + 6b - 48
Step-4 : Add up the first 2 terms, pulling out like factors :
b • (b-8)
Add up the last 2 terms, pulling out common factors :
6 • (b-8)
Step-5 : Add up the four terms of step 4 :
(b+6) • (b-8)
Which is the desired factorization
Final result :
b • (b + 6) • (b - 8)
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Answer:
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