divide(5x³+15x²) ÷(x+3)
Answers
Answer:
(5x2 - 1) • (x - 3)
Step-by-step explanation:
STEP
1
:
Equation at the end of step 1
(((5 • (x3)) - (3•5x2)) - x) + 3
STEP
2
:
Equation at the end of step
2
:
((5x3 - (3•5x2)) - x) + 3
STEP
3
:
Checking for a perfect cube
3.1 5x3-15x2-x+3 is not a perfect cube
Trying to factor by pulling out :
3.2 Factoring: 5x3-15x2-x+3
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: -x+3
Group 2: 5x3-15x2
Pull out from each group separately :
Group 1: (-x+3) • (1) = (x-3) • (-1)
Group 2: (x-3) • (5x2)
-------------------
Add up the two groups :
(x-3) • (5x2-1)
Which is the desired factorization
Trying to factor as a Difference of Squares:
3.3 Factoring: 5x2-1
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 5 is not a square !!
Ruling : Binomial can not be factored as the
difference of two perfect squares
Final result :
(5x2 - 1) • (x - 3Trying to factor as a Difference of Squares:
3.3 Factoring: 5x2-1
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 5 is not a square !!
Ruling : Binomial can not be factored as the
difference of two perfect squares
Final result :
(5x2 - 1) • (x - 3).
I hope this was helpful.
(5x³+15x²) ÷(x+3)=5x²
hope this helped have a good day!
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