Factorise the following:
5a⁴ - 5a³ + 30a² - 30a
Answers
I hope you will be able to get it!
Step-by-step explanation:
Step by Step Solution:

STEP1:Equation at the end of step 1
(((5•(a4))-(5•(a3)))+(2•3•5a2))-30a
STEP 2 :
Equation at the end of step2:
(((5 • (a4)) - 5a3) + (2•3•5a2)) - 30a
STEP 3 :
Equation at the end of step3:
((5a4 - 5a3) + (2•3•5a2)) - 30a
STEP4:
STEP5:Pulling out like terms
5.1 Pull out like factors :
5a4 - 5a3 + 30a2 - 30a =
5a • (a3 - a2 + 6a - 6)
Checking for a perfect cube :
5.2 a3 - a2 + 6a - 6 is not a perfect cube
Trying to factor by pulling out :
5.3 Factoring: a3 - a2 + 6a - 6
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: a3 - a2
Group 2: 6a - 6
Pull out from each group separately :
Group 1: (a - 1) • (a2)
Group 2: (a - 1) • (6)
-------------------
Add up the two groups :
(a - 1) • (a2 + 6)
Which is the desired factorization
Polynomial Roots Calculator :
5.4 Find roots (zeroes) of : F(a) = a2+ 6
Polynomial Roots Calculator is a set of methods aimed at finding values of a for which F(a)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers a which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 1 and the Trailing Constant is 6.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,2 ,3 ,6
Let us test ....
P Q P/Q F(P/Q) Divisor -1 1 -1.00 7.00 -2 1 -2.00 10.00 -3 1 -3.00 15.00 -6 1 -6.00 42.00 1 1 1.00 7.00 2 1 2.00 10.00 3 1 3.00 15.00 6 1 6.00 42.00
Polynomial Roots Calculator found no rational roots
Final result :
5a • (a2 + 6) • (a - 1)
Step by Step Solution:

STEP1:Equation at the end of step 1
(((5•(a4))-(5•(a3)))+(2•3•5a2))-30a
STEP 2 :
Equation at the end of step2:
(((5 • (a4)) - 5a3) + (2•3•5a2)) - 30a
STEP 3 :
Equation at the end of step3:
((5a4 - 5a3) + (2•3•5a2)) - 30a
STEP4:
STEP5:Pulling out like terms
5.1 Pull out like factors :
5a4 - 5a3 + 30a2 - 30a =
5a • (a3 - a2 + 6a - 6)
Checking for a perfect cube :
5.2 a3 - a2 + 6a - 6 is not a perfect cube
Trying to factor by pulling out :
5.3 Factoring: a3 - a2 + 6a - 6
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: a3 - a2
Group 2: 6a - 6
Pull out from each group separately :
Group 1: (a - 1) • (a2)
Group 2: (a - 1) • (6)
-------------------
Add up the two groups :
(a - 1) • (a2 + 6)
Which is the desired factorization
Polynomial Roots Calculator :
5.4 Find roots (zeroes) of : F(a) = a2+ 6
Polynomial Roots Calculator is a set of methods aimed at finding values of a for which F(a)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers a which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 1 and the Trailing Constant is 6.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,2 ,3 ,6
Let us test ....
P Q P/Q F(P/Q) Divisor -1 1 -1.00 7.00 -2 1 -2.00 10.00 -3 1 -3.00 15.00 -6 1 -6.00 42.00 1 1 1.00 7.00 2 1 2.00 10.00 3 1 3.00 15.00 6 1 6.00 42.00
Polynomial Roots Calculator found no rational roots
Final result :
5a • (a2 + 6) • (a - 1)