6x³-25x²+32x-12
(factorise the above equation)
give step by step explanation
Answers
Answer:
(x−2)⋅(3x−2)⋅(2x−3)
See steps
Step by Step Solution:
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STEP
1
:
Equation at the end of step 1
(((6 • (x3)) - 52x2) + 32x) - 12
STEP
2
:
Equation at the end of step
2
:
(((2•3x3) - 52x2) + 32x) - 12
STEP
3
:
Checking for a perfect cube
3.1 6x3-25x2+32x-12 is not a perfect cube
Trying to factor by pulling out :
3.2 Factoring: 6x3-25x2+32x-12
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: 32x-12
Group 2: 6x3-25x2
Pull out from each group separately :
Group 1: (8x-3) • (4)
Group 2: (6x-25) • (x2)
Bad news !! Factoring by pulling out fails :
The groups have no common factor and can not be added up to form a multiplication.
Polynomial Roots Calculator :
3.3 Find roots (zeroes) of : F(x) = 6x3-25x2+32x-12
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x 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 6 and the Trailing Constant is -12.
The factor(s) are:
of the Leading Coefficient : 1,2 ,3 ,6
of the Trailing Constant : 1 ,2 ,3 ,4 ,6 ,12
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 -75.00
-1 2 -0.50 -35.00
-1 3 -0.33 -25.67
-1 6 -0.17 -18.06
-2 1 -2.00 -224.00
-2 3 -0.67 -46.22
-3 1 -3.00 -495.00
-3 2 -1.50 -136.50
-4 1 -4.00 -924.00
-4 3 -1.33 -113.33
-6 1 -6.00 -2400.00
-12 1 -12.00 -14364.00
1 1 1.00 1.00
1 2 0.50 -1.50
1 3 0.33 -3.89
1 6 0.17 -7.33
2 1 2.00 0.00 x-2
2 3 0.67 0.00 3x-2
3 1 3.00 21.00
3 2 1.50 0.00 2x-3
4 1 4.00 100.00
4 3 1.33 0.44
6 1 6.00 576.00
12 1 12.00 7140.00
The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p Note that q and p originate from P/Q reduced to its lowest terms
In our case this means that
6x3-25x2+32x-12
can be divided by 3 different polynomials,including by 2x-3
Polynomial Long Division :
3.4 Polynomial Long Division
Dividing : 6x3-25x2+32x-12
("Dividend")
By : 2x-3 ("Divisor")
dividend 6x3 - 25x2 + 32x - 12
- divisor * 3x2 6x3 - 9x2
remainder - 16x2 + 32x - 12
- divisor * -8x1 - 16x2 + 24x
remainder 8x - 12
- divisor * 4x0 8x - 12
remainder 0
Quotient : 3x2-8x+4 Remainder: 0
Step-by-step explanation:
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this question is wrong
6x^3 -27x^2+32x-12
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