factorise the following polynomial.6x^3+7x^2-x-2
Answers
Answer:
go to google dear
Step-by-step explanation:
go to google dear
Answer:
Step-by-step explanation:
Changes made to your input should not affect the solution:
(1):STEP
1
:
Equation at the end of step 1
(((6 • (x3)) - 7x2) - x) + 2 "x2" was replaced by "x^2". 1 more similar replacement(s).
STEP
2
:
Equation at the end of step
2
:
(((2•3x3) - 7x2) - x) + 2
STEP
3
:
Checking for a perfect cube
3.1 6x3-7x2-x+2 is not a perfect cube
Trying to factor by pulling out :
3.2 Factoring: 6x3-7x2-x+2
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: -x+2
Group 2: 6x3-7x2
Pull out from each group separately :
Group 1: (-x+2) • (1) = (x-2) • (-1)
Group 2: (6x-7) • (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) = 6x3-7x2-x+2
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 2.
The factor(s) are:
of the Leading Coefficient : 1,2 ,3 ,6
of the Trailing Constant : 1 ,2
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 -10.00
-1 2 -0.50 0.00 2x+1
-1 3 -0.33 1.33
-1 6 -0.17 1.94
-2 1 -2.00 -72.00
-2 3 -0.67 -2.22
1 1 1.00 0.00 x-1
1 2 0.50 0.50
1 3 0.33 1.11
1 6 0.17 1.67
2 1 2.00 20.00
2 3 0.67 0.00 3x-2
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
6x3-7x2-x+2
can be divided by 3 different polynomials,including by 3x-2
Polynomial Long Division :
3.4 Polynomial Long Division
Dividing : 6x3-7x2-x+2
("Dividend")
By : 3x-2 ("Divisor")
dividend 6x3 - 7x2 - x + 2
- divisor * 2x2 6x3 - 4x2
remainder - 3x2 - x + 2
- divisor * -x1 - 3x2 + 2x
remainder - 3x + 2
- divisor * -x0 - 3x + 2
remainder 0
Quotient : 2x2-x-1 Remainder: 0
Trying to factor by splitting the middle term
3.5 Factoring 2x2-x-1
The first term is, 2x2 its coefficient is 2 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is -1
Step-1 : Multiply the coefficient of the first term by the constant 2 • -1 = -2
Step-2 : Find two factors of -2 whose sum equals the coefficient of the middle term, which is -1 .
-2 + 1 = -1 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -2 and 1
2x2 - 2x + 1x - 1
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (x-1)
Add up the last 2 terms, pulling out common factors :
1 • (x-1)
Step-5 : Add up the four terms of step 4 :
(2x+1) • (x-1)
Which is the desired factorization
Final result :
(x - 1) • (2x + 1) • (3x - 2)