f(x)=x^3-2x^2-5x+6is divided by(2x-1)
Answers
Answer:
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Answer:
(x3-2x2-5x+6):(x-1)
Final result :
(x + 2) • (x - 3)
Step by step solution :
Step 1 :
Equation at the end of step 1 :
Step 2 :
x3 - 2x2 - 5x + 6
Simplify —————————————————
x - 1
Checking for a perfect cube :
2.1 x3 - 2x2 - 5x + 6 is not a perfect cube
Trying to factor by pulling out :
2.2 Factoring: x3 - 2x2 - 5x + 6
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: -5x + 6
Group 2: x3 - 2x2
Pull out from each group separately :
Group 1: (-5x + 6) • (1) = (5x - 6) • (-1)
Group 2: (x - 2) • (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 :
2.3 Find roots (zeroes) of : F(x) = x3 - 2x2 - 5x + 6
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 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 ....