divide 4x4+3x3+2x+1 byx2+x+2
Answers
Answer:
Step by Step Solution:
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Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2". 2 more similar replacement(s).
STEP
1
:
1
Simplify ——
x2
Equation at the end of step
1
:
1
(((((4•(x4))-(3•(x3)))-2x)+——)+x)+2
x2
STEP
2
:
Equation at the end of step
2
:
1
(((((4•(x4))-3x3)-2x)+——)+x)+2
x2
STEP
3
:
Equation at the end of step
3
:
1
((((22x4 - 3x3) - 2x) + ——) + x) + 2
x2
STEP
4
:
Rewriting the whole as an Equivalent Fraction
4.1 Adding a fraction to a whole
Rewrite the whole as a fraction using x2 as the denominator :
4x4 - 3x3 - 2x (4x4 - 3x3 - 2x) • x2
4x4 - 3x3 - 2x = —————————————— = —————————————————————
1 x2
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
STEP
5
:
Pulling out like terms
5.1 Pull out like factors :
4x4 - 3x3 - 2x = x • (4x3 - 3x2 - 2)
Polynomial Roots Calculator :
5.2 Find roots (zeroes) of : F(x) = 4x3 - 3x2 - 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 4 and the Trailing Constant is -2.
The factor(s) are:
of the Leading Coefficient : 1,2 ,4
of the Trailing Constant : 1 ,2
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 -9.00
-1 2 -0.50 -3.25
-1 4 -0.25 -2.25
-2 1 -2.00 -46.00
1 1 1.00 -1.00
1 2 0.50 -2.25
1 4 0.25 -2.13
2 1 2.00 18.00
Polynomial Roots Calculator found no rational roots