Completely Factor the polynomial: y=2x^{3}+3x^{2}-11x-6

David Troyer

David Troyer

Answered question

2021-12-12

Completely Factor the polynomial: y=2x3+3x211x6

Answer & Explanation

servidopolisxv

servidopolisxv

Beginner2021-12-13Added 27 answers

part 1
factorizing y=2x3+3x211x6 using the rational roots test.
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
finding every combination of ± p/q
These are the possible roots of the polynomial function.
±1,±0.5,±6,±3,±2,±1.5±1,±0.5,±6,±3,±2,±1.5
Substituting -0.5-and simplifying the expression. In this case, the expression is equal to 0 so -0.5 is the root of the polynomial.
Since -0.5 is a known root, divide the polynomial by 2x+1 to find the quotient polynomial. This polynomial can then be used to find the remaining roots.
part 2
By Dividing 2x3+3x211x6 by 2x+1.
We get
x2+x6
Writing 2x3+3x211x6 as a set of factors.
(2x+1)(x2+x6)
(2x+1)(x2+x6)
x+x-6 using the AC method.
(2x+1)((x−2)(x+3))
Removing unnecessary parentheses.
(2x+1)(x−2)(x+3)

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