Factorize the polynomial 2x³ -9x² + 7x + 6 into linear factors using synthetic division.
Answers
Answer:
Factorize
Step-by-step explanation:
x=−2,−
2
1
and 3 is the value of x for the given cubic polynomial \bold{2 x^{3}-x^{2}-13 x-6}2x
3
−x
2
−13x−6
Given:
2 x^{3}-x^{2}-13 x-62x
3
−x
2
−13x−6
To find:
The value of x
Solution:
From the given 2 x^{3}-x^{2}-13 x-62x
3
−x
2
−13x−6 to find the value of x solve the cubic polynomial and convert them in to quadratic equation and then find the roots.
First to solve cubic polynomial use synthetic division then the result is the quadratic equation.
(x+2)\left(2 x^{2}-5 x-3\right)=0(x+2)(2x
2
−5x−3)=0
Then solving the quadratic equation using the formula \bold{\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}}
2a
−b±
b
2
−4ac
The quadratic equation is 2 x^{2}-5 x-32x
2
−5x−3
\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}
2a
−b±
b
2
−4ac
where a=2,b=-5 and c=-3
\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}=\frac{5 \pm \sqrt{25-4(2)(-3)}}{2(2)}=\frac{5 \pm 7}{4}=\frac{12}{4},-\frac{2}{4}=3,-\frac{1}{2}
2a
−b±
b
2
−4ac
=
2(2)
5±
25−4(2)(−3)
=
4
5±7
=
4
12
,−
4
2
=3,−
2
1
The value of\bold{x=-2,3,-\frac{1}{2}}x=−2,3,−
2
1
for the cubic polynomial \bold{2 x^{3}-x^{2}-13 x-6.}2x
3
−x
2
−13x−6.
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