Factorise : $2x^{3}-3x^{2}-17x+30$
(D) Let $f(x) = 2x^{3}-3x^{2}-17x+30$ be the given polynomial.
By testing values,we find $f(2) = 2(8) - 3(4) - 17(2) + 30 = 16 - 12 - 34 + 30 = 0$. Thus,$(x-2)$ is a factor.
By testing $f(-3) = 2(-27) - 3(9) - 17(-3) + 30 = -54 - 27 + 51 + 30 = 0$. Thus,$(x+3)$ is a factor.
Since $(x-2)$ and $(x+3)$ are factors,their product $(x-2)(x+3) = x^{2}+x-6$ is also a factor.
Dividing $2x^{3}-3x^{2}-17x+30$ by $(x^{2}+x-6)$:
$2x^{3}-3x^{2}-17x+30 = (x^{2}+x-6)(2x-5)$.
Further factoring $(x^{2}+x-6)$ into $(x-2)(x+3)$,we get:
$2x^{3}-3x^{2}-17x+30 = (x-2)(x+3)(2x-5)$.
By testing values,we find $f(2) = 2(8) - 3(4) - 17(2) + 30 = 16 - 12 - 34 + 30 = 0$. Thus,$(x-2)$ is a factor.
By testing $f(-3) = 2(-27) - 3(9) - 17(-3) + 30 = -54 - 27 + 51 + 30 = 0$. Thus,$(x+3)$ is a factor.
Since $(x-2)$ and $(x+3)$ are factors,their product $(x-2)(x+3) = x^{2}+x-6$ is also a factor.
Dividing $2x^{3}-3x^{2}-17x+30$ by $(x^{2}+x-6)$:
$2x^{3}-3x^{2}-17x+30 = (x^{2}+x-6)(2x-5)$.
Further factoring $(x^{2}+x-6)$ into $(x-2)(x+3)$,we get:
$2x^{3}-3x^{2}-17x+30 = (x-2)(x+3)(2x-5)$.
Explore More
Similar Questions
The degree of the polynomial $7x^5 - 4x^4 + 2(x^3)^2 - x^2 + 35$ is $\ldots \ldots \ldots$
Easy
View SolutionEvaluate $(132)^{2}$ by using suitable identities.
Medium
View SolutionExpand $\left(\frac{x}{2}-\frac{2}{5}\right)^{2}$.
Easy
View SolutionDivide $p(x) = x^{3} + 7x^{2} + 14x + 1$ by $x + 3$ and find the quotient and the remainder.
Medium
View SolutionIf $x+1$ is a factor of $ax^3+x^2-2x+4a-9$,find the value of $a$.
Easy
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo