Factorise $6x^{3} + 7x^{2} - 14x - 15$.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) Let $p(x) = 6x^{3} + 7x^{2} - 14x - 15$.
By the Factor Theorem,we test values for $x$. Let $x = -1$:
$p(-1) = 6(-1)^{3} + 7(-1)^{2} - 14(-1) - 15 = -6 + 7 + 14 - 15 = 0$.
Since $p(-1) = 0$,$(x + 1)$ is a factor.
Now,divide $6x^{3} + 7x^{2} - 14x - 15$ by $(x + 1)$ using long division or synthetic division:
$6x^{3} + 7x^{2} - 14x - 15 = (x + 1)(6x^{2} + x - 15)$.
Next,factorize the quadratic $6x^{2} + x - 15$ by splitting the middle term:
$6x^{2} + 10x - 9x - 15 = 2x(3x + 5) - 3(3x + 5) = (2x - 3)(3x + 5)$.
Thus,the complete factorization is $(x + 1)(3x + 5)(2x - 3)$.

Explore More

Similar Questions

Evaluate $(215)^{2}$.

Factorise the following quadratic polynomial by splitting the middle term:
$x^{2}+14x+33$

Show that $2x - 3$ is a factor of $x + 2x^3 - 9x^2 + 12$.

What should be subtracted from $p(x) = x^{2} + 9x + 20$ so that the resulting polynomial is divisible by $x + 2$?

Is the following expression a polynomial? Justify your answer:
$8$

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo