Name: Division of a Trinomial by a Trinomial
Uploaded: 2019-07-19
Duration: 3 min 36 s
Description: Can we divide a polynomial by another polynomial to get the quotient polynomial and the remainder polynomial? Let's explore this concept in this video.

Question

Factorise

x^{2} (y + z) + y^{2} (z + x) + z^{2} (x + y) + 2 x y z

by using factor theorem.

Accepted Answer

Let $p = x^{2} (y + z) + y^{2} (z + x) + z^{2} (x + y) + 2 x y z$

Now, consider the factors $(y + z), (z + x)$ and $(x + y)$

Put $y = - z$

So, $p (- z) = x^{2} (- z + z) + z^{2} (z + x) + z^{2} (x - z) + 2 x (- z) z = 0$

Thus, by factor theorem $(y + z)$ is a factor of given polynomial.

Also, put $z = - x$

$p (- x) = x^{2} (y - x) + z^{2} (- x + x) + x^{2} (x + y) + 2 x y (- x) = 0$

Thus, by factor theorem $(z + x)$ is a factor of given polynomial.

Also, put $x = - y$

$p (- y) = y^{2} (y + z) + y^{2} (z - y) + z^{2} (- y + y) + 2 (- y) y x = 0$

Thus, by factor theorem $(x + y)$ is a factor of given polynomial.

Thus, $x^{2} (y + z) + y^{2} (z + x) + z^{2} (x + y) + 2 x y z = (x + y) (y + z) (z + x)$

Factorise $x^{2} (y + z) + y^{2} (z + x) + z^{2} (x + y) + 2 x y z$ by using factor theorem.

Important Questions on Polynomials

Learn and Prepare for any exam you want !

Factorise x2y+z+y2z+x+z2x+y+2xyz by using factor theorem.

Important Questions on Polynomials

Learn and Prepare for any exam you want !

Factorise $x^{2} (y + z) + y^{2} (z + x) + z^{2} (x + y) + 2 x y z$ by using factor theorem.