Q. 65.0( 2 Votes )

# In each of the following, use factor theorem to find whether polynomial *g*(*x*) is a factor of polynomial *f*(*x*) or, not:

*f*(*x*) = 2*x*^{3}-9*x*^{2}+*x*+12, *g*(*x*) = 3-2*x*

Answer :

We have,

*f*(*x*) = 2*x*^{3}-9*x*^{2}+*x*+12 and *g*(*x*) = 3-2*x*

In order to find g (x) = 3 – 2x = 2 (x - ) is a factor of f (x) or not, it is sufficient to prove that f () = 0

Now,

*f*(*x*) = 2*x*^{3}-9*x*^{2}+*x*+12

f () = 2 ()^{3} – 9 ()^{2} + + 12

= - + + 12

=

= 0

Hence, g (x) is a factor of f (x).

Rate this question :

Factorize:

x^{3} – 2x^{2}y + 3xy^{2} – 6y^{3}

Find the value of a for which the polynomial is divisible by (x+3).

RS Aggarwal & V Aggarwal - MathematicsFactorize:

a^{2} + a – 3a^{2} - 3

Factorize:

2a(x + y) -3b(x + y)

RS Aggarwal & V Aggarwal - MathematicsFactorize:

8 – 4a – 2a^{3} + a^{4}

If 𝑎 + 𝑏 + 𝑐 = 9 and 𝑎𝑏 + 𝑏𝑐 + 𝑐𝑎 = 26, find 𝑎^{2} + 𝑏^{2} + 𝑐^{2}.

Show that p – 1 is a factor of p^{10} – 1 and also of p^{11} – 1.

Factorize:

a^{2} + ab(b + 1) + b^{3}

Find the value of m so that 2x – 1 be a factor of 8𝑥^{4} + 4𝑥^{3}−16𝑥^{2} + 10𝑥 + 𝑚.