Q6 of 96 Page 6

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) = 2x3-9x2+x+12, g(x) = 3-2x

We have,

f(x) = 2x3-9x2+x+12 and g(x) = 3-2x


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) = 2x3-9x2+x+12


f () = 2 ()3 – 9 ()2 + + 12


= - + + 12


=


= 0


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


More from this chapter

All 96 →
4

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) = x3-6x2-19x+84, g(x) = x-7

 5

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) = 3x3+x2-20x+12, g(x) = 3x-2

 7

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) = x3-6x2+11x-6, g(x) = x2-3x+2

 8

Show that (x-2), (x+3) and (x-4) are factors of x3-3x2-10x+24.