Use the Factor Theorem to determine whether $g (x)$ is factor of $f (x)$ or not.
$f (x) = 3 x^{3} + x^{2} - 20 x + 12, g (x) = 3 x - 2$

Open in App

Solution

Given $f (x) = 3 x^{3} + x^{2} - 20 x + 12$ the $g (x) = 3 x - 2$ is the factor
If $g (x) = 3 x - 2$ is factor then $g (x) = 3 x - 2 = 0$ or $x = \frac{2}{3}$
Replace x by $\frac{2}{3}$ in f(x) we get
$f (x) = 3 x^{3} + x^{2} - 20 x + 12$

$f (\frac{2}{3}) = 3 {(\frac{2}{3})}^{3} + {(\frac{2}{3})}^{2} - 20 (\frac{2}{3}) + 12$

$\Rightarrow f (\frac{2}{3}) = 3 \times \frac{8}{27} + \frac{4}{9} - 20 \times \frac{2}{3} + 12$

$f (\frac{2}{3}) = \frac{8}{9} + \frac{4}{9} - \frac{40}{3} + 12$

$f (\frac{2}{3}) = \frac{8 + 4 - 120 + 108}{9} = \frac{120 - 120}{9} = 0$

So f(x)is zero by g(x) then g(x) =3x-2 is factor of $f (x) = 3 x^{3} + x^{2} - 20 x + 12$

Suggest Corrections

Similar questions

Use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x)

f(x) = $3 x^{3} + x^{2}$ - 20x + 12, g(x) = 3x - 2

Using factor theorem, show that g(x) is a factor of p(x), when
$p (x) = 3 x^{3} + x^{2} - 20 x + 12, g (x) = 3 x - 2$

g (x)

f (x)

f (x) = 4 x^{3} + 20 x^{2} + 33 x + 18, g (x) = 2 x + 3

g (x)

p (x)

p (x) = 3 x^{3} + x^{2} - 20 x + 12 g (x) = 3 x - 2

g (x)

f (x)

f (x) = x^{3} - 4 x^{2} + x + 6, g (x) = x - 2

Join BYJU'S Learning Program