Determine whether (2x-3) is factor of $2 x^{3} - 9 x^{2} + x = 12$ .

Open in App

Solution

Let $p (x) = 2 x^{3} - 9 x^{2} + x + 12$ . By factor theorem, (2x-3) is a factor p(x) if $p (\frac{3}{2}) = 0$ . Now,
$p (\frac{3}{2}) = 2 {(\frac{3}{2})}^{3} - 9 {(\frac{3}{2})}^{2} + \frac{3}{2} + 12 = 2 (\frac{27}{8}) - 9 (\frac{9}{4}) + \frac{3}{2} + 12$
$= \frac{27}{4} - \frac{81}{4} + \frac{3}{2} + 12$
$= \frac{27 - 81 + 6 + 48}{4} = 0$
$∴ (2 x - 3)$ is a factor of $2 x^{3} - 9 x^{2} + x + 12$ .

Suggest Corrections

Similar questions

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

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

69 + 11 x - x^{2} + x^{3}

x + 2 x^{3} - 9 x^{2} + 12

Question 16
Show that:
(i) x + 3 is a factor of $69 + 11 x - x^{2} + x^{3}$ .

(ii) 2x – 3 is a factor of $x + 2 x^{3} - 9 x^{2} + 12$ .

(2 x - 3)

p (x) = 2 x^{3} - 9 x^{2} + x + 10

Question 16
Show that:
(i) x + 3 is a factor of $69 + 11 x - x^{2} + x^{3}$ .

(ii) 2x – 3 is a factor of $x + 2 x^{3} - 9 x^{2} + 12$ .

Join BYJU'S Learning Program