Check whether the polynomial $q (t) = 4 t^{3} + 4 t^{2} - t - 1$ is a multiple of $(2 t + 1)$ or not.

Open in App

Solution

If $(2 t + 1)$ is a factor then $t = \frac{- 1}{2}$ must be one of the zeroes of the given polynomial. Substituting in the given equation.
$q ((\frac{- 1}{2})) = 4 (\frac{- 1}{2})^{3} + 4 (\frac{- 1}{2})^{2} - (\frac{- 1}{2}) - 1 = 4 (\frac{- 1}{8}) + 4 (\frac{1}{4}) + (\frac{1}{2}) - 1 = (\frac{- 1}{2}) + 1 + (\frac{1}{2}) - 1 = 0$
Hence $(2 t + 1)$ is a common factor of $q (t)$

Suggest Corrections

Similar questions

Find the remainder when q(t) = 4t³ + 4t² – t - 1 is divided by 2t + 1

Is 2t+1 a factor of 4 $t^{3}$ +4 $t^{2}$ -t-1?

p (y) = 4 y^{3} + 4 y^{2} - y - 1

(2 y + 1)

Check whether the polynomial p(x) = 4x³+ 4x²- x - 1 is a multiple it 2x + 1

Check whether the polynomial f (x) = 4x^3+4x^2 -x -1 is a multiple of 2x +1

Join BYJU'S Learning Program