Divide $p (x) = x^{4} - 3 x^{2} + 4 x + 5$ by $g (x) = x^{2} + 1 - x$ .

Q = x^{2} + x - 5, R = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Q = x^{2} + x - 3, R = 8

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Q = x^{2} + x - 3, R = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Q = x^{2} + x - 5, R = 8

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $Q = x^{2} + x - 3, R = 8$
The polynomial $p (x) = x^{4} - 3 x^{2} + 4 x + 5$ can be divided by $g (x) = x^{2} - x + 1$ as shown below:

Clearly, the quotient is $x^{2} + x - 3$ and the remainder is $8$ .

Hence, $Q = x^{2} + x - 3$ and $R = 8$ .

Suggest Corrections

Similar questions

If $({5 x}^{2} + 14 x + 2)^{2}$ – $({4 x}^{2} - 5 x + 7)^{2}$ is divided by $(x^{2} + x + 1)$ , then quotient q and remainder r are given by:

p (x)

g (x)

p (x) = x^{3} - 3 x^{2} + 5 x - 3, g (x) = x^{2} - 2

p (x) = x^{4} - 3 x^{2} + 4 x + 5, g (x) = x^{2} + 1 - x

p (x) = x^{4} - 5 x + 6, g (x) = 2 - x^{2}

p (x) = x^{4} - 3 x^{2} + 4 x + 5

g (x) = x^{2} + 1 - x

P (x) = x^{4} - {3 x}^{2} + 4 x + 5, g (x) = x^{2} + 1 - x

Match the following (|x| < 1)

(1) ${(1 + x)}^{- 1}$ (P) 1 + 2x + 3 $x^{2}$ + 4 $x^{3}$ .........

(2) ${(1 - x)}^{- 1}$ (Q) 1 - x + $x^{2}$ - $x^{3}$ .........

(3) ${(1 + x)}^{- 2}$ (R) 1 + x + $x^{2}$ + $x^{3}$ .........

(4) ${(1 - x)}^{- 2}$ (S)1 - 2x + 3 $x^{2}$ - 4 $x^{3}$ .........

Join BYJU'S Learning Program