The quotient on dividing a polynomial $4 d^{2} + 8 d + 16 d^{4}$ by a monomial $4 d^{2}$ is

A polynomial

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

Not a polynomial

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

4 d^{2} + 1 + 2 d^{- 1}

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

Both (b) and (c).

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

Open in App

Solution

The correct option is D Both (b) and (c).
$\frac{4 d^{2} + 8 d + 16 d^{4}}{4 d^{2}}$
$= \frac{4 d (d + 2 + 4 d^{3})}{4 d^{2}}$
$= \frac{(d + 2 + 4 d^{3})}{d}$
$= \frac{4 d^{3} + d + 2}{d}$
$= 4 d^{2} + 1 + 2 d^{- 1}$

Which is not a polynomial
[For an expression to be a polynomial, the exponent of variable of each term must be a whole number.]

Suggest Corrections

Similar questions

\frac{a}{b} = \frac{c}{d}

\frac{3 a^{2} + 4 b^{2}}{3 c^{2} + 4 d^{2}} = \frac{3 a^{2} - 4 b^{2}}{3 c^{2} - 4 d^{2}}

While dividing a polynomial by a monomial, we divide each term of the polynomial in the numerator by the monomial in the denominator.

4 a^{2} - 4 a b + b^{2} - 9 c^{2} + 12 c d - 4 d^{2}

a^{2} - b^{2} - 4 c^{2} + 4 d^{2} - 4 (a d - b c)

y^{3} - 64; y - 4

Join BYJU'S Learning Program