What will be the quotient and remainder if $(a^{4} - a^{3} + a^{2} - a + 1) \div (a^{3} - 2)$ ?

Open in App

Solution

Given: $(a^{4} - a^{3} + a^{2} - a + 1) \div (a^{3} - 2)$
$\begin{matrix} a - 1 a^{3} - 2 a^{4} - a^{3} + a^{2} - a + 1 a^{4} - 2 a - + - --------------------- - - a^{3} + a^{2} + a + 1 - a^{3} + 2 + - - ----------------- - a^{2} + a - 1 - ---------------- - \end{matrix}$

Quotient = $(a - 1)$
Remainder = $(a^{2} + a - 1)$

Suggest Corrections

Similar questions

Q. If

a_{1}, a_{2}, a_{3}, a_{4}, a_{5} > 0

then

\frac{a_{1}}{a_{2} + a_{3}} + \frac{a_{2}}{a_{3} + a_{4}} + \frac{a_{3}}{a_{4} + a_{5}} + \frac{a_{4}}{a_{5} + a_{1}} + \frac{a_{5}}{a_{1} + a_{2}} \geq \frac{5}{2}

Q. It is a KVPY question Let a1,a2,a3,a4 be real number such that a1+a2+a3+a4=0 and a1^2+a2^2+a3^2+a4^2=1 then the smallest possible value of the expression (a1-a2)^2+(a2-a3)^2+(a3-a4)^2+(a4-a1)^2 lies in which interval. Not sure about the chapter..

Q. If

a_{1}, a_{2}, a_{3}, a_{4}

are in AP, then

\frac{1}{\sqrt{a_{1}} + \sqrt{a_{2}}} + \frac{1}{\sqrt{a_{2}} + \sqrt{a_{3}}} + \frac{1}{\sqrt{a_{3}} + \sqrt{a_{4}}}

is equal to

If $a_{1}, a_{2}, a_{3}, a_{4}$ be the coefficeints of four consecutive terms in the expansion of $(1 + x)^{n}$ then prove that
$\frac{a_{1}}{a_{1} + a_{2}} + \frac{a_{3}}{(a_{3} + a_{4})} = \frac{2 a_{2}}{(a_{2} + a_{3})} .$

Q. Perform the division

(a^{4} - a^{3} + a^{2} - a + 1) \div (a^{3} - 2)

Join BYJU'S Learning Program

What will be the quotient and remainder if (a4−a3+a2−a+1)÷(a3−2)?

What will be the quotient and remainder if $(a^{4} - a^{3} + a^{2} - a + 1) \div (a^{3} - 2)$ ?