Advertisements
Advertisements
Question
Divide the first polynomial by the second in each of the following. Also, write the quotient and remainder:
x4 − x3 + 5x, x − 1
Advertisements
Solution
\[\frac{x^4 {-x}^3 +5x}{x-1}\]
\[ = \frac{x^3 (x-1)+5(x-1)+5}{x-1}\]
\[ = \frac{{(x-1)(x}^3 +5)+5}{x-1}\]
\[ {=(x}^3 +5)+ \frac{5}{x - 1}\]
\[\text{Therefore, quotient} = x^3 +5\ \text{and remainder = 5 .}\]
RELATED QUESTIONS
Divide the given polynomial by the given monomial.
8(x3y2z2 + x2y3z2 + x2y2z3) ÷ 4x2y2z2
Write each of the following polynomials in the standard form. Also, write their degree.
(y3 − 2)(y3 + 11)
Simplify:\[\frac{32 m^2 n^3 p^2}{4mnp}\]
Divide x2 + 7x + 12 by x + 4.
Divide x4 + x2 + 1 by x2 + x + 1.
Divide 30x4 + 11x3 − 82x2 − 12x + 48 by 3x2 + 2x − 4 and find the quotient and remainder.
Divide the first polynomial by the second in each of the following. Also, write the quotient and remainder:
y4 + y2, y2 − 2
Divide 24(x2yz + xy2z + xyz2) by 8xyz using both the methods.
Simplify `(14"p"^5"q"^3)/(2"p"^2"q") - (12"p"^3"q"^4)/(3"q"^2)`
Statement A: If 24p2q is divided by 3pq, then the quotient is 8p.
Statement B: Simplification of `((5x + 5))/5` is 5x
