Advertisements
Advertisements
Question
Write each of the following polynomials in the standard form. Also, write their degree.
(x3 − 1)(x3 − 4)
Solution
\[( x^3 - 1)( x^3 - 4) = x^6 - 5 x^3 + 4\]
\[\text{Standard form of the given polynomial can be expressed as:} \]
\[( x^6 - 5 x^3 + 4) or (4 - 5 x^3 + x^6 )\]
\[\text{The degree of the polynomial is 6 .} \]
APPEARS IN
RELATED QUESTIONS
Write the degree of each of the following polynomials.
Write each of the following polynomials in the standard form. Also, write their degree.
(y3 − 2)(y3 + 11)
Divide 3y4 − 3y3 − 4y2 − 4y by y2 − 2y.
Verify the division algorithm i.e. Dividend = Divisor × Quotient + Remainder, in each of the following. Also, write the quotient and remainder.
Dividend | Divisor |
34x − 22x3 − 12x4 − 10x2 − 75 | 3x + 7 |
Verify the division algorithm i.e. Dividend = Divisor × Quotient + Remainder, in each of the following. Also, write the quotient and remainder.
Dividend | Divisor |
15y4 − 16y3 + 9y2 −\[\frac{10}{3}\] y+6 | 3y − 2 |
Divide 15y4 + 16y3 +\[\frac{10}{3}\]y − 9y2 − 6 by 3y − 2. Write down the coefficients of the terms in the quotient.
Find whether the first polynomial is a factor of the second.
x + 1, 2x2 + 5x + 4
Divide: 15a3b4 − 10a4b3 − 25a3b6 by −5a3b2
Divide: −14x6y3 − 21x4y5 + 7x5y4 by 7x2y2
Divide 27y3 by 3y