Write the following polynomials in standard form.

(i) $m^{3} + 3 + 5 m$ (ii) $- 7 y + y^{5} + 3 y^{3} - \frac{1}{2} + 2 y^{4} - y^{2}$

Open in App

Solution

A polynomial written in either descending or ascending powers of its variable is called the standard form of the polynomial.

(i)
The given polynomial is m³ + 3 + 5m.

The standard form of the polynomial is 3 + 5m + m³ or m³ + 5m + 3.

(ii)
The given polynomial is $- 7 y + y^{5} + 3 y^{3} - \frac{1}{2} + 2 y^{4} - y^{2}$ .

The standard form of the polynomial is $y^{5} + 2 y^{4} + 3 y^{3} - y^{2} - 7 y - \frac{1}{2}$ or $- \frac{1}{2} - 7 y - y^{2} + 3 y^{3} + 2 y^{4} + y^{5}$ .

Suggest Corrections

Similar questions

Q. Write the following polynomials in standard form.
(i)

y^{2} - 2 y^{4} + 3 y - y^{3} + 4

(ii)

5 x - 4 x^{3} + x^{4} + 4

(iii)

x^{5} + x^{2} - \sqrt{3} x + 2 x^{4}

(iv)

2 t - t^{4} + 6 - 3 t^{3}

(v)

6 u + u^{4} + 2 - 3 u^{2}

Write the following polynomials in standard form.

(i) 4x² + 7x⁴

-

x³

-

x + 9

(ii) p + 2 p³ + 10 p² + 5 p⁴

-

Rewrite each of the following polynomials in standard form.
(i) $x - 2 x^{2} + 8 + 5 x^{3}$
(ii) $\frac{2}{3} + 4 y^{2} - 3 y + 2 y^{3}$
(iii) $6 x^{3} + 2 x - x^{5} - 3 x^{2}$
(iv) $2 + t - 3 t^{3} + t^{4} - t^{2}$

Q. Find the degree of the given polynomials.

7 y - y^{3} + y^{5}

Q. Write the following polynomials in the standard form (descending type) :

3 x + 5 + x^{3}

Join BYJU'S Learning Program

Write the following polynomials in standard form. (i) m3 + 3 + 5m (ii) -7y + y5 + 3y3 - 12 + 2y4 - y2

Write the following polynomials in standard form.

(i) $m^{3} + 3 + 5 m$ (ii) $- 7 y + y^{5} + 3 y^{3} - \frac{1}{2} + 2 y^{4} - y^{2}$