Rewrite each of the following polynomials in standard form- i x-2x2-8-5x3 ii 2-3-4y2-3y-2y3 iii 6x3-2x-x5-3x2 iv 2-t-3t3-t4-t2

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Standard IX

Mathematics

Polynomials

Rewrite each ...

Question

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) $2 + t - 3 t^{3} + t^{4} - t^{2}$

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Solution

A polynomial written in descending powers of a variable is called the standard form of a polynomial.

$(i) 5 x^{3} - 2 x^{2} + x + 8 (i i) 2 y^{3} + 4 y^{2} - 3 y + \frac{2}{3} (i i i) - x^{5} + 6 x^{3} - 3 x^{2} + 2 x (i v) t^{4} - 3 t^{3} - t^{2} + t + 2$

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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}

Q. Write the polynomial in standard form:

12 x^{3} - x^{5} + 5 x^{7} - 2 x^{2} + 6 x^{3} - 2 + 3 x

Write the following polynomials in standard form.

(i) 4x² + 7x⁴

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x³

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x + 9

(ii) p + 2 p³ + 10 p² + 5 p⁴

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Q. Express the following polynomials in the coefficient form:

(i) 2x²+ 5x + 12
(ii) y⁴

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3y²+ 2y

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7
(iii) x⁵ + 3x²
(iv) y⁴

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3
(v) 9x

Which of the following expressions are polynomials? In case of a polynomial, write its degree.

(i) $x^{5} - 2 x^{3} + x + \sqrt{3}$

(ii) $y^{3} + \sqrt{3} y$

(iii) $t^{2} - \frac{2}{5} t + \sqrt{5}$

(iv) $x^{1000} - 1$

(v) $\frac{1}{\sqrt{2}} x^{2} - \sqrt{2} x + 2$

(vi) $x^{- 2} + 2 x^{- 1} + 3$

(vii) $1$

(viii) $\frac{- 3}{5}$

(ix) $\frac{x^{2}}{2} - \frac{2}{x^{2}}$

(x) $\sqrt[2]{2} x^{2} - 8$

(xi) $\frac{1}{2 x^{2}}$

(xii) $\frac{1}{\sqrt{5}} x^{\frac{1}{2}} + 1$

(xiii) $\frac{3}{5} x^{2} - \frac{7}{3} x + 9$

(xiv) $x^{4} - x^{\frac{3}{2}} + x - 3$

(xv) $2 x^{3} + 3 x^{2} + \sqrt{x} - 1$

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Rewrite each of the following polynomials in standard form. (i) x−2x2+8+5x3 (ii) 23+4y2−3y+2y3 (iii) 6x3+2x−x5−3x2 (iv) 2+t−3t3+t4−t2

A polynomial written in descending powers of a variable is called the standard form of a polynomial. (i) 5x3−2x2+x+8(ii) 2y3+4y2−3y+23(iii) −x5+6x3−3x2+2x(iv) t4−3t3−t2+t+2

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) $2 + t - 3 t^{3} + t^{4} - t^{2}$

A polynomial written in descending powers of a variable is called the standard form of a polynomial.

$(i) 5 x^{3} - 2 x^{2} + x + 8 (i i) 2 y^{3} + 4 y^{2} - 3 y + \frac{2}{3} (i i i) - x^{5} + 6 x^{3} - 3 x^{2} + 2 x (i v) t^{4} - 3 t^{3} - t^{2} + t + 2$