Identify constant- linear- quadratic and cubic polynomials from the following polynomials-i- f-x- - 0-ii- g-x- - 2x3 minus- 7x - 4-iii- h-x- - -3x-12-iv- p-x- - 2x2 minus- x - 4-v- q-x- - 4x - 3-vi- r-x- - 3x3 - 4x2 - 5x minus- 7

(i) The given expression is a Constant polynomial as there is no variable term in it. nbsp;(ii)The given expression is Cubic polynomial as the highest exponen ...

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Standard IX

Mathematics

Polynomial Expressions

Identify cons...

Question

Identify constant, linear, quadratic and cubic polynomials from the following polynomials:

(i) f(x) = 0

(ii) g(x) = 2x³ − 7x + 4

(iii) h(x) = - $3 x + \frac{1}{2}$

(iv) p(x) = 2x² − x + 4

(v) q(x) = 4x + 3

(vi) r(x) = 3x³ + 4x² + 5x − 7

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Solution

(i)
The given expression is a Constant polynomial as there is no variable term in it.

(ii)
The given expression is Cubic polynomial as the highest exponent of x is 3.

(iii)
The given expression is linear polynomial as the highest exponent of x is 1.

(iv)
The given expression is Quadratic polynomial as the highest exponent of x is 2.

(v)
The given polynomial is an linear polynomial as the highest exponent of x is 1.

(vi)
The given polynomial is Cubic polynomial as the highest exponent of x is 3.

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Q. Identify constant, linear, quadratic and cubic polynomials from the following polynomials:

(i) f(x) = 0

(ii) g(x) = 2x³ − 7x + 4

(iii) h(x) = -

3 x + \frac{1}{2}

(iv) p(x) = 2x² − x + 4

(v) q(x) = 4x + 3

(vi) r(x) = 3x³ + 4x² + 5x − 7

Identify polynomials in the following :

(i) f(x) = $4 x^{3} - x^{2}$ - 3x + 7

(ii) g(x) = $2 x^{3} - 3 x^{2} + \sqrt{x} - 1$

(iii) p(x) = $\frac{2}{7} x^{2} - \frac{7}{4} x + 9$

(iv) q(x) = $2 x^{2} - 3 x + \frac{4}{x} + 2$

(v) h(x) = $x^{4} - x^{\frac{3}{2}} + x - 1$

(vi) f(x) = 2 + $\frac{3}{x} + 4 x$

Q. Identify polynomials in the following:

(i) f(x) = 4x³ − x² − 3x + 7

(ii) g(x) = 2x³ − 3x²+

\sqrt{x}

− 1

(iii) p(x) =

\frac{2}{3} x^{2} - \frac{7}{4} x + 9

(iv) q(x) = 2x² − 3x +

\frac{4}{x}

+ 2

(v) h(x) =

x^{4} - x^{\frac{3}{2}} + x - 1

(vi) f(x) =

2 + \frac{3}{x} + 4 x

Q. Find the zero of the polynomial:
(i) p(x) = x − 5
(ii) q(x) = x + 4
(iii) r(x) = 2x + 5
(iv) f(x) = 3x + 1
(v) g(x) = 5 − 4x
(vi) h(x) = 6x − 2
(vii) p(x) = ax, a ≠ 0
(viii) q(x) = 4x

P (x) = {5 x}^{5} + {3 x}^{3} - 7

g (x) = {2 x}^{2} + 1

Find q(x) and r(x) by dividing p(x) by g(x)

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Identify constant, linear, quadratic and cubic polynomials from the following polynomials: (i) f(x) = 0 (ii) g(x) = 2x3 − 7x + 4 (iii) h(x) = -3x+12 (iv) p(x) = 2x2 − x + 4 (v) q(x) = 4x + 3 (vi) r(x) = 3x3 + 4x2 + 5x − 7

Identify constant, linear, quadratic and cubic polynomials from the following polynomials:

(i) f(x) = 0

(ii) g(x) = 2x³ − 7x + 4

(iii) h(x) = - $3 x + \frac{1}{2}$

(iv) p(x) = 2x² − x + 4

(v) q(x) = 4x + 3

(vi) r(x) = 3x³ + 4x² + 5x − 7