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Classification of Polynomials According to Their Degree

Identify cons...

Question

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

(i) f(x) = 0

(ii) g(x) = $2 x^{3}$ - 7x + 4

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

(iv) p(x) = $2 x^{2}$ - x + 4

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

(vi) r(x) = $3 x^{3} + 4 x^{2}$ + 5x - 7

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Solution

(i) f(x) = 0 : It is a constant polynomial as it has no variable.

(ii) g(x) = $2 x^{3}$ - 7x + 4 : It is a cubic polynomial.

(iii) h(x) = - $3 x + \frac{1}{2}$ : It is a linear polynomial.

(iv) p(x) = $2 x^{2}$ - x + 4 : It is a quadratic polynomial.

(v) q(x) = 4x + 3 : It is linear polynomial.

(vi) r(x) = $3 x^{3}$ + $4 x^{2}$ + 5x - 7 : It is a cubic polynomial.

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Similar questions

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

\sqrt{x}

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

\frac{4}{x}

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

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

Now for each pair of polynomials p(x) and q(x) given below, find p(x) + q(x) and p(x) − q(x). Also compute p(1) + q(1) and p(1) − q(1) for each.

(i)

(ii)

(iii)

(iv)

(v)

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

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

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