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Conditions of a Polynomial

Which of the ...

Question

Which of the following polynomials are trinomials?

(1) p(x) = $x + x^{2} + π$

(2)q(x)= $\sqrt{2} + x - x^{2}$

(3) r(x) = $x^{3} + x^{2} + 1$

(4)t(y) = $y^{4} + y + 5$

A

1

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B

1, 2 and 3

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C

1 and 2

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D

All of these

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Solution

The correct option is D
All of these

Polynomials having 3 terms are trinomials.

(1) p(x) = $x + x^{2} + π$ – 3 terms

(2)q(x)= $\sqrt{2} + x - x^{2}$ – 3 terms

(3) r(x) = $x^{3} + x^{2} + 1$ – 3 terms

(4)t(y) = $y^{4} + y + 5$ – 3 terms

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Q. Which of the following polynomials are binomials?
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Q. A polynomial

p (x)

g (x)

, the obtained quotient

q (x)

and the remainder

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Sl.	$p (x)$	$g (x)$	$q (x)$	$r (x)$
i	?	$x - 2$	$x^{2} - x + 1$	$4$
ii	?	$x + 3$	$2 x^{2} + x + 5$	$3 x + 1$
iii	?	$2 x + 1$	$x^{3} + 3 x^{2} - x + 1$	$0$
iv	?	$x - 1$	$x^{3} - x^{2} - x - 1$	$2 x - 4$
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Q. Which of the following polynomials are binomials?
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If dividend = $x^{4} + x^{3} - 2 x^{2} + x + 1$ and divisor = $(x - 1)$ , find the quotient, $q (x)$ and remainder $r (x)$ .

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