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Factorisation of Quadratic Polynomials

Factorise the...

Question

Factorise the polynomial $P (x) = \frac{2 x^{3} + 7 x^{2} - 6 x - 8}{x + 4}$

A

2 x^{2} - x - 2

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B

3 x^{2} - x + 3

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C

x^{2} + 5 x + 1

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D

x^{3} - 4 x - 2

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Solution

The correct option is A $2 x^{2} - x - 2$
By long division method we get
$p (x) = 2 x^{2} - x - 2$
So option $(A)$ is correct.

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

Q. Match the following.

	Column - I		Column - II
(P)	$(x^{2} + 5) (x^{3} + 3) + 5$	(1)	${- x}^{3} - 3 x^{2} + 3 x + 2$
(Q)	$(\frac{- 10}{3} x y^{3}) \times (\frac{6}{5} x^{3} y)$	(2)	$- x^{3} + x^{2} + 3 x - 6$
(R)	$(x^{3} - x^{2} - x - 2) - (2 x^{3} + 2 x^{2} - 4 x - 4)$	(3)	$x^{5} + 5 x^{3} + 3 x^{2} + 20$
(S)	$(x^{3} - x^{2} - x - 2) + (2 x^{2} - 2 x^{3} + 4 x - 4)$	(4)	$- 4 x^{4} y^{4}$

Q. A polynomial

p (x)

g (x)

, the obtained quotient

q (x)

and the remainder

r (x)

are given in the table. Find

p (x)

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	?	$x - 1$	$x^{3} - x^{2} - x - 1$	$2 x - 4$
v	?	$x^{2} + 2 x + 1$	$x^{4} - 2 x^{2} + 5 x - 7$	$4 x + 12$

Q. Divide the polynomial

p (x)

by the polynomial

g (x)

and find the quotient and remainder in each of the following:
(i)

p (x) = x^{3} - 3 x^{2} + 5 x - 3, g (x) = x^{2} - 2

p (x) = x^{4} - 3 x^{2} + 4 x + 5, g (x) = x^{2} + 1 - x

p (x) = x^{4} - 5 x + 6, g (x) = 2 - x^{2}

Q. Find the limits :

i .

lim x \to 1 [\frac{x^{2} + 1}{x + 100}]

i i .

lim x \to 2 [\frac{x^{3} - 4 x^{2} + 4 x}{x^{2} - 4}]

i i i .

lim x \to 2 [\frac{x^{2} - 4}{x^{3} - 4 x^{2} + 4 x}]

i v .

lim x \to 2 [\frac{x^{3} - 2 x^{2}}{x^{2} - 5 x + 6}]

v .

lim x \to 1 [\frac{x - 2}{x^{2} - x} - \frac{1}{x^{3} - 3 x^{2} + 2 x}]

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