Q. 4 C3.9( 14 Votes )

Factorize the expressions and divide them as directed:

(p2 + 5p + 4) ÷ (p + 1)

Answer :

In the given term


Dividend = (p2 + 5p + 4)


The given expression looks as


x2 + (a + b)x + ab


where a + b = 5; and ab = 4;


factors of 4 their sum


1 × 4 1 + 4 = 5


2 × 2 2 + 2 = 4


the factors having sum 5 are 4 and 1


(p2 + 5p + 4) = p2 + (4 + 1)p + 4


= p2 + 4p + p + 4


= p(p + 4) + 1(p + 4)


= (p + 1)(p + 4)


Divisor = (p + 1)


=


= (p + 4)


Hence dividing (p2 + 5p + 4) by (p + 1) gives out (p + 4)


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