Q. 4 B4.4( 7 Votes )

# Factorize the expressions and divide them as directed:

(x^{2} – 8x + 12) ÷ (x – 6)

Answer :

In the given term

Dividend = (x^{2} - 8x + 12)

The given expression looks as

x^{2} + (a + b)x + ab

where a + b = -8; and ab = 12;

factors of 12 their sum

-1 × -12 -1-12 = -13

-6 × -2 -2-6 = -8

-4 × -3 -4-3 = -7

∴ the factors having sum 7 are 4 and 3

x^{2} - 8x + 12 = x^{2} + (-6-2)x + 12

= x^{2} - 6x - 2x + 12

= x(x - 6) -2(x - 6)

= (x - 6)(x - 2)

Divisor = (x - 6)

=

= (x – 2)

Hence dividing (x^{2} – 8x + 12) by (x – 6) gives out (x – 2)

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