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Factorize each of the following algebrai...

Factorize each of the following algebraic expressions:
(1) `x^2+14 x+45`
(2) `x^2-22 x+120`
(3) `x^2-11 x-42`
(4) `a^2+2a-3`

Text Solution

Verified by Experts

By using mid-term splitting:
(1) `x^2+14x+45`
`=x^2+5x+9x+45`
`=x(x+5)+9(x+5)`
`=(x+9)(x+5)`

(2) `x^2-22 x+120`
`=x^2-12x-10x+120`
`=x(x-12)-10(x-12)`
`=(x-10)(x-12)`

(3) `x^2-11 x-42`
`=x^2+3x-14x- 42`
`=x(x+3)-14(x+3)`
`=(x-14)(x+3)`

(4) `a^2+2a-3`
`=a^2+3a-a-3`
`=a(a+3)-1(a+3)`
`=(a-1)(a+3)`
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