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Resolve each of the following quadratic ...

Resolve each of the following quadratic trinomials into factors:
(1) `7x^2-19 x-6`
(2) `28-31 x-5x^2`
(3) `3+23 y-8y^2`
(4) `11 x^2-54 x+63`

Text Solution

Verified by Experts

By using mid-term splitting:
(1) `7x^2-19 x-6`
`=7x^2+2x–21x–6`
`=x(7x+2)–3(7x+2)`
`=(7x+2)(x-3)`

(2) `28-31x-5x^2`
`=-5x^2-31x+28`
`=5x^2+31x–28`
`=5x^2–4x+35x-28`
`=x(5x–4)+7(5x–4)`
`=(x+7)(5x–4)`

(3) `3+23y-8y^2`
`=-8y^2+23y+3`
`=8y^2-23y-3`
`=8y^2-24y+y-3`
`=8y(y-3)+1(y-3)`
`=(8y+1)(y-3)`

(4) `11 x^2-54 x+63`
`=11x^2-33x-21x-63`
`=11x(x-3)-21(x – 3)`
`=(11x-21)(x-3)`
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