Question

Разложите квадратный трёхчлен на линейные множители:

1. х^2 – 15х + 44

2. х^2 + 6х – 55

3. х^2 + 12х + 32

4. 6х^2 – 31х + 5

5. 9х^2 – 18х – 40

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Answer 1

1.

$x^2-15x+:44=\=left(x^2-4xright)+left(-11x+44right) =\ =xleft(x-4right)-11left(x-4right)\ =(x-4)(x-11)$

2.

$x^2+6x-55=\=left(x^2-5xright)+left(11x-55right)=\=xleft(x-5right)+11left(x-5right)=\=left(x-5right)left(x+11right)$

3.

$x^2+12x+32=\=left(x^2+4xright)+left(8x+32right)\=xleft(x+4right)+8left(x+4right)\=left(x+4right)left(x+8right)$

4.

$6x^2-31+5=\=left(6x^2-xright)+left(-30x+5right)=\=xleft(6x-1right)-5left(6x-1right)=\=left(6x-1right)left(x-5right)$

5.

$9x^2-18x-40 = \=left(9x^2+12xright)+left(-30x-40right)=\=3xleft(3x+4right)-10left(3x+4right)=\=left(3x+4right)left(3x-10right)$