Question

Factor w2 + 8w + 16, if possible. If the polynomial is prime, say soFactor 3y2 + 10y + 7, using the AC method. If the polynomial is prime, say so.

Answer 1

`w^(2) + 8w + 16`

when we compare the given equation to
`ax^(2) + bx + c`

a=1, b=8,c=16

So, ac=1*16=16 and b=8

We need factor pair of ac, 16, which sum upto b, 8.

As, 4*4=16 and 4+4=8

4 and 4 are required factor pair.

`w^(2) + 4w+4w + 16`

`w(w+4) + 4(w+4)`

`(w+4)(w+4)`

`(w+4)^(2)`

So,
`w^(2) + 8w + 16`=
`(w+4)^(2)`

`3y^(2) + 10y + 7`

when we compare the given equation to
`ax^(2) + bx + c`

a=3, b=10,c=7

So, ac=3*7=21 and b=10

We need factor pair of ac, 21, which sum upto b, 10.

As, 3*7=21 and 3+7=10

3 and 7 are required factor pair.

`3y^(2) + 3y+7y + 7`

`3y(y+1)+7(y+1)`

`(3y+7)(y+1)`

`3y^(2) + 10y + 7`=
`(3y+7)(y+1)`