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.

$3y^{2} + 3y+7y + 7$

$3y(y+1)+7(y+1)$

$(3y+7)(y+1)$

$3y^{2} + 10y + 7$=$(3y+7)(y+1)$