Question

factor the given polynomial.
$(y^2 +5y)( {y}^{2} + 5y - 2) - 24$
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Answer 1

Answer:

(y2+5y)(y2+5y−2)−24=0

Let, y2+5y=a

a(a−2)−24=0

a2−2a−24=0

a2−6a+4a−24=0

a(a−6)+4(a−6)=0

(a−6)(a+4)=0

a−6=0 or a+4=0

By resubstituting,

y2+5y=a

y2+5y−6=0 or y2+5y+4=0

y2+6y−y−6=0 or y2+4y+y+4=0

y(y+6)−1(y+6)=0 or y(y+4)+1(y+4)=0

(y+6)(y−1)=0 or (y+4)(y+1)=0

y−1=

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Answer 2

Step-by-step explanation:

(y

2

+5y)(y

2

+5y−2)−24=0

Let, y

2

+5y=a

a(a−2)−24=0

a

2

−2a−24=0

a

2

−6a+4a−24=0

a(a−6)+4(a−6)=0

(a−6)(a+4)=0

a−6=0 or a+4=0

By resubstituting,

y

2

+5y=a

y

2

+5y−6=0 or y

2

+5y+4=0

y

2

+6y−y−6=0 or y

2

+4y+y+4=0

y(y+6)−1(y+6)=0 or y(y+4)+1(y+4)=0

(y+6)(y−1)=0 or (y+4)(y+1)=0

y−1=0 or y+6=0 or y+4=0 or y+1=0

∴y=1 or y=−6 or y=−4 or y=−1

y=−6,−4,−1,1.

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