How do I factor 4p^8-60p^4-225p^2

this is how you would do it on paper

Step-by-step explanation:

For a polynomial of the form

a

x

2

+

b

x

+

c

, rewrite the middle term as a sum of two terms whose product is

a

⋅

c

=

4

⋅

−

1

=

−

4

and whose sum is

b

=

3

.

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Reorder terms.

4

p

2

−

q

2

+

3

p

q

Reorder

−

q

2

and

3

p

q

.

4

p

2

+

3

p

q

−

q

2

Factor

3

out of

3

p

q

.

4

p

2

+

3

(

p

q

)

−

q

2

Rewrite

3

as

−

1

plus

4

4

p

2

+

(

−

1

+

4

)

(

p

q

)

−

q

2

Apply the distributive property.

4

p

2

−

1

(

p

q

)

+

4

(

p

q

)

−

q

2

Remove unnecessary parentheses.

4

p

2

−

1

p

q

+

4

(

p

q

)

−

q

2

Remove unnecessary parentheses.

4

p

2

−

1

p

q

+

4

p

q

−

q

2

Factor out the greatest common factor from each group.

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p

(

4

p

−

1

q

)

+

q

(

4

p

−

q

)

Factor the polynomial by factoring out the greatest common factor,

4

p

−

1

q

.

(

4

p

−

1

q

)

(

p

+

q

)

Rewrite

−

1

q

as

−

q

.

(

4

p

−

q

)

(

p

+

q

)

ratio is 2 : 9

the answer is three

13.5 : 3