# Factor (p^2-4)/(2p-7)*(2p^2+11p-63)/(p^(2+11p+18))

p2-42p-7⋅2p2+11p-63p2+11p+18
Rewrite 4 as 22.
p2-222p-7⋅2p2+11p-63p2+11p+18
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=p and b=2.
(p+2)(p-2)2p-7⋅2p2+11p-63p2+11p+18
Factor by grouping.
For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=2⋅-63=-126 and whose sum is b=11.
Factor 11 out of 11p.
(p+2)(p-2)2p-7⋅2p2+11(p)-63p2+11p+18
Rewrite 11 as -7 plus 18
(p+2)(p-2)2p-7⋅2p2+(-7+18)p-63p2+11p+18
Apply the distributive property.
(p+2)(p-2)2p-7⋅2p2-7p+18p-63p2+11p+18
(p+2)(p-2)2p-7⋅2p2-7p+18p-63p2+11p+18
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(p+2)(p-2)2p-7⋅(2p2-7p)+18p-63p2+11p+18
Factor out the greatest common factor (GCF) from each group.
(p+2)(p-2)2p-7⋅p(2p-7)+9(2p-7)p2+11p+18
(p+2)(p-2)2p-7⋅p(2p-7)+9(2p-7)p2+11p+18
Factor the polynomial by factoring out the greatest common factor, 2p-7.
(p+2)(p-2)2p-7⋅(2p-7)(p+9)p2+11p+18
(p+2)(p-2)2p-7⋅(2p-7)(p+9)p2+11p+18
Factor (p^2-4)/(2p-7)*(2p^2+11p-63)/(p^(2+11p+18))

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