Question

factorise p^2 - 8p - 65​

Answer 1

Explanation:

Changes made to your input should not affect the solution:

(1): "p2" was replaced by "p^2".

STEP

1

:

Trying to factor by splitting the middle term

1.1 Factoring p2-8p-65

The first term is, p2 its coefficient is 1 .

The middle term is, -8p its coefficient is -8 .

The last term, "the constant", is -65

Step-1 : Multiply the coefficient of the first term by the constant 1 • -65 = -65

Step-2 : Find two factors of -65 whose sum equals the coefficient of the middle term, which is -8 .

-65 + 1 = -64

-13 + 5 = -8 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -13 and 5

p2 - 13p + 5p - 65

Step-4 : Add up the first 2 terms, pulling out like factors :

p • (p-13)

Add up the last 2 terms, pulling out common factors :

5 • (p-13)

Step-5 : Add up the four terms of step 4 :

(p+5) • (p-13)

Which is the desired factorization

Final result :

(p + 5) • (p - 13)

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