Question

Factorise p2

+ 12p + 35 by using the middle term:​

Answer 1

Answer:

Given,

Factoring p2-12p+35

The first term is, p2 its coefficient is 1 .

The middle term is, -12p its coefficient is -12 .

The last term, "the constant", is +35

Step-1 : Multiply the coefficient of the first term by the constant 1 • 35 = 35

Step-2 : Find two factors of 35 whose sum equals the coefficient of the middle term, which is -12 .

-35 + -1 = -36

-7 + -5 = -12 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -7 and -5

p2 - 7p - 5p - 35

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

p • (p-7)

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

5 • (p-7)

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

(p-5) • (p-7)

Which is the desired factorization

Answer 2

Answer:

(p + 7)(p + 5)

Step-by-step explanation:

p² + 12p + 35 = p² + 7p + 5p + 35 =

(p² + 7p) + (5p + 35) = p(p + 7) + 5(p + 7) = (p + 7)(p + 5)