Question

factorise
a) 90-q-q∧2
b) 25-4a∧2-4ab-b∧2
C) (2a-b)∧2-121
d) 9x∧2-6x+1-81
e) 343p∧6-64
pla answer

Answer 1

Answer:

1.1 Factoring p2-13p-48

The first term is, p2 its coefficient is 1 .

The middle term is, -13p its coefficient is -13 .

The last term, "the constant", is -48

Step-1 : Multiply the coefficient of the first term by the constant 1 • -48 = -48

Step-2 : Find two factors of -48 whose sum equals the coefficient of the middle term, which is -13 .

-48 + 1 = -47

-24 + 2 = -22

-16 + 3 = -13 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -16 and 3

p2 - 16p + 3p - 48

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

p • (p-16)

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

3 • (p-16)

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

(p+3) • (p-16)

Which is the desired factorization

Final result :

(p + 3) • (p - 16)

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