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
Answers
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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