Q- factorise
p²-23 p+132
Answers
Step-by-step explanation:
The first term is, p2 its coefficient is 1 .
The middle term is, +23p its coefficient is 23 .
The last term, "the constant", is +132
Step-1 : Multiply the coefficient of the first term by the constant 1 • 132 = 132
Step-2 : Find two factors of 132 whose sum equals the coefficient of the middle term, which is 23 .
-132 + -1 = -133
-66 + -2 = -68
-44 + -3 = -47
-33 + -4 = -37
-22 + -6 = -28
-12 + -11 = -23
-11 + -12 = -23
-6 + -22 = -28
-4 + -33 = -37
-3 + -44 = -47
-2 + -66 = -68
-1 + -132 = -133
1 + 132 = 133
2 + 66 = 68
3 + 44 = 47
4 + 33 = 37
6 + 22 = 28
11 + 12 = 23 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 11 and 12
p2 + 11p + 12p + 132
Step-4 : Add up the first 2 terms, pulling out like factors :
p • (p+11)
Add up the last 2 terms, pulling out common factors :
12 • (p+11)
Step-5 : Add up the four terms of step 4 :
(p+12) • (p+11)
Which is the desired factorization
Answer:
There is no need to factorise this expression as the 3 terms don't have any common factors.