SOLUTION: Hi, I am having trouble with the following question, ant help would be gratefully received. Kind regards, Hugh Factorise the following expressions. Question A (

Algebra ->  Equations -> SOLUTION: Hi, I am having trouble with the following question, ant help would be gratefully received. Kind regards, Hugh Factorise the following expressions. Question A (      Log On


   

Question 836899: Hi,
I am having trouble with the following question, ant help would be gratefully received.
Kind regards,
Hugh
Factorise the following expressions.
Question A
(i) x2 − x − 42
(ii) 9m2 − 81n2
Question B
In parts (i), (ii) below you should include each step in your
reasoning and check that your solution is correct.
(i) Factorise then solve the equation x2 + 2x−24 = 0.
(ii) Explain how you could use your answer to part (B)(i) to solve the
equation 7x2 + 14x−168 = 0.


Found 2 solutions by josgarithmetic, LinnW:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
The same question for (i) and (ii) in "question A" was answered one or two days ago.

(i) Use the integers, 6 and 7.
+6-7=-1

(ii) This is the difference of squares so the factorization is based on the formula, %28x-a%29%28x%2Ba%29=x%5E2-a%5E2


Question B
Each term in (ii) contains a factor of 7.
This is 7%28x%5E2%2B2x-24%29.
Look then at the factorizations for -24=-1*6*4 and you should be able to factor the quadratic expression.
%28x-4%29%28x%2B6%29=x%5E2%2B2x-24

Answer by LinnW(1048) About Me  (Show Source):
You can put this solution on YOUR website!
Factorise the following expressions.
Question A
(i) x2 − x − 42
(ii) 9m2 − 81n2
Question B
In parts (i), (ii) below you should include each step in your
reasoning and check that your solution is correct.
(i) Factorise then solve the equation x2 + 2x−24 = 0.
(ii) Explain how you could use your answer to part (B)(i) to solve the
equation 7x2 + 14x−168 = 0.
A(i) x%5E2+-+x+-+42
We want a pair of numbers such that their product is 42 and
their sum is -1
-7 and + 6 work for this and x%5E2+-+x+-+42 factored is
(x - 7)(x + 6)
A(ii) 9m%5E2-81n%5E2
Binomials of the form x%5E2-y%5E2 factor as %28x%2By%29%28x-y%29
so think of 9m%5E2-81n%5E2 as %283m%29%5E2-%289n%29%5E2
which means the factors are
(3m+9n)(3m-9n)
B(i) x2 + 2x−24 = 0.
Here we want a pair of numbers whose product is -24 and their sum is +2
+6 and -4 work for this
(x + 6)(x - 4) = 0
B(ii)
(ii) Explain how you could use your answer to part (B)(i) to solve the
equation 7x2 + 14x−168 = 0.
7 is a factor of each term, so 7x2 + 14x−168 = 0 factored is
7%28x%5E2+%2B+2x+-+24%29+=+0+