I dont know how to get this. Please explain the concept!?

Question

k^2 -k -20 = (k)^2 + (4 +-5)k + (4)(5)= (k+4) (k+5)

Answer 1

Just factorising....

k^2 - k - 20

We need factors of 20 that add or subtract to give -1 (for the middle term -k)
Factors of 20 are-:
20 and 1
10 and 2
5 and 4

We can see that only the last option can add/subtract to become -1 for the -k term in the middle......therefore.....

(k - 5) (k + 4)

Working it back through we get.....
k^2 -5k + 4k - 20

k^2 -k - 20
(The original equation hence we prove our factorising)

Answer 2

when you multiply 2 binomials, say (x + 3) and (x - 5), you multiply each part of 1st one by each part of second:

x•x + x(-5) + 3(x) + 3(-5) = x² - 2x - 15

look at the parts and look at the results. the 2 middle terms that add up to -2x are based on factors of 15.

so when you go to factor k² - k - 20, you look at the 20 and start thinking about factors of 20, and the minus in front of 20 tells you the factors have different signs, and finally the -1 in front of the middle k tells you the factors of 20 have to add up to -1, so they can't be 20 and 1 or 10 and 2, they must be 5 and 4, and the 5 gets the minus sign. result: (k+4)(k-5)

Answer 3

What is this- a factorisation or an equation to be solved?if it is to be factored.you have erred in the third step
It should be (k+4)(k-5) and not (k+4)(k+5)
For your convenience,I am factoring it afresh
k^2-k-20
=k^2+(4-5)k+(4)(-5)
=k^2+4k-5k+(4)(-5)
=k(k+4)-5(k+4)
=(k+4)(k-5)

Answer 4

It needs to be: (k+4)(k-5)

What you are showing is breaking down how to factor the polynomial. The factors of 20 are 4 and 5, and when they are subtracted, they will give you the -1 you need for the middle term.

Answer 5

I think that you didn't type it right! The meaning is how to present the same relation with three different ways. Maybe it is helpful if you have fractions and you want to simplify them, so you can delete the same term from the numerator and the denominator! Maybe the right type is k^2 -k -20=k^2 + (4-5)k -20=(k+4)(k-5)..........!

Answer 6

it should be (k+4)(k-5)

basically its a sort of inspection for factorisation, where you find that 2 factors of -20 is 4 and -5, and these 2 numbers coincidentally sum up to the coefficient of k in the quadratic eqn.

as such, you can find the factorised form of the quadratic eqn easily with this info to be (k+4)(k-5).

hope this helps=)