Question

How do i factorise x^2+6x-40 ?

Answer 1

9514 1404 393

Answer:

  (x +10)(x -4)

Step-by-step explanation:

Compare the factored and expanded forms:

  (x +p)(x +q) = x^2 +(p+q)x +pq = x^2 +6x -40

That is, the constants in the binomial factors will be factors of -40 that have a sum of 6. This is where your knowledge of multiplication tables is helpful.

  -40 = -1×40 = -2×20 = -4×10 = -5×8

The sums of these factor pairs are 39, 18, 6, 3, respectively. So, the one we want is (-4)(10) = -40. Now that we know the values of 'p' and 'q', we can write the factorization ...

  x^2 +6x -40 = (x -4)(x +10)