Answer:
1.(x - 4) (x - 3)
2.(x + 4) (x + 15)
3.(x - 3) (x + 8)
Explanation:
1. x^2 - 7x + 12:
To solve find two factors that multiplies to 12 and adds up to -7
so two factors of 12 which add up to -7 are: -3 and -4
cause -3 x -4 is 12 and -3 + -4 is -7 we can factor using those two numbers.
then we split our -7x into two terms joining our two factors -3 and -4 with a variable which gives -3x - 4x. once we have done that we can then factorize by grouping.
x^2 - 3x - 4x + 12
(x^2 - 3x) - (4x + 12)
we then find the h.c.f of each group of terms and we can factor.
x(x - 3) - 4(x - 3) = (x - 4) (x - 3)
now we can follow the same procedure to solve the other problems or factorize.
2.x^2 + 19x + 60
let's try to find pairs of factors which multiply to 60.
60 = (5, 12), (6, 10), (15, 4)
once we find a pair of factors which adds to 19 which the pair is (15, 4)
we split the 19x again so we can get a four term expression:
x^2 + 15x + 4x + 60
let's group
(x^2 + 15x) + (4x + 60)
hcf and factorize
x(x + 15) + 4(x + 15)
now factorize completely
(x + 4)(x + 15)
3.x^2 + 5x - 24
pairs of factors of -24: (6, -4), (8, -3), (12, -2)
pair which adds to 5: (8, -3)
x^2 + 8x - 3x - 24
(x^2 + 8x) - (3x - 24)
HCF and Factorize completely.
x(x + 8) -3(x + 8) = (x - 3)(x + 8)