Equations

Factoring into Brackets

Two numbers with product c and sum b

  • High school
  • about 4 min
  • 2 of 3 in the family
Not started
x2−x−12=0x^2 - x - 12 = 0

We look for two numbers m, n: m⋅n=−12m \cdot n = -12, m+n=−1m + n = -1

Pairs of numbers with product c and their sums
mnm · nm + n
-121-12-11
-112-1211
-62-12-4
-26-124
-43-12-1 ✓ = b
-34-121
-34
b = -1
c = -12
(x−4)(x+3)=0(x - 4)(x + 3) = 0
x1=−3,x2=4x_1 = -3,\quad x_2 = 4

A product is zero when one bracket is zero - so the solutions have the opposite sign to the numbers in the brackets.

Where it is taught