Step-by-step explanation:
To factor ax² + bx + c, use the AC method.
- Multiply a and c
- Find factors of ac that add up to b
- Divide those two factors by a. Reduce the fractions.
- The numerators are the constants, and the denominators are the coefficients.
(b) 3x² + 11x − 4 = 0
- a = 3, b = 11, c = -4
- ac = (3)(-4) = -12
- Factors of -12 that add up to 11 are 12 and -1.
- Divide by 3: -1/3 and 12/3 = 4/1
- The factors are 3x − 1 and x + 4.
(3x − 1) (x + 4) = 0
3x − 1 = 0, or x + 4 = 0
x = 1/3, or x = -4
(c) 12x² + 8x = 0
Here, you can simply factor the greatest common factor, 4x.
4x (3x + 2) = 0
4x = 0, or 3x + 2 = 0
x = 0, or x = -2/3
