Answer:
The factors are (2x + 7)(x - 3) and the solutions are -3.5 and 3
Step-by-step explanation:
* Lets explain how to factor a trinomial in the form ax² ± bx ± c:
- Look at the c term first.
# If the c term is a positive number, then its factors r , s will both
be positive or both be negative.
# a has two factors h and k
# The sum of c and a is b.
# The brackets are (hx ± r)(kx ± s) where a = hk , c = rs and b = rk + hs
# If the c term is a negative number, then either r or s will be negative,
but not both.
# a has two factors h and k
# The difference of c and a is b.
# The brackets are (hx + r)(kx - s) where a = hk , c = rs and b = rk - hs
* Lets solve the problem
∵ The equation is 2x² + x - 21 = 0
∵ The general form of the equation is ax² + bx + c = 0
∴ a = 2 , b = 1 , c = -21
∵ c is negative
∴ its factors r and s have different sign
∵ a = 2
∵ The factors of a are h , k
∵ 2 = 2 × 1
∴ h = 2 and k = 1
∵ -21 = 7 × -3
∴ r = 7 and s = -3
∵ The brackets are (hx + r)(kx - s)
∴ 2x² + x - 21 = (2x + 7)(x - 3)
∵ 2x² + x - 21 = 0
∴ (2x + 7)(x - 3) = 0
- Equate each bracket by 0
∴ 2x + 7 = 0 ⇒ subtract 7 from both sides
∴ 2x = -7 ⇒ divide both sides by 2
∴ x = -7/2 = -3.5
- OR
∴ x - 3 = 0 ⇒ add 3 to both sides
∴ x = 3
∴ The solutions are -3.5 and 3
* The factors are (2x + 7)(x - 3) and the solutions are -3.5 and 3
