Which of the following equivalent forms of the function f(x) = 4x² + 4x − 24 is the most suitable to indicate the x-coordinates of the x‑intercepts of the graph of y = f(x) in the xy‑plane?

The correct answer is: f(x) = 4(x − 2) (x + 3)

Step by step explanation:
Given:
f(x) = 4x² + 4x − 24
Step 1.
Factorise the equation
Take 4 common from all terms.
⇒ 4x² + 4x − 24
⇒ 4(x² + x − 6)
Step 2.
The above equation can be written as,
⇒ 4(x² + x − 6) {General form is ax² + bx + c}
Now multiply a and c,
If sign of ac is +ve, split b as sum of factors of ac,
If sign of ab is -ve, split b as subtraction of factors of ac,
In above expression,
a  c = 1 - 6 = - 6
And sign of ac is -ve
∴ b = - 4 + (- 4) as factors of 6 = 1 × 6
1 = 3 - (2) = 3 × 2
⇒ 4(x² + 3x - 2x − 6)
Step 3.
Take common terms out
⇒ 4[x(x + 3) - 2(x + 3)]
⇒ 4[(x - 2) (x + 3)]
⇒ 4(x - 2) (x + 3)
Hence, 4(x - 2) (x + 3) is the most suitable to indicate the x-coordinates of the x‑intercepts of the graph of y = f(x) in the xy‑plane.
f(x) = 4(x - 2) (x + 3).