Question

1. determine the factors of the following quadratic equation: $3x^2 + x - 10 = 0$. teks a2.4(f)

a) $(5x - 2)(x - 2)$
b) $(2x + 1)(x - 2)$
c) $(3x - 5)(x - 2)$
d) $(3x - 5)(x + 2)$

Explanation:

Step1: Expand Option A

Multiply \((5x - 2)(x - 2)\) using the distributive property (FOIL method):

$$
LATEXBLOCK0
$$

This does not match \(3x^{2}+x - 10\), so A is incorrect.

Step2: Expand Option B

Multiply \((2x + 1)(x - 2)\):

$$
LATEXBLOCK1
$$

This does not match \(3x^{2}+x - 10\), so B is incorrect.

Step3: Expand Option C

Multiply \((3x - 5)(x - 2)\):

$$
LATEXBLOCK2
$$

This does not match \(3x^{2}+x - 10\), so C is incorrect.

Step4: Expand Option D

Multiply \((3x - 5)(x + 2)\):

$$
LATEXBLOCK3
$$

This matches the given quadratic equation.

Answer:

D) \((3x - 5)(x + 2)\)