1

Problem

Factorize the quadratic expression: \$3x^2 - 10x - 8 \$.

2

Step

Write down the quadratic expression

\$3x^2 - 10x - 8 \$

3

Hint

Identify the coefficients of the quadratic, linear, and constant terms. In this case, the coefficient of the quadratic term \$(x^2)\$ is 3, the coefficient of the linear term (x) is -10, and the constant term is -8.

4

Hint

Look for two numbers whose product is equal to the product of the coefficient of the quadratic term and the constant term. For this expression, the product is

5

Step

Find two numbers that add up to the coefficient of the linear term. In this case, we need to find numbers that add up to -10. After some trial and error, we find that -12 and 2 satisfy these conditions since

-12 + 2 = -10

6

Step

Rewrite the middle term (-10x) using the numbers found in the previous step. Split the -10x term into -12x and 2x

\$ 3x^2 - 12x + 2x - 8 \$

7

Step

Factor out the greatest common factor from each group. Factor out 3x from the first group and 2 from the second group

3x(x - 4) + 2(x - 4)

8

Step

Notice that we now have a common binomial factor, (x - 4), in both terms, then combine the terms using the common factor

(x - 4)(3x + 2)

9

Solution

The quadratic expression \$3x^2 - 10x - 8\$ is fully factorized as (x - 4)(3x + 2).

10

Sumup

Please summarize Problem, Clue, Hint, Formula, Steps and Solution

Choices

11

Choice-A

This is correct because the expanded form corresponds accurately with the quadratic equation

Correct (x - 4)(3x + 2)

12

Choice-B

This is incorrect as the expanded form does not correspond to the quadratic equation

Wrong (x - 4)(3x - 2)

13

Choice-C

This is incorrect as the expanded form does not correspond to the quadratic equation

Wrong (x + 4)(3x + 2)

14

Choice-D

This is incorrect as the expanded form does not correspond to the quadratic equation

Wrong (x - 4)(3x + 3)

15

Answer

Option

A

16

Sumup

Please summarize choices