Factorize the following 3x² - 10x + 8.

Solution:

We will factorize the polynomial 3x² - 10x + 8 to find the value of x by splitting the middle term.

Step 1: Identify the values of a, b and c.

In the above equation, a is coefficient of x² = 3, b is the coefficient of x = - 10 and c is the constant term = 8.

Step 3: Multiply a and c and find the factors that add up to b.

3 × (8) = 24

⇒ - 6 and - 4 are the factors that add up to b.

Step 4: Split bx into two terms.

3x² - 6x - 4x + 8 = 0

Step 5: Take out the common factors by grouping.

3x(x - 2) - 4(x - 2) = 0

(3x - 4) (x - 2) = 0

By putting the factors equal to zero we get two values of x

3x - 4 = 0 and x - 2 = 0

x = 4/3 and x = 2

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Factorize the following 3x² - 10x + 8.

Summary:

The factors of the equation 3x² - 10x + 8 are x = 4/3 or x = 2.