The polynomial 3x² - 10x + 8 has a factor of 3x - 4. What is the other factor of 3x² - 10x + 8?

Solution:

Let us factorize the given polynomial 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 the coefficient of x² = 3,

b is the coefficient of x = -10 and

c is the constant term = 8.

Step 2: Multiply a and c and find the factors that add up to b.

1 × (8) = 24

⇒ -6 and -4 are the factors of 24 that add up to b.

Step 3: Split bx into two terms.

3x² - 6x - 4x + 8

Step 4: Take out the common factors by grouping.

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

(x - 2)(3x - 4)

Given one factor is (3x - 4)

Thus the other factor of 3x² - 10x + 8 is (x - 2).

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The polynomial 3x² - 10x + 8 has a factor of 3x - 4. What is the other factor of 3x² - 10x + 8?

Summary:

The factors of the equation 3x² - 10x + 8 are (3x - 2) (x - 2).