# The polynomial 3x^{2} - 10x + 8 has a factor of 3x - 4. What is the other factor of 3x^{2} - 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 x^{2 }= 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.

3x^{2} - 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 3x^{2} - 10x + 8 is (x - 2).

## The polynomial 3x^{2} - 10x + 8 has a factor of 3x - 4. What is the other factor of 3x^{2} - 10x + 8?

**Summary:**

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