What is the factored form of 5x² - 18x - 8?

Solution:

The given equation is a quadratic equation that can be factored by splitting the middle term.

On finding the factors of 5 × 8 i.e. 40.

The factors of 40 are 1, 2, 4, 5, 8, 10, and 20.

We will use factors 2 and 20.

5x² - 18x - 8

= 5x² - 20x + 2x - 8

= 5x(x - 4) + 2(x - 4)

= (x - 4)(5x + 2)

Hence the factored form of the given equation is (x + 4)(5x - 2).

The factors can be used to find the values of x by finding the zeroes of the equation as shown:

x + 4 = 0 ⇒ x = -4

5x - 2 = 0 ⇒ x = 2/5

These values of x are the solutions of the given equation too.

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What is the factored form of 5x² - 18x - 8?

Summary:

The factored form of 5x² - 18x - 8 is (x + 4)(5x - 4).