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# FACTOR 6cos^2x-13cosx-5?

### 3 Answers

Relevance
• 6 cos^2(x) -13 cos (x) - 5

= (2 cos(x) - 5) (3 cos(x) + 1)

• Let u = cos x:

Factor:

6u² - 13u - 5

Method:

Multiply the outer coefficients --> 6 * -5 = -30

Think of two numbers that multiply to be -30 but add to be -13

Answer:

-15 * 2 = -30

-15 + 2 = -13

Split the middle term into -15u and 2u:

6u² - 15u + 2u - 5

Factor each pair:

3u(2u - 5) + 1(2u - 5)

(3u + 1)(2u - 5)

Substitute back:

(3 cos x + 1)(2 cos x - 5)

• 6 cos^2(x) - 13 cos(x) - 5

= 6 cos^2(x) - 15 cos(x) + 2 cos(x) - 5

= 3 cos(x)(2 cos(x) - 5) + 2 cos(x) - 5

= (3 cos(x) + 1)(2 cos(x) - 5).  Final.

Just simple FOIL.

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