complete the factoring and PLEASE SHOW STEPS. x² - 17x + 60?

x² - 17x + 60

= x² - 5x - 12x + 60

= x(x - 5) - 12(x - 5)

= (x - 5)(x - 12)

Find a pair of numbers that multiply to 60 and add up to -17. How about -12 and -5?

(x - 12)(x - 5)

:--

(x_____)(x______)

(x___12)(x_____5)

( x - 12 ) ( x - 5 )

You start by thinking of two numbers that will multiply to be 60. Because 60 is positive, the two numbers will have the same sign (both positive or both negative).

Next you need those numbers to add to be -17. That means the two numbers will both be *negative*.

Let's focus on the positive factor pairs of 60 to see which two add to be 17.

1 x 60 = 60

2 x 30 = 60

3 x 20 = 60

4 x 15 = 60

5 x 12 = 60 <-- 5 + 12 = 17

6 x 10 = 60

Notice how 5 and 12 add to be 17. But since we want -17, that will be -5 and -12.

Answer:

x² - 17x + 60

= (x - 5)(x - 12)

x² - 17x + 60

= x² - 12x - 5x + 60

= x(x - 12) - 5(x - 12)

= (x - 5)(x - 12)

Factors of 60 are 5 and 12 so x^2 -17x +60 = (x -5)(x -12) when factored

x² - 17x + 60

=(x - 12)(x - 5) answer//

x² - 17x + 60

→ x² + 2(-17/2)x + (-17/2)² + 60 - (-17/2)²

→ (x - 17/2)² - 49/4

→ (x - 17/2)² - (7/2)²

→ (x - 17/2 - 7/2)(x - 17/2 + 7/2)

→ (x - 12)(x - 5)

x² - 17x + 60 => x² - 5x - 12x + 60

i.e. x(x - 5) - 12(x - 5)

=> (x - 12)(x - 5)

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