The polynomial p(w) = 3w^3 - 20w^2 + 37w - 20 has a known factor of (w-4). Rewrite p(w) as a product of linear factors.

(w - 4)(w - 1)(3w - 5)

Step-by-step explanation:

Using Synthetic division to find the quotient on dividing p(w) by (w - 4)

4 | 3   - 20   37   - 20

            12   - 32    20

    3     - 8     5        0 ← remainder = 0

quotient = 3w² - 8w + 5 = (3w - 5)(w - 1)

p(w) = (w - 4)(w - 1)(3w - 5)

point a is the center of the circle that passes through points e, f, and g and the center of the circle that passes through points x, y, and z.

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.