What are all the potential rational roots of f(x)=15x^11 -6x^8 +x^3-4x+3

The theorem of rational solutions states that, given a polynomial with integer coefficients, every potenial rational solution is written as , where divides the constant term, and divides the leading term.

So, our choices for are , while our choices for are .

Combine all possible numerator and denominator to get all the potenial rational solutions:

6 (3) - 4 + 32

hope this

let soccer = x and golf = y

part a

1st equation: x + y = 125

2nd equation: x = y +45

part b

replace x in the 1st equation with the 2nd one:

y + 45 + y = 125

simplify:

2y + 45 = 125

subtract 45 from each side:

2y = 80

divide both sides by 2:

y = 80/2

y = 40

she plays golf for 40 minutes.

part c

no because she plays soccer for 45 minutes longer than golf 40 +45 =   85 minutes, not 80 minutes.