2b² +11b=40
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  b = -8, 2.5

Step-by-step explanation:

The equation can be rewritten to standard form:

  2b² +11b -40 = 0

In this form, it can be factored by looking for factors of (2)(-40) that have a total of +11.

  -80 = 80(-1) = 40(-2) = 20(-4) = 16(-5) = 10(-8)

The factors 16 and -5 total 11, so we can now write the equation in a form suitable for factoring by grouping:

  2b² +16b -5b -40 = 0 . . . . write the b term using the numbers we found

  2b(b +8) -5(b +8) = 0 . . . . factor pairs of terms

  (2b -5)(b +8) = 0 . . . . . . . . finish the factoring

Solutions are values of b that make these factors zero:

  2b -5 = 0  ⇒  b = 5/2

  b +8 = 0  ⇒  b = -8

Solution to the equation are b = -8 and b = 5/2.

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answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

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