Which is one of the binomial factors of the polynomial x^3+3x-2x-8?

a. x-1
b. x+1
c. x-2
d. x+2

  d.  x+2

Step-by-step explanation:

The question is essentially asking which of -2, -1, 1, 2 is a zero of the polynomial. All of them are plausible, because all are factors of -8, the constant term.

So, we don't have much choice but to try them. That means we evaluate the function to see if any of these values of x make it be zero.

±1:

The value 1 is easy to substitute for x, as it makes all of the x-terms equal to their coefficient. Essentially, you add all of the coefficients. Doing that gives ...

  1 +3 -2 -8 = -6

Similarly, the value -1 is easy to substitute for x, as it makes all odd-degree terms equal to the opposite of their coefficient. Here, ...

  f(-1) = -1 +3 -(-2) -8 = -4

Neither one of these values (-1, +1) is a zero of the polynomial, so choices A and B are eliminated.

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(x-2):

To see if this is a factor, we need to see if x=2 is a zero. Evaluation of a polynomial is sometimes easier when it is written in Horner form:

  ((x +3)x -2)x -8

Substituting x=2, we get ...

  ((2 +3)2 -2)2 -8 = (8)2 -8 = 8 . . . not zero

This tells us there is a zero between x=1 and x=2, but that is not what the question is asking.

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(x+2):

We can similarly evaluate the function for x=-2 to see if (x+2) is a factor.

  ((-2 +3)(-2) -2)(-2) -8 = (-4)(-2) -8 = 0

Since x=-2 makes the function zero, and it makes the factor (x+2) equal to zero, (x+2) is a factor of the polynomial.

So, the factor (x+2) is a factor of the given polynomial.

_____

I find that a graphing calculator answers questions like this quickly and easily. If you're allowed one, it is a handy tool.

hello from mrbilldoesmath!

answer:

25x^2 + 90x + 84

discussion:

mn(x) = m(n(x)) = m( 5x + 9) =

(5x + 9)^2 + 3 =>

25x^2 + 90x + 9^2 + 3 =

25x^2 + 90x + 84                 (as 9^2 = 9*9 = 81)

which is the second choice

regards,  

mrb

p.s.   i'll be on vacation from friday, dec 22 to jan 2, 2019. have a great new year!

answer: answer: d) v= 1/6 bh  

step-by-step explanation:

since according to the given question,   a pyramid is placed inside a prism.

step-by-step explanation: