Answer:
x^4 -53x^2 +108x +160
Step-by-step explanation:
If <em>a</em> is a zero, then (<em>x-a</em>) is a factor. For the given zeros, the factors are ...
p(x) = (x +8)(x +1)(x -4)(x -5)
Multiplying these out gives the polynomial in standard form.
= (x^2 +9x +8)(x^2 -9x +20)
We note that these factors have a sum and difference with the same pair of values, x^2 and 9x. We can use the special form for the product of these to simplify our working out.
= (x^2 +9x)(x^2 -9x) +20(x^2 +9x) +8(x^2 -9x) +8(20)
= x^4 -81x^2 +20x^2 +180x +8x^2 -72x +160
p(x) = x^4 -53x^2 +108x +160
_____
The graph shows this polynomial has the required zeros.
Answer:
The probability of getting 6's on both cubes is .
The probability that the total score is at least 11 is .
Step-by-step explanation:
Consider the provided information.
A red cube has faces labeled 1 through 6, and a blue cube has faces labeled in the same way.
Part (A) Both cubes show 6’s.
Probability of getting 6 on red cube is
Probability of getting 6 on blue cube is
Thus, the probability of getting 6's on both cubes is:
Hence, the probability of getting 6's on both cubes is .
Part (B) The total score is at least 11.
The possible number of outcomes in which total score is at least 11 is:
Red shows 6 and Blue shows 5.
Blue shows 6 and Red shows 5.
Blue shows 6 and Red shows 6.
Thus, the probability of total score is at least 11.
Hence, the probability that the total score is at least 11 is .