Find a degree 4 polynomial having zeros -8,-1,4 and 5 and the coefficient of x^4 equal 1.

  x^4 -53x^2 +108x +160

Step-by-step explanation:

If a is a zero, then (x-a) 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.

true

step-by-step explanation:

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,