Chapter 8.1, Problem 4P

To determine

To find: a polynomial for the total number of pounds, in millions, of carrots, celery, and broccoli consumed in U.S during a 6- year period.

Answer to Problem 4P

  $-12x^3+120x^2-255x+6022$

Explanation of Solution

Given information:

The polynomial for the consumption of carrots and celery over a 6- year period:

  $-12x^3+106x^2-241x+4477$

The polynomial for the consumption of broccoli over a 6- year period:

  $14x^2-14x+1545$

In each polynomial above defined, $x=0$ corresponds to the first year in the 6 − year period

Formula Used:

The word total implies addition, so add two polynomials to find a polynomial that represents the total.

Addition of polynomials involves adding the coefficient of like terms (Like terms means terms having same variable and same exponent)

Calculation:

Since $14x^2-14x+1545$ does not have $x^3$ term it can also written as $0x^3+14x^2-14x+1545$

The best method to add polynomials is to add horizontally.

That is, Group up like terms and then add corresponding coefficients.

  $\left(-12x^3+106x^2-241x+4477\right)+\left(0x^3+14x^2-14x+1545\right)$

  $=\left(-12+0\right)x^3+\left(106+14\right)x^2+\left(-241-14\right)x+\left(4477+1545\right)$

  $=-12x^3+120x^2-255x+6022$

Therefore, polynomial for the total number of pounds, in millions, of carrots, celery, and broccoli consumed in the U.S during the 6- year period is $-12x^3+120x^2-255x+6022$