A polynomial in x has m nonzero terms. Another polynomial in x has n nonzero terms. These polynomials are multiplied and all like terms are combined. The resulting polynomial in x has a maximum of how many nonzero terms?

Resulting polynomial contains a maximum mn positive terms.

Step-by-step explanation:

Given one polynomial contains m nonzero terms and second polynomial contains n nonzero terms.

To show after multiplication and combining similar terms how many positive terms contan by both polynomial.

Now let,

So we see that after multiplication of m and n positive terms, there are mn positive terms are there.

To prove this we have to apply mathematical induction. So let the statement is true for m=p and n=q number of positive terms, then mn=pq.

We have to show avobe ststement is hold for m+1, n+1. Considering,

(m+1)(n+1)=mn+m+n+1=pq+p+q+1=p(q+1)+1(q+1)=(p+1)(q+1)

Hence above statement is true for m+1 and n+1.

Thus there will be mn nonzero terms after multiplication and combine positive terms.

a is the right answer

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: