Need to solve DQ-2

1).In your own words, detail the process of polynomial division when the divisor is a monomial. Demonstrate the process with an example. How does this process change when the divisor is not a monomial?

I can split the numerator into separate terms. Each one of those separate terms is divided by the monomial.

Example (x^4 + 3x) / x

We can split it like this

X^4 / x + 3x / x

This simplifies to:

X^3 + 3

If the divisor is not monomial, then you have to do long division. I can’t split the terms up like I did for monomial.

Here is one to simplify:

(Here is one to simplify:

3x^4 - 9x) / (3x)

Divide each of the terms by 3x:

x^3 - 3

Explain in your own words how to evaluate a polynomial for a given value of the variable. Demonstrate the process with an example.

To evaluate a polynomial I can substitute the value of the variable inside the polynomial.

F(x) = x^3 + 2x - 3

Evaluating it for x = 2

F(2) = 2^3 + 2(2) - 3 = 9

2)1.The polynomial division depends on the number of terms in the denominator which is the divisor. A polynomial can be divided by any monomial and subtract exponents when the bases are the same. Also divide the coefficients.

The first step is to separate the fraction example (Polynomial divided by monomial

Example 1.2x^2+x-10 Divide every term of 2x^2 + x-10 by x.

x
2x^2 + x -10 =2x+1- 10

xx x x Step 2: Divide each monomial

2. When the divisor is not a monomial the polynomial is written in descending order and then write the missing terms. First divide the first term by the first term and ignore the term 2. Then multiply x above by the divisor, and then subtract. Example: x-3/x^2+3x-6 divide x^2+3x-6 by x-3

x-3/x^2+3x-6 divide the first term by the first term: x^3/x=x then ignore the term 2.

Next multiply x above by the divisor, x-3, x^2-3x

Subtract: (x^2+3x)-(x^2-3x)=x^2+3x-x^2-3x=-x then bring down the next term of the dividend – by 6. Divide the first term by the first term: x/x=x. Then bring down the 6 and multiply 1 by the divisor, x-3. Subtract (1x-6)-(1x+6)=3x+6-3x-6+0. The quotient is x+1, and the remainder is 0, expressed as R=0.

3.Explain in your own words how to evaluate a polynomial for a given value of the variable.

To evaluate take the polynomial and plug it in a value of x. Evaluate a^2b for a=-3, b=4, c=-2, and d=2 then plug in the given values, and use the parentheses around the minus signs: (-3)^2(4)=(9)(4)=36

1. Solve the problem. Evaluate (b+d)^2 for a=-4,b=4,c=-2, and d=2

Plug in b and d:

(4+2)^2

= 6^2

= 36

2.Solve the problem to divide a polynomial by a monomial.Divide: (8x^4+6x^3)/(2x^2)

Divide each term by 2x^2:

4x^2 + 3x

3. Solve the problem.

8^2/2x

= 64/2x

= 32/x

3).The Division of one polynomial by a monomial is to.
1. Get ride of parentheses by rewrite the problem without the parentheses.
2. Add the number or subtract which one the problem calls for.
3. Than divide the answer in lowest terms.
Example. ( 4+6-2) /2
4+6-2/ 2 = 8/2 = 4
Example. (12+4-6)/2
12+4-6/2 = 10/2 = 5
The process changes, by the type of solution is used. Which the terms can not be split, so you would have to do long division.
Example. 12x^4 * 9x^3 - 5
108^7 -5
Example. 10x^2 - 3x * 2x ^2 -2
10x^2- 6x ^2 -2
4x-2
Example of monomial 7xy and 3x^3

If you want to divide these:

7xy / (3x^3)

= 7y / (3x^2)

4).How would you solve the following problem:
12x^4+ 9x^3 - 15x^2
3x

Assuming this is division, divide each by 3x:

4x^3 + 3x^2 – 5x

5).The process of polynomial division when the divisor is a monomial is the following:

  1. Divide each of the terms of the polynomial by the monomial. First, divide the coefficients, and then subtract the exponents.
  2. The number of terms in the polynomial is going to be the same number of terms in the answer when dividing by a monomial.

When the divisor is not a monomial, the process will then involve dividing, multiplying and subtracting, just like rational numbers.

EXAMPLE:

(28 + 32) / (4) =

= + = * + *

= 7 + 8

= 7 +8

An example for the class to solve:

(12 + 8 + 4x) / (2x)

Divide through by 2x:

6x^2 + 4x + 2

6.)When dividing a polynomial by a monomial you will take each variable and divide them individually by the denominator. For example first set would be to take the problem and put it together. Step 1

Step 2

To check if this is correct you would multiply the denominator 3x2 by the final answer. Ex.

Which is what the original problem started with.

SOLVE:

Dividing through by 2x:

x^2 + 3x + 2

7.) You brought up a good point during your comment about polynomials divided by a divisor that is not monomial. You said the numerator and denominator sometimes cancel out.Show the in between steps of your example to demonstrate that point to the class.
Example: ( 3x^2 + 2x)/(x+1)

The answer is:
3x-1+1/(x+1)

8)1.) Polynomial Division with monomial
-Separate terms
-Divide monomial
Example- (3+5-2)/2
3+5-2/2=6/2=3
Example for class to solve- (6+4-2)/4

If that’s a minus in front… (but this isn’t a polynomial)

-(8)/4

= -2

2.) Divisor not monomial
Must use division, multiplication, addition, and subtraction
Example- 3x^2*5x^2-6
x=2
3(2^2)*5(2^2)-6
3*4*5*4=240-6
240-6=234
Example for class to solve- 6x^3*7x^3-10

There is no division here… only multiplication:

42x^6 - 10

3.)Evaluate polynomial
Substitute the Value inside of polynomial
Example- f(x)=2x+4+x^2 x=2
2(2)+4+2^2
4+4+4=12
Example for class to solve- f(x)=6x+30-4x^2 x=2
Example for class to solve- f(x)=6x+30-4x^2 x=2

Plug in x = 2:

6(2) + 30 – 4(2)^2

= 26