Question

Simplify the given polynomial and use it to complete the statement.

Answer 1

Answer:

Option A,C,B

The polynomial simplifies to an expression that is a quadratic binomial with the degree 2.

Step-by-step explanation:

Given : Expression $(-5x^2-2x+4)+(8x^2-x-1)-(x+2)(x-5)$

To find : Simplify the given polynomial and use it to complete the statement?

Solution :

Step 1 - Write the expression

$(-5x^2-2x+4)+(8x^2-x-1)-(x+2)(x-5)$

Step 2 - Open the last bracket using distributive property $(a+b)(c+d)=ac+ad+bc+bd$

$=(-5x^2-2x+4)+(8x^2-x-1)-(x^2-5x+2x-10)$

Step 3 - Open all the parenthesis

$=-5x^2-2x+4+8x^2-x-1-x^2+5x-2x+10$

Step 4 - Add the like terms and solve

$=2x^2+13$

So, The simplified expression is

$(-5x^2-2x+4)+(8x^2-x-1)-(x+2)(x-5)=2x^2+13$

The simplified form contains two elements hence the given polynomial is binomial and the highest power is 2 so, the degree is 2.

The polynomial simplifies to an expression that is a quadratic binomial with the degree 2.

Answer 2

Answer:

1)  $2x^{2}+13$

2) Option C.

3) Option B.

Step-by-step explanation:

1. You must apply the Distributive property as following:

$(-5x^2-2x+4)+(8x^2-x-1)-(x^{2}-5x+2x-10)$

2. Now, you must distribute the negative sign, then you have:

$-5x^2-2x+4+8x^2-x-1-x^{2}+5x-2x+10$

3. Finally, you must add the like terms. Then you obtain the polynomial:

$2x^2+13$

4. By definition, a polynomial that has two terms is classified as a binomial. Therefore, the answer is the option C.

5. The degree of a polynomial is determined by highest exponent of the variable. So, it is a polynomial of degree 2 (option B).