Simplify the expression using long division. (10x2 – 85x – 10) ÷ (x – 8)

5 • (2x2 - 17x - 2)

 ———————————————————

        x - 8      

Step-by-step explanation:

Step by step solution :

Step  1  :

Equation at the end of step  1  :

Step  2  :

           10x2 - 85x - 10

Simplify   ———————————————

                x - 8      

Step  3  :

Pulling out like terms :

3.1     Pull out like factors :

  10x2 - 85x - 10  =   5 • (2x2 - 17x - 2)  

Trying to factor by splitting the middle term

3.2     Factoring  2x2 - 17x - 2  

The first term is,  2x2  its coefficient is  2 .

The middle term is,  -17x  its coefficient is  -17 .

The last term, "the constant", is  -2  

Step-1 : Multiply the coefficient of the first term by the constant   2 • -2 = -4  

Step-2 : Find two factors of  -4  whose sum equals the coefficient of the middle term, which is   -17 .

     -4    +    1    =    -3  

     -2    +    2    =    0  

     -1    +    4    =    3  

Observation : No two such factors can be found !!  

Conclusion : Trinomial can not be factored

the correct answer is

c. 4

step-by-step explanation:

the given polynomial is

the degree of the polynomial is the highest exponent which is 4.

the -4 is called the leading coefficient.

this polynomial has only one term so it is a monomial.

the correct answer is option c.