SAT preparation test practice help!!!

Question

How can i find the degree, leading coefficient, and the value of constant of this polynomial function:

y = 5 (2x+1) (x-2)

Thank You so much!!!

Answer 1

One way to answer this question is just to multiply out all of the terms so you don't have anything in parentheses. From there, you can easily identify all of these things you asked for.

Using FOIL to multiply (2x+1) by (x-2):

2x*x + 2x*-2 + 1*x + 1*-2

= 2x² - 4x + x - 2

= 2x² - 3x - 2

Then we multiply by 5:

= 10x² - 15x - 10

The degree of a polynomial is the largest present exponent of the terms in this polynomial. This would be in the term 10x², so the degree is 2.

The leading coefficient is the coefficient of the term of the greatest degree. We identified that term as 10x², so the leading coefficient would be 10.

The constant term of a polynomial is the term that does not have any x's multiplied by it; whatever value of x we use, this number of constant. In this polynomial, it is -10. I hope this was helpful!