Coefficient of Terms

Recall that a quadratic expression has 2 as its highest power.

A quadratic expression is also known as a polynomial of the second degree.

The general form of a quadratic expression is

\( \scriptsize ax^2 + bx + c \)

 Where (a ≠ 0)

a is not equal to zero.

where a, b and c represent any number 

a is called the coefficient of  x² 

b is called the coefficient of x 

c is a constant term.

Worked Example 6.2.1:

Write down the coefficient of x², x, and the constant in the following expressions.

a. x²  + 3x + 1
b. 2x² – 8
c. 7x² – x – 2
d. 4x² – 6x + 4
e. (x – 1)(x – 2)

Solution

a. x²  + 3x + 1

⇒ \( \scriptsize ax^2 + bx + c \) compare coefficients

a = 1, b = 3, c = 1

b. 2x² – 8

⇒ \( \scriptsize ax^2 + bx + c \) compare coefficients

We can see that we only have a and c after comparing coefficients.

a = 2 and c = – 8

c. 7x² – x – 2

⇒ \( \scriptsize ax^2 + bx + c \) compare coefficients

a = 7,  b =  -1,    c =  -2

d. 4x² – 6x + 4

⇒ \( \scriptsize ax^2 + bx + c \) compare coefficients

 a = 4,   b = -6,   c =  4

e. (x – 1)(x – 2)

= x(x – 2) -1(x – 2)

= x² – 2x – x + 2

= x² – 3x + 2

⇒ \( \scriptsize ax^2 + bx + c \) compare coefficients

a = 1,   b = -3,   c = 2