Page 7 - Algebra

• Quadratic polynomial
A polynomial of degree two is called a quadratic polynomial, and the equation is called a quadratic equation.
2x2 + 3x – 1 is a quadratic polynomial in x
3z2 – z + 2 is a quadratic polynomial in z
• Cubic polynomial
A polynomial of degree three is called a cubic polynomial, and the equation is called a cubic equation.
2x3 + 3x2 – x + 1 is a cubic polynomial in x 3z3 – z2 + 2 is a cubic polynomial in z
Finding the Value of an Expression
The value of an algebraic expression depends upon the value of the variables.
For example, the area of a square is a2, where ‘a’ is the side of the square. When ‘a’ is 4 cm, the area is
22 16 cm and when ‘a’ is 9 cm, the area is 81 cm .
Worked Example
Find the value of the expression for x = 3.
a. 4x2 – 1 b. 3x2 – 2x + 1
Solution:
a.4x2 –1
Put the value of x = 3
4 (3)2 – 1
= 4(9) – 1 = 35
b. 3x2 – 2x + 1
Put the value of x = 3
3(3)2 – 2(3) + 1
= 3(9) – 6 + 1 = 27 – 6 + 1 = 22
Page 6 of 177
Algebra I & II