Variables And Algebraic Expressions

Question 0

Define an algebraic expression.

Answer 0

A combination of letters and arithmetic operations, such as F+5 or 19x^2-6x+3.

Question 1

What is algebra based on?

Answer 1

It is based on the operations of arithmetic and on the concept of an unknown variable. Letters such as x often represent unknown quantities.

Question 2

Define a quadratic polynomial.

Answer 2

An expression where the highest power of x is 2.

Question 3

Define a linear polynomial.

Answer 3

When the highest power of the variable is 1.

Question 4

How can you simplify an algebraic expression?

Answer 4

If there are common factors in the numerator and denominator of an expression, they can be divided out, provided that they are not equal to zero.

Example:

If x is not equal to 1, then x-3/x-3 is equal to 1; therefore, 3xy-9y/x-3=3y(x-3)/x-3=(3y)(1)=3y

Question 5

How do you multiply an algebraic expression?

Answer 5

Each term of one expression is multiplied by each term of the other expression.

Example:

(3x-4)(9y+x)
3x(9y+x)-4(9y+x)
(3x)(9y)+(3x(x)+(-4)(9y+x)+(-4)(x)
27xy+3x^2-36y-4x

Question 6

How can an algebraic expressions be evaluated?

Answer 6

By substituting values of the unknowns in the expression.

Example:

If x=3 and y=-2, then 3xy-x^2+y is:

3(3)(-2)-(3)^2+(-2)=-18-9-2=29