In this lecture, you'll learn about monomials and polynomials specifically on how to find the degree of each, understanding what constant and coefficients are, learn about powers, and understand the different polynomials and their terms. The best way to evaluate an expression is by following the standard order of operations which is by calculating exponents first, then, multiplying and dividing from left to right, and finally adding and subtracting from left to right. Be cautious to work within parentheses first as parentheses always override the standard rules. And be careful when doing addition and subtraction with different terms because not every two terms can be added. The video examples will give you more chances to practice evaluating the algebraic expressions.
When evaluating an expression, follow the standard order of operations: first calculate exponents, then multiply and divide from left to right, then add and subtract from left to right. BUT: parentheses always override the standard rules. Always work within parentheses first.
Review and understand the key terms: variable, expression, monomial, constant, coefficient, polynomial, term, like terms, binomial, trinomial.
Expressions and Formulas
Evalaute the expression x3 − 2x2 − xy when x = − 1 and y = − 2
Subsitute x = − 1 and y = − 2 into the expression. Use parenthesis.
( − 1)3 − 2( − 1)2 − ( − 1)( − 2)
Follow the order of operations. Exponents First.
− 1 − 2(1) − ( − 1)( − 2)
Followed by multiplication
− 1 − 2 − 2
Add the three negative numbers to find your solution.
Evaluate the expression [(x2 + 3x − 3)/(y2 − 2z)] when x = − 2, y = 3 and z = 1
Substitute x = − 2, y = 3 and z = 1 into the equation. Remember, always use parehtnesis
[(( − 2)2 + 3( − 2) − 3)/(32 − 2(1))]
Now do exponents first. Followed by multiplication.
[(4 + 3( − 2) − 3)/(9 − 2(1))]
Now multiply any necessary terms.
[(4 − 6 − 3)/(9 − 2)]
Simplify the numerator and denominator
Classify the polynomial 3x2 + 3x + 3 as monomial, binomial or trinomial and state the power of each term.
The polynomial 3x2 + 3x + 3 is a trinomial because it has 3 terms.
The power of the first term = 2
The power of the second term = 1
The power of the third term = 0. The power is zero because recall that any number or variable raised to the zero power is always 1, therefore 3 can be written as 3x0 = 3.
Classify the polynomial − [3/5]x2y3z5 as monomial, binomial or trinomial and state the power of each term.
The polynomial − [3/5]x2y3z5 is a monomial because it only has one term.
In this case, the power is determined by the highest power in the term, therefore, the power = 5.
Classify the polynomial x2 − 25 as monomial, binomial or trinomial and state the power of each term.
The polynomial x2 − 25 is a binomial because there are 2 terms.
The power of the first term = 2.
The power of the second term = 0. It's zero because any variable or number raised to the zero power is always 1.
A ball is thrown upwards into the air at a speed of 64ft/s. The formula h = − 16t2 + 64t tells you the height of the ball from the air after t seconds. How far is the ball from the ground after 2 seconds?
Given the equation for height, substitute t = 2 for t.
*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.
Expressions and Formulas
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.