Review of polynomials
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Transcript of Review of polynomials
Review of Polynomials
Classifying
•A monomial is an expression with a single term. It is a real number, a variable, or the product of real numbers and variables.
•For example, 4 , 3x 2 and 15xy 3 are all monomials.
Classifying
•The degree of a polynomial is the largest of the degrees of its monomial terms.
•A polynomial can be arranged in ascending order.
•The polynomial3 + 12x - xy + 7x 2 y + y 5 -12x 3 y 3 is written in ascending order as -12x 3 y 3 + y 5 +7x 2 y - xy + 12x + 3 is written in descending order.
Classifying - Examples
1) 2p4 + p3
2) -10a3) 2x2
Answers:
4) # of terms: 2, degree: 45) # of terms: 1, degree: 16) # of terms: 1, degree: 2
Adding & Subtracting
•Simplify (2x + 5y) + (3x – 2y) • I'll clear the parentheses, group like
terms, and then simplify:•(2x + 5y) + (3x – 2y)
= 2x + 5y + 3x – 2y = 2x + 3x + 5y – 2y = 5x + 3y
Adding & Subtracting• Simplify (3x3 + 3x2 – 4x + 5) + (x3 – 2x2 + x –
4) • Horizontally(3x3 + 3x2 – 4x + 5) + (x3 – 2x2 + x – 4)
= 3x3 + 3x2 – 4x + 5 + x3 – 2x2 + x – 4 = 3x3 + x3 + 3x2 – 2x2 – 4x + x + 5 – 4 = 4x3 + 1x2 – 3x + 1
• Vertically3x3 + 3x2 – 4x + 5+x3 – 2x2 + x - 44x3 + 1x2 - 3x + 1
Either way you getthe same answer
Multiplying
•(3x – 5)(5x + 2)
3x -5
5x
+2
Multiplying
3x -5
5x 15x2 -25x
+2 6x -10
Combine like terms to write your answer.
15x2 – 19x - 10