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EXAMPLES & SOLUTIONS
Anchor 1
A monomial is one term that has one number, variable or the product of both. A polynomials is the sum of one or more monomials, that form to create a expression.
Polynomial equations are formed with more than one term.
Monomials has only one term.
Grouped polynomials can be multiplied by one monomial.
A Binomial are polynomials that have only 2 terms.
A Trinomial are polynomials that have only 3 terms.
Grouped polynomials can be added, subtracted, multiplied, divided and factored.
MONOMIALS & POLYNOMIALS
Explanation monomials and polynomials (binomials & trimonmials)
One term:
monomial expression: 3x
2
polynomial expression: 3x + 7 -4x +
2
3
One (1) or more terms:
n
2
Two (2) terms:
binomial expression: 3x - 5y
2
Three (3) terms:
trinomial expression: 3x - y + ab
2
5
POLYNOMIALS
Explanation of adding polynomials
2
6
evaluate expression: (2x + 3x - 3 + x ) + (4x + 8 - x)
3
2
2
Write in standard form (highest to lowest exponents)
2x + 3x - 3 + x = x + 2x + 3x - 3
3
2
6
6
3
4x + 8 - x = 4x - x + 8
2
2
Align commom terms
x + 2x + 3x - 3 --expression #1
6
3
2
+
4x - x + 8 --expression #2
2
x + 2x + 7x - x + 5
6
3
2
POLYNOMIALS
Examples of how to add polynomials
Adding Binomials
(3x + 4) + (2x + 1)
2
2
--standard form and align
2
3x + 4
+ 2x + 1
5x + 5
2
2
Adding Trinomials
3
(3x + 4 - 3x) + (2x + 5 + x )
2
--standard form and align
3x - 3x + 4
+ x + 2x + 5
x + 3x - x + 9
3
2
2
6
+
POLYNOMIALS
Explanation of subtracting polynomials
evaluate expression: (2x + 3x - 3 + x ) - (2x + 8 - x)
2
6
5
2
2x + 3x - 3 + x = x + 2x + 3x - 3
2
Write in standard form (highest to lowest exponents)
5
2
6
6
5
2x + 8 - x = 2x + x - 8
2
2
Align commom terms
x + 2x + 3x - 3
6
5
2
--expression #1
-
2x + x - 8
2
--expression #2
Follow subtraction rule for expression #2
Rewrite problem
x + 2x + 3x - 3
5
2
-2x - x + 8
2
--updated expression #2
x + 2x + 1x - x + 5
6
5
2
POLYNOMIALS
Examples of how to subtract polynomials
Substracting Binomials
(3x + 4) - (2x + 1)
2
--standard form and align
2
3x + 4
- 2x + 1
2
3x + 4
+ -2x - 1
1x + 3
--subtract rule and rewrite
2
2
2
Subtracting Trinomials
2
3
(3x + 4 - 3x) + (2x + 5 + x )
--standard form and align
3x - 3x + 4
- x + 2x + 5
3
2
--subtract rule and rewrite
-x + 3x - 5x - 1
3x - 3x + 4
+ -x - 2x - 5
3
2
3
2
2
POLYNOMIALS
Explanation of multiplying polynomials
evaluate expression: (4x + 3) (x + 2)
(4x + 3) (x + 2)
)
)
)
)
First term
Last term
Outer
Inner
Foil first & second polynomial:
Multiply the first terms
= (4x * x)
= 4x
2
Multiply the last terms
d polynomial
= (3 * 2)
= 6
Multiply the inner terms
= (3 * x)
= 3x
Multiply the outer terms
= (4x * 2)
= 8x
Add updated polynomials
4x + 6 + 3x + 8x --combine terms
2
4x + 8x + 3x + 6 --add terms
2
4x + 11x + 6 --updated terms
2
POLYNOMIALS
Examples of how to multiply polynomials
Multiplying Binomials
(3x + 4) * (2x + 1)
2
3x * (2x) = 6x = 6x --first terms
2
2 + 1
3
4 * 1 = 4 --last terms
4 * 2x = 8x --inner terms
3x * (1) = 3x --outer terms
2
2
6x + 3x + 8x + 4 --updated expression
3
2
Multiplying Trinomials
Arriving Soon!!
Polynomials
Explanation of divide polynomials
Arriving Soon!!!
Polynomials
Explaining how to factor polynomials
Arriving Soon!!!
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