MPM2DPolynomials Review
Addition and Subtraction of Polynomials
- Only like terms can be added or subtracted.
Simplify:
a)b)
c)d)
e)f)
Addition and Subtraction of Polynomials with Brackets
- Remove the brackets, then gather like terms. (Make sure to “apply” what is immediately outside the bracket to each term within the brackets)
Simplify:
a)b)
c)d)
Multiplication and Division of Polynomials
- Multiply or Divide signs and numerical coefficients first.
- Multiply or Divide variables using exponent rules
- When multiplying powers with same base, keep the base and add the exponents.
- When dividing powers with same base, keep the base and subtract the exponents.
Simplify:
a)b)c)
d)e)f)
g)h)i)
j)k)l)
m)n)o)
p)q)r)
Power to a Power
- For the power terms, when removing brackets, keep the base and multiply the exponents. (Make sure to “apply” the exponent to the numerical coefficient as well as the variables.
Simplify:
a)b)c)d)
e)f)g)h)
i)j)k)l)
Simplify:
a)b)c)
Substitute and Evaluate
- Using the values for the variables given, evaluate the expressions
Evaluate if x = -2 , y = -1 and z = 3
a)b)c)
d)e)f)
Monomials times Polynomials
- Remove the brackets using the distributive property. (Make sure to multiply each term within the brackets by what is immediately outside the brackets)
Simplify:
a)b)c)d)
e)f)
g)h)
i)j)
Common Factoring
- Removing the Greatest Common Factor (GCF) of both the numerical coefficients and the variable portions of the expression
Factor:
a)b)c)
d)e)f)
g)h)i)
j)k)l)
m)n)o)
p)q) r)
s)t)u)
Difference of Squares
- Two terms that are each perfect squares (ie: same thing x same thing) with a minus sign between
Factor:
a)b)c)
d)e)f)
g)h)i)
j)k)l)
m)n)o)
p)q)r)
s)t)u)
v)w)x)
y)z)aa)
Simple Trinomials
Factor:
a)b)c)
d)e)f)
g)h)i)
j)k)l)
m)n)o)
p)q)r)
s)t)u)
v)w)x)
y)z)aa)
bb)cc)dd)
Complex Trinomials
Factor:
a)b)c)
d)e)f)
g)h)i)
j)k)l)
m)n)o)
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