Drill 37 Factor the following polynomials Simplify Find
- Slides: 22
Drill #37 Factor the following polynomials Simplify. Find the value of r:
Drill #38 Factor the following polynomials Simplify.
Drill #60 Factor the following polynomial Evaluate the following roots:
7 -4 Nth Roots Objective: To simplify radicals having various indices, and to use a calculator to estimate the roots of numbers.
Square Roots What power is a square root? A square is the inverse of a square root…
Square Root* Definition: For any real numbers a and b, if then a is a square root of b or We can also write square roots using the ½ power.
Cube Root* Definition: For any real numbers a and b, if then a is a cube root of b or We can also write cube roots using the 1/3 power.
nth Root* Definition: For any real numbers a and b, if then a is a nth root of b or We can also write nth roots using the power.
How many ways can you … Multiply two numbers to get a positive #? Multiply two numbers to get a negative #?
Examples: Roots (of powers of 2) Even Roots: Odd Roots:
Principal Root* Definition: When there is more than one real root of a number (even numbered roots), the non-negative root is the principal root Principal Root Negative Root Both
Examples: Roots (of powers of 2) Both Roots: Principal Roots: Negative Roots:
Roots of negative numbers* Even roots: Negative numbers have no even roots. (undefined) Odd Roots: Negative numbers have negative roots.
Examples: Roots (of powers of 2) Even Roots: Odd Roots:
Roots: Number and Types Even Roots Odd Roots Positive 2 (one positive, one 1 (positive) negative) Negative 0 (undefined) 1 (negative)
Even Roots (of variable expressions)* When evaluating even roots (n is even) use absolute values (if resulting power is odd).
Odd Roots (of variable expressions)* When evaluating odd roots (n is odd) do not use absolute values.
Evaluating Roots of Monomials To evaluate nth roots of monomials: (where c is the coefficient, and x, y and z are variable expressions) or • Simplify coefficients (if possible) • For variables, evaluate each variable separately
Evaluating Roots of Monomials* To find a root of a monomial • Split the monomial into a product of the factors, and evaluate the root of each factor. • Variables: divide the power by the root Coefficients: re-write the number as a product of prime numbers with powers, then divide the powers by the root.
Use a calculator to find the roots* Find the following roots using a calculator (round to the 3 decimal places):
Examples: Simplify
Examples: Simplify
- Harry regan and kelan share £450
- Simplify the ratio 10:15
- K map
- Simplify the following trigonometric expression
- Simplify the following expression using k-map
- Simplify the following:
- Derivative of ln u
- Exponent
- Simplify the following expressions
- Simplify the following expressions
- Simplify the ratios 18 is 72 is 162
- 8-8 factoring by grouping
- Polynomial equations
- Factor difference of cubes
- Factorise fully -a-16
- List factors of 54
- Multiplying polynomials find each product
- Find the least common multiple of x^2+x-12 and x^2+2x-15
- Multiplying polynomials find each product
- Division algorithm
- Add/subtract the following polynomials
- 8-2 factoring by gcf
- Factoring greatest common factor