Unit 4 Operations & Rules
5x – 14 15x + 3 6x2 Warm up Combine Like Terms Exponent Rules 3) What is 2x 3x? 5x – 14 15x + 3 6x2
Degree The exponent for a variable
Degree of the Polynomial Highest (largest) exponent of the polynomial
Standard Form Terms are placed in descending order by the DEGREE Write all answers in Standard Form!
Leading Coefficient Once in standard form, it’s the 1st NUMBER in front of the variable (line leader)
# of Terms Name by # of Terms Monomial 2 Binomial 3 Trinomial 4+ Polynomial
Degree Name by degree 0 Constant 1 Linear 2 Quadratic 3 Cubic (largest exponent) Name by degree 0 Constant 1 Linear 2 Quadratic 3 Cubic
Linear Binomial -2 Special Names: Degree Name: # of Terms Name: Leading Coefficient: Binomial -2
Special Names: Degree Name: # of Terms Name: Cubic Monomial
Quadratic Binomial 4 Special Names: Degree Name: # of Terms Name: Leading Coefficient: Binomial 4
Cubic Trinomial 1 Special Names: Degree Name: # of Terms Name: Leading Coefficient: Trinomial 1
Adding Polynomials
1. 3x2 + x + 2
2. x2 + 2x – 2
Subtracting Polynomials
When SUBTRACTING polynomials Distribute the NEGATIVE
3. 3a2 + 10a – 8a2 + a – 5a2 + 11a
4. 3x2 + 2x – 4 – 2x2 – x + 1 x2 + x – 3
Multiplying Polynomials
5. -2x(x2 – 4x + 2)
(x + 3) (x – 3) 6.
(3x – 1)(2x – 4) 7.
8. Find the area of the rectangle.
9. Find the volume.
Warm up Find an expression for the area of the following figure:
Challenge Find an expression for the volume of cylinder:
Multiply: Polynomial Ops Q8 of 20
Find the perimeter Find the Perimeter:
Find an expression for the volume of cylinder: Polynomial Ops Q11 of 20
Write an expression for the volume of the box: Polynomial Ops Q14 of 20
Find the area of the label. Polynomial Ops Q16 of 20
Skills Check
Square Roots and Simplifying Radicals
No number where the index is means it’s a square root (2) Parts of a radical No number where the index is means it’s a square root (2)
Radicals are in SIMPLEST FORM when.. 1. No perfect square factors other than 1 are under the radical. No fractions are under the radical. No radicals are in the denominator.
You try! 1.
You try! 2.
You try! 3.
Variables Under Square Roots Even Exponent – ODD Exponent – Take HALF out (nothing left under the radical) Leave ONE under the radical and take HALF of the rest out
Nth Roots & Rational Exponents
No number where the root is means it’s a square root (2) Parts of a radical No number where the root is means it’s a square root (2)
Break down the radicand in to prime factors. Simplifying Radicals Break down the radicand in to prime factors. Bring out groups by the number of the root.
Simplify
Simplify
Simplify
Simplify
Rewriting a Radical to have a Rational Exponent
Rewriting Radicals to Rational Exponents Power is on top Roots are in the ground
Rewriting Radicals to Rational Exponents Power is on top Roots are in the ground
Rewrite with a Rational Exponent
Rewrite with a Rational Exponent
Rewrite with a Rational Exponent
Rewrite with a Rational Exponent
Rewrite with a Rational Exponent
Rewriting Rational Exponents to Radicals
Rewrite with a Rational Exponent (don’t evaluate)
Rewrite with a Rational Exponent (don’t evaluate)
Rewrite with a Rational Exponent (don’t evaluate)
Warm up
Powers of i and Complex Operations
“I one, I one!!” Negatives in the middle.
Try these!
Add and Subtract Complex Numbers
Add/Subt Complex Numbers Treat the i’s like variables Combine the real parts then combine the imaginary parts Simplify (no powers of i higher than 1 are allowed) Write your answer in standard form a + bi
Simplify
Simplify
Simplify
Simplify
Simplify
Multiplying Complex Numbers
Multiplying Complex Numbers Treat the i’s like variables Simplify all Powers of i higher than 1 Combine like terms Write your answer in standard form a + bi
Multiplying Complex Numbers
Multiplying Complex Numbers
Multiplying Complex Numbers
Dividing Complex Numbers
What is a Conjugate?
17. Dividing – Multiply top & bottom by the Conjugate