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Slide Notes

A polynomial is an expression that has no other operations other than addition, subtraction, and multiplication.
The degree of a polynomial with one variable is the exponent of the highest power of that variable.
First degree- linear ex. 7x+3
Second degree- quadratic 7x
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Bonus Project for math

Published on Nov 28, 2015

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PRESENTATION OUTLINE

1.

NAME OF POLYNOMIALS

  • A polynomial has only addition, subtraction, and multiplication
  • The degree is the exponent of the highest power
  • First degree(linear)- 7x+3
  • Second degree(quadratic)- 7x^2+2x-4
  • Third degree(cubic)- x^3-6
A polynomial is an expression that has no other operations other than addition, subtraction, and multiplication.
The degree of a polynomial with one variable is the exponent of the highest power of that variable.
First degree- linear ex. 7x+3
Second degree- quadratic 7x
Photo by Dominic Alves
2.

CONTINUE OF NAMES OF POLYNOMIALS

  • One term(monomial)- 7x
  • Two terms(binomial)- 7x+9
  • Three terms(trinomial)- 7x^2+4x-3
  • Examples- 13x-6 is a linear binomial
  • 6x^2+11x-8 is a quadratic trinomial
Photo by Andreas.
3.

PRODUCT OF TWO BINOMIALS

  • Multiply each term by each term of the other
  • Combine like terms
  • Use the FOIL method f- first o- outer i- inner l- last
  • Examples- (x+4)(x+6)= x^2+10x+24
  • (3x+1)(x-6)= 3x^2+-17x-6
Photo by David Jackmanson
4.

FACTORING QUADRATIC POLYNOMIALS

  • To transform it to product of two or more factors
  • If it cannot be factored write prime
  • Examples- x^2+11x+28= (x+4)(x+7)
  • x^2-20x+30= prime
Photo by XcBiker
5.

FACTORING QUADRATIC TRINOMIALS

  • Transform it to a product of two or more factors
  • If it cannot be factored write prime
  • Examples- x^2+8x-20= (x+10)(x-2)
  • x^2+6x-10= prime
Photo by Ben Grey
6.

FACTORING QUADRATIC TRINOMIALS

  • Factor the trinomial
  • Examples- 2x^2+15x+7= (2x+1)(x+7)
  • 4x^2-8x+3= (2x-3)(2x-1)
Photo by blair_25
7.

FACTORING A DIFFERENCE OF TWO SQUARES

  • Conjugate binomials are the same except for the sign
  • A difference of two squares are conjugate binomials
  • Examples- x^2-25= (x+5)(x-5)
  • x^2+25= prime
8.

SQUARING A BINOMIAL

  • Square the first term
  • Add twice the product of the two terms
  • Add the square of the last term
  • Examples- (x+5)^2= x^2+10x+25
  • (3x+7)^2 = 9x^2+42x+49
9.

FACTORING TRINOMIAL SQUARES

  • When you square a binomial
  • Check the first and last terms. Are they perfect squares?
  • Check the middle term. Is it twice the product of the square roots of the first and last terms?
  • Examples- 196 yes it is a perfect square, 14
  • x^2+14x+49= (x+7)^2

Louise Johnston