Difference of Squares
What is the difference of squares identity?
(a-b)(a+b)=a^2-b^2
Factor:
x^2-64
(x-8)(x+8)
Factor
(x+5)^2
x^2+10x+25
(x-y)^2=x^2-2xy+y^2
Is this a polynomial? If so, define by terms and degree. If not, explain why.
5x^2-4x+3
A quadratic trinomial
Define a conjugate pair
Two binomials with the same terms, except for different signs between them.
ex. (x-2)(x+2)
Simplify
(3x^3-2)(3x^3+2)
9x^6-4
Simplify
x^2+4x+4
(x+2)^2
Simplify
(x-7)^2
x^2-14x+49
Is this a polynomial? If so, define by terms and degree. If not, explain why.
7x^-9+76
No, because there is a negative exponent.
Simplify:
(x-5)(x+5)
x^2-25
Factor:
49x^8-25
(7x^4-5)(7x^4+5)
Factor
(3x+5)^2
9x^2+30x+25
Factor
x^2-8x+16
(x-4)^2
What are the rules for defining polynomials.
1. Exponents are whole numbers
2. Coefficients are any real number
Simplify:
(2x-4)(2x+4)
4x^2-16
Simplify
(4x^2-11)(4x^2+11)
16x^4-121
What is the identity for perfect square trinomials
(x+y)^2=x^2+2xy+y^2
Simplify
(x^3-9)^2
x^6-18x^3+81
Is this a polynomial? If so, define by terms and degree. If not, explain why.
3.7x^3+9
Yes, it is a cubic binomial.
(4x^2+9)(4x^2-9)
16x^4-81
Factor:
9x^10-36
(3x^5-6)(3x^5+6)
Simplify
(x^3+8)^2
x^6+16x^3+64
Factor
4x^2-24x+36
(2x-6)^2
Is this a polynomial? If so, define by terms and degree. If not, explain why.
1/x-3
No, because there can not be an variable in the denominator