This chapter is about adding and subtracting polynomials, common factors, multiplying a monomial by a polynomial, multiplying two binomials, polynomial division, and applying algebraic modelling.
Adding/Subtracting polynomials:
To add polynomials we simply add any like terms together
To subtract Polynomials, first reverse the sign of each term we are subtracting (in other words turn "+" into "-", and "-" into "+"), then add as usual.
Common factors:
numbers that divide exactly into two or more numbers.
Multiplying a Monomial by a Polynomial:
What is (2x)(3x^2 + 4x + 9) ?
We use the distributive property to distribute (2x) over the longerpolynomial, then simplify the resulting terms.
(2x)(3x^2 + 4x + 9) = (2x)(3x2) + (2x)(4x) + (2x)(9) = 6x^3 + 8x^2 + 18
Multiplying two Binomials:
(x + -2) * ( 1 + x)
First, do:
x * 1 = x and
x * x = x2
Then,do
-2 * 1 = -2
-2 * x = -2x
Putting it all together, we get:
x + x2 + -2 + -2x = x2 + -x + -2 ( x + -2x = -x)
Polynomial Division:
Adding/Subtracting polynomials:
To add polynomials we simply add any like terms together
To subtract Polynomials, first reverse the sign of each term we are subtracting (in other words turn "+" into "-", and "-" into "+"), then add as usual.
Common factors:
numbers that divide exactly into two or more numbers.
Multiplying a Monomial by a Polynomial:
What is (2x)(3x^2 + 4x + 9) ?
We use the distributive property to distribute (2x) over the longerpolynomial, then simplify the resulting terms.
(2x)(3x^2 + 4x + 9) = (2x)(3x2) + (2x)(4x) + (2x)(9) = 6x^3 + 8x^2 + 18
Multiplying two Binomials:
(x + -2) * ( 1 + x)
First, do:
x * 1 = x and
x * x = x2
Then,do
-2 * 1 = -2
-2 * x = -2x
Putting it all together, we get:
x + x2 + -2 + -2x = x2 + -x + -2 ( x + -2x = -x)
Polynomial Division: