Polynomials in General
Which part of term will tell you the degree of the term?
The exponent
When adding polynomials, you have to combine like terms. What two things make terms "like terms"?
Same variable raised to the same power.
When "adding the opposite" what would happen to the values in the second polynomial?
(k3 + 4k) - (4k - 3k3)
(-4k + 3k3)
When multiplying polynomials, what do you do with the coefficients?
Multiply them
In general, what is the greatest common factor of two or more numbers?
Write the exponent in standard form:
-4x + 3x6 - 17x5 + 6 - x7
-x7 + 3x6 - 17x5 - 4x +6
Identify the like terms in the polynomial addition:
(3x3 + 2x - 6) + (2x2 -4x + 10)
-4x and 2x
-6 and 10
like terms
When multiplying polynomials, what do you do with the exponents?
add them
What is the greatest common factor of 24, 72, and 88?
8
What do you call polynomials with 1, 2, and 3 terms?
monomial, binomial, trinomial
Complete the polynomial addition:
(3x3 + 2x - 6) + (2x2 -4x + 10)
3x3 + 2x2 - 2x + 4
Subtract the polynomials:
(k3 + 4k) - (4k - 3k3)
4k3
Multiply the polynomials:
7x2(5x - 1)
35x3 - 7x2
What is the greatest common factor of x4, x5, and x2?
x2
What do you call polynomials to the first, second, and third degree?
linear, quadratic, cubic
Add the polynomials:
(-4x4 - 3x) + (4x4 + 6x)
6x
Subtract the polynomials:
(4 + 6v2) - (5v2 + 1)
v2 + 3
Multiply the polynomials:
(5a - 5)(4a - 5)
20a2 - 45a + 25
What is the greatest common factor of the polynomial:
40p7 + 5p3 - 50p2
5p2
Name the polynomial according to its degree and number of terms:
3x3 + 4x
cubic binomial
Add the polynomials:
(6x2 + 8x4) + (7x4 - 5x2)
15x4 + x2
Subtract the polynomials:
(3n + 8n2) - (5n2 - 4n)
3n2 + 7n
Multiply the polynomials:
(n - 4)(3n2 + 3n - 5)
3n3 - 9n2 - 17n + 20
Find the greatest common factor, then factor it out of the polynomial:
12x2 + 3x + 15
(3)(4x2 + r + 5)