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.
After distributing, what does the 2nd binomial become?
(k3 + 4k) - (4k - 3k3)
-4k + 3k3
When multiplying polynomials, what do you do with the coefficients?
Multiply them
Multiply:
(x - 4)2
x2 - 8x +16
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
Multiply:
(p + 5)(p - 5)
p2 - 25
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 difference between a MONOMIAL and a POLYNOMIAL?
Monomial is one term with no plus or minus signs.
Polynomials are monomials with plus and/or minus signs.
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 degree of the polynomial?
2x4y7z + 4x3y5z2 - 2x2y2z2
12th degree
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
Multiply:
(2x - 5)(2x2 + 2x - 4)
4x3 - 6x2 - 18x + 20