All about Polynomials
What are like terms?
Terms with exactly the same variable part (variable and exponent the same.)
Add the Polynomials
(4x + 9) +(x - 4)
5x + 5
Multiply the Polynomials:
3x2 (2x4)
6x6
Multiply the polynomials:
(a + 5)(a - 5)
a2 - 25
What is the number in front of the variable in a term, called?
Coefficient
When adding polynomials, what do the exponents do?
Remain the same.
Subtract the polynomials:
(-5h - 2) - (7h +6)
-12h - 8
Multiply the Polynomials:
3(2x + 4x2 - 5)
12x2 + 6x - 15
What results in the trinomial a2 + 2ab + b2?
(a + b)2
What do we use the FOIL method?
When multiplying two binomials
When multiplying polynomials, what do the exponents do?
Exponents add.
Add the polynomials:
(x2 +3x + 5) + ( -x2 +6x)
9x + 5
Multiply the Polynomials:
(x - 1)(−8x2 − 6x − 12 )
-8x3 - 6x2 - 12x + 8x2 + 6x + 12
-8x3 + 2x2 - 6x + 12 (Correct Answer)
Is 9x - 16 a difference of squares?
No.
But 9x2 - 16 is because = (3x + 4)(3x - 4).
When do we add exponents?
When we multiply polynomials.
A polynomial with 1 term is called:
Monomial.
Subtract the Polynomials:
(2x - 3x) - (x2 -2x + 4)
-x2 + x - 4
Multiply the Polynomials:
(x-2)(x+6)
x2+4x-12
What is (2x - 7)2?
4x2 - 28x +49
What is missing in this multiplication?
(3x2 - 5)( _____ ) = 9x4 - 25
3x2 + 5
A polynomial with 2 terms is called:
Binomial
Add the polynomials:
(-1 + x2 + 2x) + (1 -2x + 2x2)
3x2
Multiply the Polynomials:
(3x-6)(5x+3)
15x2-21x-18
What is (3x3 - 2y)2?
9x6 - 12x3y + 4y2
When do we subtract exponents?
When we divide polynomials.
A polynomial with 3 terms is called:
Trinomial
Subtract the Polynomials:
(k2 + 6k3 -4) - (5k3 + 7k -3k2)
k3 + 4k2 -7k -4
Multiply the following polynomials
(3x+ 5)2
9x2 + 30x + 25
Subtract the following polynomials
(3 - 6x5 - 8x4) - (-6x4 - 3x - 8x5)
2x5 - 2x4 + 3x + 3
What is missing in this multiplication?
(2x - 3)( _____ ) = 8x2 + 2x -21
4x + 7