Adding Polynomials
Subtracting Polynomials
Multiplying Polynomials
Dividing Polynomials
Rational and Irrational Numbers
100
Simplify
(5x4 – 3x2 + 4) + (6x3 – 4x2 – 7)
Final Solution
100
(2r2+3r+9) - (2r+1)
2r2+r+8
100
(t+1)2
t2+2t+1
100
( - 4z5–7z4–8z3)÷z2
-4z3-7z2-8z
100
numbers that cannot be written as a ratio of two integers are called _______.
Irrational numbers
200
(4s+3)+(s+6)
5s+9
200
(6t^2+5t+3)–(4t^2+t)
2t2+4t+3
200
v2(4v2+9)
4v 4+9v2
200
(9k4–10k3–10k2)÷k
9k3-10k2-10k
200
1,2,3,4,5...
-1,-2,-3,-4,-5...
1.5,1.67,67.1,111110.2,14536484830.98
These are examples of what?
Rational Numbers
300
(6m+8)+(3m+4)
9m+12
300
(7k2+7)–(5k2+4)
2k2+3
300
(2r–2)(3r+4)
6r2+2r-8
300
( - 7q6+4q5–7q4)÷q3
-7q3+4q2-7q
300
The sum of two rational numbers is ________. Why?
RATIONAL
Explanation: Adding two rationals is the same as adding two such fractions, which will result in another fraction of this same form since integers are closed under addition and multiplication.
400
(6m+1)+(9m2+6m)
9m2+12m+1
400
(6k2+4k+3)–(k+2)
6k2+3k+1
400
- x2( - 4x2–2x–1)
4x4+2x3+x2
400
( - d4+6d3+2d2)÷d
-d3+6d2+2d
400
The sum or product of a rational and irrational number is ___________.
IRRATIONAL
Explanation: So, adding a rational and an irrational number is the same as adding two such fractions, which will result in another fraction of this same form since integers are closed under addition and multiplication.
500
(6u+6)+(u+9)
7u+15
500
(7y2+4y+2)–(7y2+2)
4y
500
(4t–2)(2t2–t–4)
8t3-8t2-14t+8
500
( - 7q4–13q3–5q2)÷q
-7q3-13q2-5q
500
The product of a nonzero rational number and an irrational number is _________.
If you multiply any irrational number by the rational number zero, the result will be zero, which is rational. Any other situation (nonzero numbers), however, of a rational multiplied by an irrational number will be irrational.