Polynomials
(3x+5) + (4x+1)
what is 7x+6?
(3x+4x)+(5+1)
(3+4)x+(5+1)
7x+(5+1)
=7x+6
√45, simplify
What is 3√5?
find a square number that goes into 45 (9)
9*5, break it down to 3*3*5
so you get 32*5
square √32*5 and you get:
3√5
(205, 637) Find the range
What is 637?
(hint: what is y?)
12a-4b
What is 4(3a-b)?
Find the GCF (4) and then simplify
12/4 and 4/4
3 and 1
so:
= 4(3a-b)
√10*√30, multiply
What is 10√3?
multiply: 10*30 = √300
simplify 300: 10√3
= 10√3
2x-2
What is 2(x-1)
2x-2 (Find the GCF: Divide by 2)
=2(x-1)
√125+√5 (simplify the product)
What is 5√5+√5?
find a square number that goes into 125 (25)
√25*5+√5
Square the numbers
= 5√5+5 (or 6√5)
(2, 8), (7, 2), (107, 91), (1, 4) Find domains
What is 2, 7, 107, 1?
(hint: what is x?)
(x-7)(x+2)
What is x2-5x-14?
Distribute (x+2)
x(x+2)-7(x+2)
Simplify
(x2+2x)+(-7x-14)
The final answer
= x2-5x-14
√98, simplify
What is 7√2?
find prime factors: √2*7*7
simplify to: √49*2
solve: = 7√2
6(x+12)
What is 6x+72?
Distribute 6: into x, and into 12
6*x, 6*12
= 6x+72
√3*√27, simplify
What is 9?
multiply 3 and 27 to make a square number (81)
9 times 9 is 81 (92)
square 92 and you get
= 9
(10, 4) (56, 4) (4, 5) (7, 37) (942, 78) Find ranges
What is 4, 4, 5, 37, 78?
x2 + 12x + 20
What is (x+10) (x+2)?
Factor: what adds to 12, and multiples to 20?
10, and 2
both will be positive, and use (a+b)(a+b) we get:
(x+10)(x+2)
√54/24, simplify
What is 3/2? (or 1.5)
Simplify 54 to 9 and 24 to 4
√9 = 3, √4 =2
so: = 3/2
x2 - 81
what is (x - 9) (x + 9)?
Use difference of squares:
(a+b)(a-b)
= (x+9) (x-9)
√584, Simplify
What is 2√146?
Find a square number that get go into 584 (4)
4*2*73
Square it
2√2*73
simplify
2√146
(0,4)(12,6)(65,9) Find domains, and if it is a function or not
What is 0, 12, 65 and not a function?
(5x-3) + (4x+7) + (2x-6)
What is 11x-2?
Combine like terms:
5x+4x+2x, and -3+7-6
simplify the 2 groups:
11x, and -2
add together to make our answer:
= 11x-2
√8n*√9n multiply
What is 6√2n?
separate 8 from n √8√n√9n
simplify: √8 = 2√2 which makes 2√2√n√9n
now separate 9 from n like we did with 8n
you should simply get 3, as a 9 is a square number
so far we should be at: 2√2√n*3√n
now we can add like terms and simplify:
6√2n2, now solve √2n2 which should come out as:
= 6n√2, which is the final answer
-3(2x-6)
what is -6x+18?
Distribute the -3, into the parentheses
-3(2x)-3(-6)
-6x, -3(-6)
= -6x+18
(-√5-1)*(-√5-1), simplify
What is 6+2√5?
Use FOIL
-√5*-√5-(√5*-1)-(1*-√5)-(1*-1)
simplify
√25-(-√5)-(-√5)-(-1)
add together radicals (simplify more)
√25+2√5+1
simplify some more:
√25 = 5
5+1 = 6
final answer should be:
= 6+2√5
(96,7)(6,-61)(8,43)(-2,8) Domain + range, and if it is a function or not
What is
Domain: 96, 6, 8, -2
Range: 7, -61, 43, 8
and not a function?
(factor) 12x2-17x+6
What is (4x-3)(3x-2)?
Factor out -17 from the polynomial
sum must be -17, must multiply too 72
-8x, -9x
therefore we get:
(12x2-9x)(-8x+6)
Now we find the GCF:
3x(4x-3)-2(4x-3)
our first group is (4x-3), then we bring together the 2 GCF's 3x and -2, so the 2nd group is (3x-2)
therefore our answer is:
= (4x-3)(3x-2)
3√12/√3 Divide
What is 6?
simplify √12 into 2√3
and include 3, so 3*2√3 = 6√3
now with the top simplified we can divide
6√3/√3
rationalize and multiply each side by √3
you should get 6√3√3 / 3
simplify the top and get 6√9 (the square root of 9 is 3)
so 9*3 / 3, and multiply 9 by 3 and get 18 / 3
which = 6