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F.O.I.L.
Quadratics
Factoring and Using Discriminant
Adding/Subtracting Polynomials
Special Products
100
What do the letters in F.O.I.L. stand for?
F - First O- Outer I - Inner L - Last (4x-2) * (3x-2) The F.O.I.L. method is useful for multiplying two binomials.]. You take the first term from each binomial (in this case 4x and 3x) and multiply them together first. Then you take the outer terms (in this case 4x and -2) and multiply them together as well. After this you multiply the inner terms (in this case -2 and 3x). And finally you multiply the last terms in each binomial ( -2 and -2). This gives you a simplification of : 12x²-14x+4.
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What is the Quadratic formula?
http://i1040.photobucket.com/albums/b408/mathproject5/Quad.png
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What is the discriminant?
Answer: b² - 4(a)(c) Remember: This is the equation under the radical sign in the quadratic formula.
100
Add: (2x² + x – 5) + (x + x² +6)
Answer: 3x² + 2x + 1
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Factor: (a+b)(a-b)
Answer: a²-b²
200
Find the roots of the equation: x² + 2x − 8
Answer: −4 and 2
200
Solve using the quadratic equation Y²+11+10
-10,-1
200
Factor the equation: x² - 9x + 20
Answer: (x - 4)(x - 5)
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Subtract: (x² – 8) – (7x + 4x²)
Answer: -3x² -7x - 8
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Factor: a²+2ab+b²
Answer: (a+b)²
300
Find Roots, X- Intercepts, Zeros, and Solutions of this equation: 2x² + 7x - 15 = 0
Answer: (x= -5) (x= 3/2) Remember: roots, x-intercepts, zeros, and solutions are all different words for the same thing.
300
Solve Using graphing -x²+3x+4=0
x=1 and x=4 Graph: http://i1040.photobucket.com/albums/b408/mathproject5/200points.png
300
Use the discriminant to check how many solutions this equation has and whether or not it is factorable: x² + 2x + 1
Answer: The discriminant equals 0, so there is 1 real solution Remember: If the discriminant equals 0, there is ONE real solution. If it equals a positive number there are TWO real solutions. If it equals a negative number there are NO real solutions. Also, the equation is only factorable if the discriminant equals a PERFECT SQUARE.
300
Subtract: (3x² - 5x + 3) – (2x² – x - 4)
Answer: x² - 4x + 7
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Factor: x² - 12x + 36
Answer: (x - 6)²
400
Use the F.O.I.L. method to simplify this equation: (3+7x)(6+2x)
You should have gone through this process: 18 → 18+6x → 18+6x+42x → 18+6x+42x+14x² → FINAL ANSWER: 18+48x+14x2
400
Solve using graphing -7x-21x-14
x=-1 and x=-2 Graph: http://i1040.photobucket.com/albums/b408/mathproject5/300points.png
400
Factor this equation completely: 3m³ - 15m² - 6m + 30 *Make sure to take out the GCF*
Answer: 3(m² - 2)(m - 5) GCF: 3 Remember: A good way to start solving a problem like this is to group the terms into pairs like so: (3m³ - 15m²)(-6m + 30)
400
Add: (5x³ – x + 2x² + 7) + (3x² + 7 – 4x) + (4x² – 8 – x³)
Answer: 4x³ + 9x² – 5x + 6
400
Factor: 50 - 98x²
Answer: 2(5 + 7x)(5 - 7x)
500
Find the x-intercepts of the equation: 8x³ - 18x = 0
Answer: x = 0 x = 3/2 x = -3/2
500
4x²-13x+3=0
X=3 and X=1/4
500
Factor: 2x² + 7x + 3
Answer: (2x+1)(x+3)
500
Subtract: (-2x³ + 5x² – x + 8) – (-2x³ + 3x - 4 )
Answer: 5x² – 4x + 12
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Factor: 16y² + 24y + 9
Answer: (4y + 3)²