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Scientific Notation and GCF
Binomials
Trinomials
4 term polynomials
Exponent Rules
100
Write 0.000052 in scientific notation.
5.3*10^-5
100
Factor x^2 - 9
(x-3)(x+3)
100
Make the complete product sum table for 2x^2 - 11x - 6
a = 2, b = -11, c = -6 So a*c = 2*-6 = -12 (put top of 1st column) b = -11 (put top of 2nd column) -12 | -11 ___________ 1* -12| 1+ -12 = -11 2* -6 | 2 + -6 = -4 3* -4 | 3 + -4 = -1 Note: since -12 is neg need 1 neg and 1 positive Since -11 is negative, the larger is negative. Note 2: We would pick 1 and -12 Giving 2x^2 + x - 12x - 6 which we could now group.
100
Factor x^3 + x^2 + x + 1
(x^3 + x^2) + (x + 1) GROUP x^2 (x + 1) + 1(x + 1) Pull out GCF of each group =(x+1)(x^2 + 1) Note x^2 + 1 is Prime, so we are done.
100
x^5 * x^-2
x^3
200
Multiply 3*10^105 times 4*10^2
1.2*10^108 WHY? =12*10^(105+2) =12*10^107 (NOT SCIENTIFIC NOTATION) --> 12 = 1.2*10^1 -->1.2*10^1*10^107 -->1.2*10^108
200
Factor 4x^4 - 9
(2x^2 - 3)(2x^2 + 3)
200
Factor x^2 + 5x - 14
(x - 2)(x+7)
200
Factor x^3 + 3x^2 - 2x - 6
(x^3 + 3x^2) + (-2x - 6) GROUP x^2(x + 3) - 2(x + 3) Factor GCF of each pair = (x+3)(x^2 - 2) Note: (x^2 - 2) is prime so we are done.
200
x^7 / x^ -2
x ^ 9 WHY??? 9 = 7 - (-2)
300
Factor out the GCF 3x - 6
GCF = 3 3(x - 2)
300
Factor 3x^3 - 3x
3x (x^2 - 1) which factors to: 3x(x-1)(x+1)
300
Factor 3x^2 - 5x - 2
(x-2)(3x + 1) Why? a*c = 3*-2 = -6 b = -5 So the numbers we want are -6 and 1 3x^2 - 5x - 2 3x^2 - 6x + x - 2 (3x^2 - 6x) + (x - 2) 3x(x - 2) + 1(x - 2) (x-2)(3x + 1)
300
Factor completely x^3 + 3x^2 - x - 3
(x^3 + 3x^2) + (-x - 3) GROUP x^2 (x + 3) - 1(x + 3) Factor out GCF of each pair. (x+ 3) (x^2 - 1) (x^2 - 1) is difference of squares --> =(x+3)(x-1)(x+1)
300
(x^3)^2
x^6
400
Factor out the NEGATIVE GCF -4x^2 - 16x Read x^2 as x squared.
-4x(x+4)
400
Factor x^2 + 1
PRIME
400
20x^4 + 18x^2 + 4
2(5x^2 + 2)(2x^2 + 1) WHY? 2(10x^4 + 9x^2 + 2) a*c = 20 b = 9 so get numbers 4 and 5 10x^4 + 9x^2 + 2 --> 10x^4 + 4x^2 + 5x^2 + 2 (10x^4 + 4x^2) + (5x^2 + 2) 2x^2(5x^2 + 2) + 1(5x^2 + 2) (5x^2 + 2)(2x^2 + 1) So we get 2(5x^2 + 2)(2x^2 + 1)
400
Factor completely: 4x^4 + 8x^3 - 6x^2 - 12x
2x(x+2)(2x^2 - 3) Why? GCF = 2x 2x(2x^3 + 4x^2 - 3x - 6) Then group: To factor 2x^3 + 4x^2 - 3x - 6 (2x^3 + 4x^2) + (-3x - 6) 2x^2(x+2) - 3(x + 2) --> (x+2)(2x^2 - 3) 2x^2 - 3 is PRIME SO the final answer is 2x(x+2)(2x^2 - 3) DONT LOSE THE GCF!!!!
400
-3x^0
-3
500
Factor out a GCF. Then factor completely. -3x^2 + 12
-3 (x^2 - 4) --> -3 (x - 2)(x+2)
500
Factor x^4 - 1
(x^2 - 1)(x^2 + 1). Then x^2 - 1 is still difference of squares. so you get (x - 1)(x + 1)(x^2 + 1)
500
Factor 4x^4 +7x^2 - 36
(x^2 + 4)(2x-3)(2x+3) Why? No GCF: 4* - 36 = -144 b = 7 so using the product sum table I get 16 and -9 4x^4 + 16x^2 - 9x^2 - 36 (4x^4 + 16x^2) + (-9x^2 - 36) 4x^2 (x^2 + 4) - 9(x^2 + 4) (x^2 + 4)(4x^2 - 9) Now, x^2 + 4 (SUM) is prime, x^2 - 9 is difference of squares. --> (x^2 + 4)(2x-3)(2x+3)
500
Factor completely: -x^4 + 3x^3 + 4x^2 - 12x
-x (x-3)(x-2)(x+2) WHY? GCF = -x: -x(x^3 - 3x^2 - 4x + 12) Now factor x^3 - 3x^2 - 4x + 12: (x^3 - 3x^2) + (-4x + 12) = x^2 (x - 3) - 4(x-3) = (x-3) (x^2 - 4) BUT x^2 - 4 is difference of squares = (x-2)(x+2) So we get -x (x-3)(x-2)(x+2) when we put it all together.
500
Write without negative exponents: -3y^-3
-3/y^3