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Algebra, Trig
Perform the indicated operation and simplify completely: (x + 10)(x^2 + 9x - 8)
(x + 10)(x^2 + 9x - 8) = x^3 + 9x^2 -- 8x + 10x^2 + 90x -- 80 = x^3 + 19x^2 +82x --
Perform the indicated operation and simplify completely:
(5x + 5) / (5x + 9) + (5x + 13) / (5x+9)
(5x + 5) / (5x + 9) + (5x + 13) / (5x+9) = (5x + 5 + 5x + 13) / (5x + 9)
= (10x + 18) / (5x + 9) = 2(5x + 9) / (5x + 9) = 2
Perform the indicated operation and simplify completely:
(8x^6 + 7x^3 + 3x) + (3x^6+5x^3 -5x)
(8x^6 + 7x^3 + 3x) + (3x^6+5x^3 -5x) = 8x^6 + 7x^3 + 3x + 3x^6 + 5x^3 -- 5x
= 11x^6 + 12x^3 -- 2x
Perform the indicated operation and simplify completely: (x - 3)^
3)^3 = (x -- 3)(x -- 3)(x -- 3) = (x^2 -- 3x -- 3x + 9)(x -- 3) = (x^2 -- 6x + 9)(x -- 3)
= x^3 -- 3x^2 -- 6x^2 + 18x + 9x -- 27 = x^3 -- 9x^2 + 27x -
Factor: 4x^2-9y^2 completely
4x^2 -- 9y^2 = (2x + 3y)(2x -- 3y)
Factor: 4x - 40 completely
4x -- 40 = 4(x -- 10)
Perform the indicated operation and simplify completely: (x + 11)(x -11)
(x + 11)(x -11) = x^2 + 11x -- 11x -- 121 = x^2 -- 121
8. Perform the indicated operation and simplify completely:
(x^3 + 3xy - 8y^2) - (6x^3 + 8xy + y^2)
(x^3 + 3xy - 8y^2) - (6x^3 + 8xy + y^2) = x^3 + 3xy -- 8y^2 -- 6x^3 -- 8xy -- y^2
= -5x^3 -- 5xy -- 9y^2
9. Perform the indicated operation and simplify completely:
[2x / (4x + 2)] * [(6x + 3) / 5)]
[2x / (4x + 2)] * [(6x + 3) / 5)] = (12x^2 + 6x) / (20x + 10) = [6x (2x + 1)] / [10(2x + 1)]
= 6x / 10 = 2(3x) / 2(5) = 3x / 5
10. Factor: x (x + 12) + 11(x + 12) completely x (x + 12) + 11(x + 12) = (x + 11)(x + 12)
11. Factor: x^2 + 10x + 21 completely x^2 + 10x + 21 = (x + 7)(x + 3)
12. Perform the indicated operation and simplify completely: (x-2)^2
(x -- 2)^2 = x^2 -- 2x -- 2x + 4 = x^2 -- 4x + 4
13. Perform the indicated operation and simplify completely: (4x -9)(x - 10)
(4x -- 9)(x -- 10) = 4x^2 -- 9x -- 40x + 90 = 4x^2 -- 49x + 90
14. Factor: x^2-8x + 16 completely:
x^2 -- 8x + 16 = (x -- 4)^2
15. Perform the indicated operation and simplify completely: (x - 4y)(5x - 9y)
(x -- 4y)(5x -- 9y) = 5x^2 -- 9xy -- 20xy + 36y^2 = 5x^2 -- 29xy + 36y^2
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By observing x on the graph, then we make the connection that the slope of x on the graph represents rate of change of the linear function. Once we have done this, it is then possible to move to the development of a quadratic equation and see what the impact of the increase (or perhaps decrease) means to the data. Have we proven that the rate of change is linear?
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