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Changed line(s) 138 (click to see context) from:
** Something you can understand now that will come up more in precalculus: The exponent on a variable is equal to the number of answers it will have.[[note]]More precisely: Every polynomial equation of degree n with complex number coefficients has n (complex) solutions. Solutions may repeat. This rule is also known as the ''Fundamental Theorem of Algebra''.[[/note]] X[[superscript:1]] (Or simply "X") has only one answer. X[[superscript:2]] has two answers. X[[superscript:3]] has three answers. X[[superscript:478]] has 478 answers!
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** Something you can understand now that will come up more in precalculus: The exponent on a variable is equal to the number of answers it will have.[[note]]More precisely: Every polynomial equation of degree n with complex number coefficients has n (complex) solutions. Solutions may repeat. This rule is also known as the ''Fundamental Theorem of Algebra''.Algebra'', and you will be just as confused as everyone else that you don't actually learn the "fundamental" Theorem of Algebra until after you've finished Algebra.[[/note]] X[[superscript:1]] (Or simply "X") has only one answer. X[[superscript:2]] has two answers. X[[superscript:3]] has three answers. X[[superscript:478]] has 478 answers!
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Changed line(s) 47 (click to see context) from:
** "Where will this come in handy?" Well, factors are the guts of numbers, and by factoring them out you can make big fat numbers smaller and easier to work with. In later algebra you'll also learn that equations can be factored in the same way to make them easier to answer.
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** "Where will this come in handy?" Well, factors are the guts of numbers, and by factoring them out you can make big fat numbers smaller and easier to work with. In later algebra you'll also learn that equations can be factored in the same way to make them easier to answer. Hate fractions? Factors will become your very best friend.
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** "Where will this come in handy?" Well, factors are the guts of numbers, and by factoring them out you can make big fat numbers smaller and easier to work with. In later algebra you'll also learn that equations can be factored in the same way to make them easier to answer.
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Changed line(s) 143 (click to see context) from:
* '''Imaginary numbers''' begin to appear here, as there's no reason to take the square root of -1 in a basic math class. They're denoted by the letter "i", mean "the square root of -1", and are actual numbers, [[NonIndicativeName not imaginary]]. Think of them as the "guts" of numbers -- you'll come across them as you pull numbers apart but they'll sort out before the answer when you put the numbers back together. In regular-old algebra unless you're studying '''complex numbers'''[[note]]numbers with imaginary numbers added or subtracted from them; (3+i) would be one example.[[/note]] or have a parabola which doesn't cross the x-axis, your final answer will have no imaginary numbers in it.
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* '''Imaginary numbers''' begin to appear here, as there's no reason to take the square root of -1 in a basic math class. They're denoted by the letter "i", mean "the square root of -1", and are actual numbers, [[NonIndicativeName not imaginary]].imaginary]][[note]]In basic mathematics, it's impossible to squareroot a negative number since multiplying any number by itself gives a positive answer. One day, a mathematician basically went "Okay, but what if there was such a thing?", hence "Imaginary". [[YourMindMakesItReal But as it turns out, this impossible number has many mathematical uses and is key to understanding things like electrical currents.]][[/note]]. Think of them as the "guts" of numbers -- you'll come across them as you pull numbers apart but they'll sort out before the answer when you put the numbers back together. In regular-old algebra unless you're studying '''complex numbers'''[[note]]numbers with imaginary numbers added or subtracted from them; (3+i) would be one example.[[/note]] or have a parabola which doesn't cross the x-axis, your final answer will have no imaginary numbers in it.
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Spelling/grammar fix(es)
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** Important: Always make sure all variables representing a letter mean one variable. If you've found X equals 7, then ''every X in that problem must equal 7''. Use other letters if you need to represent other numbers.
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** Important: Always When using letters as variables, always make sure all variables representing a instances of that letter mean one variable. only ever represent the same variable. If you've found X equals 7, then ''every X in that problem must equal 7''. Use other letters if you need to represent other numbers.
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*** If you've every heard someone mumble or say "Please Excuse My Dear Aunt Sally", it's a mnemonic to remember PEMDAS.
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*** If you've every ever heard someone mumble or say "Please Excuse My Dear Aunt Sally", it's a mnemonic to remember PEMDAS.
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** '''Commutative''': You can add or multiply in any order you want, but still following the order of operations[[note]]multiplication comes before addition[[/note]].
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** '''Commutative''': You can add or multiply in any order As long as you want, but still following follow the order of operations[[note]]multiplication comes before addition[[/note]].addition[[/note]], you can add numbers in any order or multiply them in any order you want. 2 + 7 will equal 7 + 2, and 2 x 7 is the same as 7 x 2.
