Well, the school year just started and I could use a little help with some of the following.
Factor the following completely.
2x^2-5x+3
x^4+2x^3-x-2
x^8-3x^4-10
Some Precalculus Questions?
2008-08-19 3:47 pm
回答 (5)
2008-08-19 4:02 pm
✔ 最佳答案
2x² - 5x + 3( 2x - 3 )( x - 1 )
x^4 + 2x³ - x - 2
x³ ( x + 2 ) - ( x + 2 )
(x³ -1) ( x + 2)
( x + 2 ) ( x - 1) ( x² + x + 1)
x^8 - 3x^4 - 10
( x^4 + 2)( x^4 - 5 )
the second one was the one that required the most work. First factor by grouping and then use the rule for a binomial difference of cubes.
The other two were just simple factoring.
2008-08-19 5:15 pm
1)
2x^2 - 5x + 3
= 2x^2 - 2x - 3x + 3
= (2x^2 - 2x) - (3x - 3)
= 2x(x - 1) - 3(x - 1)
= (x - 1)(2x - 3)
2)
x^4 + 2x^3 - x - 2
= (x^4 + 2x^3) - (x + 2)
= x^3(x + 2) - 1(x + 2)
= (x + 2)(x^3 - 1)
3)
x^8 - 3x^4 - 10
= x^8 + 2x^4 - 5x^4 - 10
= (x^8 + 2x^4) - (5x^4 + 10)
= x^4(x^4 + 2) - 5(x^4 + 2)
= (x^4 + 2)(x^4 - 5)
2x^2 - 5x + 3
= 2x^2 - 2x - 3x + 3
= (2x^2 - 2x) - (3x - 3)
= 2x(x - 1) - 3(x - 1)
= (x - 1)(2x - 3)
2)
x^4 + 2x^3 - x - 2
= (x^4 + 2x^3) - (x + 2)
= x^3(x + 2) - 1(x + 2)
= (x + 2)(x^3 - 1)
3)
x^8 - 3x^4 - 10
= x^8 + 2x^4 - 5x^4 - 10
= (x^8 + 2x^4) - (5x^4 + 10)
= x^4(x^4 + 2) - 5(x^4 + 2)
= (x^4 + 2)(x^4 - 5)
2008-08-19 3:58 pm
x^4+2x^3-x-2
x^3(x+2)-1(x+2)
(x+2)(x^3-1)
(x+2)(x-1)(x^2+x+1)
x^3(x+2)-1(x+2)
(x+2)(x^3-1)
(x+2)(x-1)(x^2+x+1)
2008-08-19 3:55 pm
2x²-5x+3
=>2x² - 3x – 2x + 3
=> x(2x- 3) – 1 (2x – 3)
=> (x – 1)(2x-3)
x^4+2x^3-x-2
=>x^4 – x + 2x^3 - 2
=>x(x^3 - 1) + 2(x^3 – 1)
=> (x^3 – 1)(x + 2)
x^8-3x^4-10
=> x^8 – 5x^4 + 2x^4 – 10
=> x^4(x^4 – 5) + 2(x^4 – 5)
=> (x^4 – 5)(x^4 + 2)
=>2x² - 3x – 2x + 3
=> x(2x- 3) – 1 (2x – 3)
=> (x – 1)(2x-3)
x^4+2x^3-x-2
=>x^4 – x + 2x^3 - 2
=>x(x^3 - 1) + 2(x^3 – 1)
=> (x^3 – 1)(x + 2)
x^8-3x^4-10
=> x^8 – 5x^4 + 2x^4 – 10
=> x^4(x^4 – 5) + 2(x^4 – 5)
=> (x^4 – 5)(x^4 + 2)
2008-08-19 3:55 pm
the first one goes like this:
(2x -3)(x - 1)
the second:
= x^3(x + 2) - (x + 2)
= (x^3 - 1)(x + 2)
the third:
(x^4 - 5)(x^4 + 2)
(2x -3)(x - 1)
the second:
= x^3(x + 2) - (x + 2)
= (x^3 - 1)(x + 2)
the third:
(x^4 - 5)(x^4 + 2)
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