burhan101
When polynomial mx³-3x²+nx+2 is divided by x+3, the remainder is -1. When it is divided by x-2, the remainder is -4. Determine the values of 'm' and 'n'.
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helder_edwin
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use synthetic division
lgbasallote
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are you familiar with the remainder theorem?
helder_edwin
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that's better. sorry
burhan101
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burhan101
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and yes i am familiar with the remainder theorem, am i doing this right so far ?
lgbasallote
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yup
lgbasallote
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now...just add 1 to both sides...to get something fun
burhan101
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lgbasallote
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right to..add 4 to both sides there
lgbasallote
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too*
burhan101
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burhan101
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now i dont know what to do next
lgbasallote
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yes. now simplify those
lgbasallote
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-27m -3n - 24 = 0
everything is divisible by 3
lgbasallote
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8m + 2n - 6 = 0
everything is divisible by 2
burhan101
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burhan101
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like that ?
burhan101
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or with the coeff
lgbasallote
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right
lgbasallote
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-9m - n - 8 = 0
4m + n - 3 = 0
now you can do system of linear eqn
burhan101
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i can let is equal any number right ?
lgbasallote
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yes. you can also do elimination
burhan101
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let m=1
-9(1)-n-8=0
-9-n-8=0
-n=9+8
n=17
subst. n=17 in 2nd equation
4m+17-3=0
4m+14=0
m= -7/2
lgbasallote
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that's an unorthodox method...
lgbasallote
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where did you learn that?
burhan101
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i dont know, i think im confusing it with something else
lgbasallote
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it's the plotting of points method...it doesn't work here lol
burhan101
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oh woops !
lgbasallote
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anyway...
-9m - n - 8 = 0
4m + n - 3 = 0
try adding the equations...what do you get?
burhan101
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m= -11/5
burhan101
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and now subst
lgbasallote
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right
burhan101
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n=29/5
lgbasallote
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right. so there you go
burhan101
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thank you so much ! :)
lgbasallote
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welcome