using division find 2x-3 is a factor of 6x³+x²-19x+6 or not I just want to know wether it is factor or not i also want full explaination also
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2x-3 is a factor of 6x³+x²-19x+6
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- Using division find 2x-3 is a factor of 6x³+x²-19x+6 or use factor or remainder theorem to find if its a factor
- Whether 2x-3 is a factor of 6x³+x²-19x+6 by long divison or remainder theorem or factor theorem
Let p(x)= 6x³+x²-19x+6 and f(x)= 2x-3
Remainder theorem or Factor theorem says that when p(x) is divided by f(x) then the value of x is x=3/2. So substitute the value of x in p(x)
p(x)= 6x³+x²-19x+6
p(3/2)= 6(3/2)³+(3/2)²-19(3/2)+6
p(3/2)= 6(27/8)+9/4-57/2+6
p(3/2)= 81/4+9/4-57/2+6
p(3/2)= 81+9-114+24/4
p(3/2)= 114-114/4
p(3/2)= 0/4= 0
- 2x-3)6x³+x²-19x+6(3x²+2x-2
- 6x³-9x²
- ----------------------------
- 10x²-19x
- 10x²-6x
- ----------------------------
- -4x+6
- -4x+6
- --------------------------
- 0
- ----------------------------
- As we got remainder as 0 2x-3 is a factor of 6x³+x²-19x+6
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