To divide the polynomial [tex]6x^2+11x-3[/tex] by the polynomial [tex]2x-1,[/tex] you have to do such steps:
1 step. Multiply the polynomial [tex]2x-1[/tex] by [tex]3x[/tex]. You get the polynomial [tex]6x^2-3x.[/tex]
2 step. Subtract the polynomial [tex]6x^2-3x[/tex] fro mthe polynomial [tex]6x^2+11x-3:[/tex]
[tex]6x^2+11x-3-(6x^2-3x)=6x^2+11x-3-6x^2+3x=14x-3.[/tex]
Step 3. Multiply the polynomial [tex]2x-1[/tex] by [tex]7[/tex] to get the polynomial [tex]14x-7.[/tex]
Step 4. Subtract the polynomial [tex]14x-7[/tex] from the polynomial [tex]14x-3:[/tex]
[tex]14x-3-(14x-7)=14x-3-14x+7=4.[/tex]
Step 5. Write the division result:
[tex]6x^2+11x-3=(2x-1)(3x+7)+4.[/tex]
Here the quotient is the polynomial [tex]3x+7[/tex] and the remainder is the polynomial [tex]4.[/tex]
Answer: the remainder is 4.
Answer:
-1
Step-by-step explanation:
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