How do you divide #(2x^3-5x^2+4x+12)/(x-7) #?

Answer 1

#color(blue)(2x^2+9x+67# plus remainder of #color(blue)481#

# color(white)(.............)ul(color(blue)(2x^2+9x+67)# #color(white)(aa)x-7##|##2x^3-5x^2+4x+12# #color(white)(..............)ul(2x^3-14x^3)# #color(white)(........................)9x^2+4x# #color(white)(........................)ul(9x^2-63x)# #color(white)(..............................)67x+12# #color(white)(..............................)ul(67x-469)# #color(white)(........................................)481#
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Answer 2

#2x^2+9x+67+481/(x-7)#

#"one way is to use the divisor as a factor in the numerator"#
#"consider the numerator"#
#color(red)(2x^2)(x-7)color(magenta)(+14x^2)-5x^2+4x+12#
#=color(red)(2x^2)(x-7)color(red)(+9x)(x-7)color(magenta)(+63x)+4x+12#
#=color(red)(2x^2)(x-7)color(red)(+9x)(x-7)color(red)(+67)(x-7)color(magenta)(+469)+12#
#=color(red)(2x^2)(x-7)color(red)(+9x)(x-7)color(red)(+67)(x-7)+481#
#"quotient "=color(red)(2x^2+9x+67)", remainder "=481#
#rArr(2x^3-5x^2+4x+12)/(x-7)#
#=2x^2+9x+67+481/(x-7)#
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Answer 3

To divide (2x^3-5x^2+4x+12) by (x-7), you can use long division or synthetic division. Here is the solution using long division:

     2x^2 + 9x + 67
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x - 7 | 2x^3 - 5x^2 + 4x + 12 - (2x^3 - 14x^2) ------------------- 9x^2 + 4x - (9x^2 - 63x) --------------- 67x + 12 - (67x - 469) -------------- 481

Therefore, the quotient is 2x^2 + 9x + 67 and the remainder is 481.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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