How do you divide #(25x^2-30x+12) div (5x-3)#?

Answer 1

#=5x-3#

#=21#

Give -

#(25x^2-30x+12) -:(5x-3)#

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Answer 2

#5x-3+3/(5x-3)#

#"one way is to use the divisor as a factor in the numerator"#
#"consider the numerator"#
#color(red)(5x)(5x-3)color(magenta)(+15x)-30x+12#
#=color(red)(5x)(5x-3)color(red)(-3)(5x-3)color(magenta)(-9)+12#
#=color(red)(5x)(5x-3)color(red)(-3)(5x-3)+3#
#"quotient "=color(red)(5x-3)," remainder "=3#
#rArr(25x^2-30x+12)/(5x-3)=5x-3+3/(5x-3)#
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Answer 3

To divide (25x^2-30x+12) by (5x-3), you can use long division or synthetic division. Here is the step-by-step process using long division:

  1. Divide the first term of the dividend (25x^2) by the first term of the divisor (5x). The result is 5x.
  2. Multiply the entire divisor (5x-3) by the quotient obtained in step 1 (5x). The result is 25x^2 - 15x.
  3. Subtract the result obtained in step 2 from the dividend (25x^2-30x+12) to get the new dividend: -15x + 12.
  4. Bring down the next term from the original dividend (-15x) and divide it by the first term of the divisor (5x). The result is -3.
  5. Multiply the entire divisor (5x-3) by the quotient obtained in step 4 (-3). The result is -15x + 9.
  6. Subtract the result obtained in step 5 from the new dividend (-15x + 12) to get the new dividend: 3.
  7. Since the new dividend (3) is a constant term and has a degree lower than the divisor (5x-3), the division process is complete.

Therefore, the quotient is 5x - 3 and the remainder is 3.

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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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