How do you divide #(x^2+20x+5) / (x-4)#?

Answer 1

Quotient #color(green)(x + 24)#, Remainder #color(red)(101/(x-4))#

Let's calculate the remainder and quotient using synthetic division.

#color(white)(aaa aaa aa aaa) 0 color(white)(aaa aa ) 1 color(white)(aaa a ) 24 # # color(white)(aaa aaa aa ) ———————- # # color(white)(aaa ) 4 color(white)(aaa ) | color(white)(aaa ) 1 color(white)(aaaa) 20 color(white)(a aaa) 5 # # color(white)(aaa aaaa ) | color(white)(aa ) darr color(white)(aaa a ) 4 color(white)(aaaa) 96 # # color(white)(aaa aaa a) | color(white)(aaa ) ——- ——- # #color(white)(aaa aaa aaa aaa ) 1 color(white)(aa aa ) 24 color(white)(aaa) 101 #
Quotient #color(green)(x + 24)#, Remainder #color(red)(101/(x-4))#
Verification : #(x + 24) * (x - 4) = x^2 + 20x -94 + 101 = x^2 + 20x + 5#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To divide (x^2+20x+5) by (x-4), you can use long division or synthetic division. Here is the solution using long division:

Step 1: Divide x^2 by x, which gives x. Write x above the line. Step 2: Multiply (x-4) by x, which gives x^2-4x. Subtract this from (x^2+20x+5) to get 24x+5. Write this below the line. Step 3: Bring down the next term, which is 24x. Step 4: Divide 24x by x, which gives 24. Write 24 above the line. Step 5: Multiply (x-4) by 24, which gives 24x-96. Subtract this from 24x+5 to get 101. Write this below the line. Step 6: Since there are no more terms to bring down, the division is complete. Step 7: The quotient is x+24 and the remainder is 101.

Therefore, (x^2+20x+5) divided by (x-4) equals x+24 with a remainder of 101.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
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.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7