SYNTHETIC DIVISION Algebra question?

you can do the ' long division '

- 7 | 1...9...6....-65...-63

............-7..-14..56....63

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...... 1...2...-8...- 9.....0----> x^3 + 2 x² - 8 x - 9

Synthetic division focuses on the coefficients only. If you have an equation like x³ + x + 4, you would need to put in a 0 for the x² term to get the right answer. You also need to solve the term you are given for x. For example x + 7 = 0, x = -7. Now synthesize -7. I use ··· to space things out, ignore it

-7 ¦ 1 ··· 9 ··· 6 ··· -65 ··· -63

····· 0 ·· -7 · -14 ··· 56 ···· 63

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····· 1 ··· 2 ··· -8 ··· -9 ······ 0

You now take each number and drop the exponent by 1. The answer would therefore be,

x³ + 2x² - 8x - 9.

Now using the much more involved, harder, division.

······· x³ + 2x² - 8x - 9

······· ------------------------------

(x+7) | x^4 + 9x³ + 6x² - 65x - 63

(x + 7) goes into x^4, x³ times (since x³ * (x+7) = x^4 + 7x^3

Subtract the two equations

(x^4 + 9x³ + 6x² - 65x - 63) - (x^4 + 7x³)

2x³ + 6x² - 65x - 63

(x + 7) goes into 2x³, 2x² times (2x² * (x + 7) = 2x³ + 14x²

Subtract the two equations

(2x³ + 6x² - 65x - 63) - (2x³ + 14x²)

-8x² - 65x - 63

(x + 7) goes into -8x², -8x times (-8x * (x + 7) = -8x² - 56x)

Subtract the two equations

(-8x² - 65x - 63) - (-8x² - 56x)

-9x - 63

(x + 7) gos into -9x, 9 times (-9 * (x + 7) = -9x - 63

Subtract the two equations

(-9x - 63) - (-9x - 63)

0

Therefore the answer is x³ + 2x² - 8x - 9. I hope this helps. Have a good day.

synthetic division: -7 | 1 9 6 -65 -63

| -7 -14 56 63

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1 2 -8 -9 0 -> x^3 + 2x^2 -8x - 9

long division: x^3 + 2x^2

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x+7 | x^4 + 9x^3 + 6x^2 - 65x -63

x^4 +7x^3

__________

2x^3 + 6x^2

2x^3 + 14x^2 and so on

Sorry this all lines up on the entry page then yahoo munges it into a mess.

(-15x^3 - 34x^2 - 35x - 9) ÷ (5x + 3) To get our x^2 coefficient, we seem at at -15x^3 / 5x. it particularly is -3x^2. -3x^2(5x+3) = -15x^3 - 9x^2 Our quotient so a techniques is -3x^2, and we now subtract (-15x^3 - 9x^2) from our dividend: (-15x^2 - 34x^2 - 35x - 9) - (-15x^3 - 9x^2) = -25x^2 - 35x - 9 Now we seem at -25x^2 / 5x, and we get -5x. So our quotient is now -3x^2 - 5x, and we would desire to subtract (-5x)(5x+3), that's -25x^2-15x, from our dividend: (-25x^2 - 35x - 9) - (-25x^2 - 15x) = -20x - 9 Now we seem at -20x / 5x, and we get -4. So our quotient is now -3x^2 - 5x - 4, and we would desire to subtract (-4)(5x+3), that's -20x-12, from our dividend: (-20x - 9) - (-20x - 12) = 3 Hmm. We ended up with a the remainder of three. This leaves us observing a effect of: -3x^2 - 5x - 4 + 3/(5x+3)