Is synthetic division the same as polynomial division?

Mathematics

1 answer:

Elena-2011 [213]1 year ago

8 0

The synthetic division is not same as the polynomial long division.

Given:

Let's take a polynomial function f(x) = $x^3+2x^2-5x-6$ divided by x-2.

Using synthetic divison:

2 1 2 -5 -6

0 2 8 6

1 4 3 0

(x-2)(x^2+4x+3)

= (x-2)(x+3)(x+1)

Polynomial long division:

x-2) $x^3+2x^2-5x-6$ (x^2+4x+3

x^3- 2x^2

4x^2 - 5x + 6

4x^2 - 8x

3x + 6

3x - 6

=(x-2)(x^2+4x+3)

Learn more about the division here:

brainly.com/question/21416852

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2/x-5=4x<br><br> What is the value of x

kati45 [8]

Answer:

$\large\boxed{x=\dfrac{5\pm3\sqrt3}{2}}$

Step-by-step explanation:

$Domain:\ x-5\neq0\to x\neq5\\\\\dfrac{2}{x-5}=4x\\\\\dfrac{2}{x-5}=\dfrac{4x}{1}\qquad\text{cross multiply}\\\\(4x)(x-5)=(2)(1)\qquad\text{use the distributive property}\\\\(4x)(x)+(4x)(-5)=2\\\\4x^2-20x=2\\\\2^2x^2-20x=2\\\\(2x)^2-2(2x)(5)=2\qquad\text{add}\ 5^2\ \text{to both sides}\\\\(2x)^2-2(2x)(5)+5^2=2+5^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\(2x-5)^2=2+25\\\\(2x-5)^2=27\to2x-5=\pm\sqrt{27}\qquad\text{add 5 to both sides}$

$2x=5\pm\sqrt{9\cdot3}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\2x=5\pm\sqrt9\cdot\sqrt3\\\\2x=5\pm3\sqrt3\qquad\text{divide both sides by 2}\\\\x=\dfrac{5\pm3\sqrt3}{2}$