Question

divide x3-3√5x2-5x+15√5 by x-√5​

Answer 1

Answer:

(x -3)(x + √5)

Step-by-step explanation:

Let's regroup and factorize it first:

x³-3√5x²-5x+15√5= x³-√5x²-2√5x² + 10x- 15x + 15√5 =

= x²(x -√5) -2√5x (x - √5) - 15(x - √5)= (x² - 2√5x - 15)(x - √5)

= (x² +√5x - 3√5x - 15)(x - √5) = (x (x + √5) -3(x + √5))(x - √5)

= (x -3)(x + √5)(x - √5)

So, it has 3 factors:

x3-3√5x2-5x+15√5 = (x -3)(x + √5)(x - √5)

And we divide it:

(x3-3√5x2-5x+15√5) : (x-√5) = ​(x -3)(x + √5)

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