Question

Math Help!!
When you solve (x^3 + 4x -4) / (x + 2) by long division, what is the remainder?
10
-20
-5
15

Answer 1

this would be easier with synthetic division

Answer 2

Can you show me with synthetic division then? I did it with synthetic division and I got -8. help please!

Answer 3

Thanks so much!! very helpful. Could you please help me with one more?

Answer 4

sure

Answer 5

Factor: 12x^2 – 75 completely.

3(2x+5) (2x-5)
3(4x^2 – 25)
3(2x+5) (2x+5)
3(2x-5)^2

Answer 6

Factor out the GCF of 3.
12x2−75=3(4x2−25)

Now we need to factor 4x2−25.

To factor 4x2−25 use difference of squares formula, because both terms are perfect squares.

The difference of squares formula is a2−b2=(a−b)(a+b)

In this example we have
4x2−25=(2x)2−52=(2x−5)(2x+5)

so the answer would be 3(2x+5)(2x−5)

Answer 7

Another way to find the remainder just in case you don't know how to do the polynomial division. You know that x + 2 is the divisor so split the polynomial in accordance with it as follows:

x^3 + 2x^2 - 2x^2 - 4x + 8x + 16 - 20 <--- -20 is obviously the remainder
x^2(x + 2) -2x(x + 2) + 8(x + 2) - 20
(x + 2)(x^2 - 2x + 8) - 20

So it is clear that -20 is the remainder. Really the truth is, if you figure out this method, you can figure out that -20 is the remainder as soon as you split the polynomial appropriately.