Question

What is the answer. ​

Answer 1

Step-by-step explanation:

x⁴ + 5x³ - 6x² - 5x - 2

should become

x³ - 3x² + x -1

so, what do I need to subtract from the top terms to get the bottom terms ?

because we can only look from one x- term to the next. we can only combine them, when they have the same x exponent.

so, we see there is no x⁴ in the desired result.

therefore, we know as a first item that x⁴ had to be subtracted.

the next x exponent is 3.

we have 5x³ on the top, and x³ on the bottom.

so, clearly, we need to subtract 4x³ as second term.

the next x exponent is 2.

we have -6x² on the top, and -3x² on the bottom.

so, we should actually add 3x². and how do we do this in a subtraction ? by subtracting a negative value, which actual adds it.

so, we need to subtract -3x² as third term.

the next x exponent is 1 (just x).

we have -5x on the top and x on the bottom.

so, the same trick as before, as we need to add something.

so, we need to subtract -6x as fourth term.

and finally, the x exponent 0, which just shows the constant numbers.

we have -2 on the top and -1 on the bottom.

again the same trick to actually add 1.

we need to subtract -1 as fifth term.

so, in total, this is what we need to subtract from the top line to get the bottom line :

x⁴ + 4x³ - 3x² - 6x - 1

Answer 2

Answer:

$x^{4}$ + 4x³ - 3x² - 6x - 1

Step-by-step explanation:

By subtracting x³ - 3x² + x - 1 , that is

$x^{4}$ + 5x³ - 6x² - 5x - 2 - (x³ - 3x² + x - 1) ← distribute by - 1

= $x^{4}$ + 5x³ - 6x² - 5x - 2 - x³ + 3x² - x + 1 ← collect like terms

= $x^{4}$ + 4x³ - 3x² - 6x - 1