Answer :
To subtract the polynomial
[tex]$$4x^3 - 2x^2 + 5$$[/tex]
by
[tex]$$3x^3 + x - 4,$$[/tex]
follow these steps:
1. Write the subtraction as:
[tex]$$
(4x^3 - 2x^2 + 5) - (3x^3 + x - 4).
$$[/tex]
2. Distribute the negative sign to the terms in the second polynomial:
[tex]$$
4x^3 - 2x^2 + 5 - 3x^3 - x + 4.
$$[/tex]
3. Combine like terms:
- For the [tex]$x^3$[/tex] terms:
[tex]$$
4x^3 - 3x^3 = x^3.
$$[/tex]
- For the [tex]$x^2$[/tex] term:
[tex]$$
-2x^2 \text{ (no other } x^2 \text{ term)}
$$[/tex]
- For the [tex]$x$[/tex] term:
[tex]$$
-x \text{ (no other } x \text{ term)}
$$[/tex]
- For the constant terms:
[tex]$$
5 + 4 = 9.
$$[/tex]
4. Write the final result:
[tex]$$
x^3 - 2x^2 - x + 9.
$$[/tex]
Thus, the result of subtracting the two polynomials is
[tex]$$x^3 - 2x^2 - x + 9.$$[/tex]
[tex]$$4x^3 - 2x^2 + 5$$[/tex]
by
[tex]$$3x^3 + x - 4,$$[/tex]
follow these steps:
1. Write the subtraction as:
[tex]$$
(4x^3 - 2x^2 + 5) - (3x^3 + x - 4).
$$[/tex]
2. Distribute the negative sign to the terms in the second polynomial:
[tex]$$
4x^3 - 2x^2 + 5 - 3x^3 - x + 4.
$$[/tex]
3. Combine like terms:
- For the [tex]$x^3$[/tex] terms:
[tex]$$
4x^3 - 3x^3 = x^3.
$$[/tex]
- For the [tex]$x^2$[/tex] term:
[tex]$$
-2x^2 \text{ (no other } x^2 \text{ term)}
$$[/tex]
- For the [tex]$x$[/tex] term:
[tex]$$
-x \text{ (no other } x \text{ term)}
$$[/tex]
- For the constant terms:
[tex]$$
5 + 4 = 9.
$$[/tex]
4. Write the final result:
[tex]$$
x^3 - 2x^2 - x + 9.
$$[/tex]
Thus, the result of subtracting the two polynomials is
[tex]$$x^3 - 2x^2 - x + 9.$$[/tex]
