Can someone please help me get the sum difference and product of this problem I am so lost
x^3+ 2x-5∶ x^4-x^3+ 3x^2- 2x+3
Hey, Terrence. As I said before,
what does the ":" mean? If it just separates two polynomials, then if we call them f(x) and g(x),
f+g = x^3 + x^2 + 2x - 2
f-g = -x^3 + 3x^2 - 2x
f*g = 2x^5 - 2x^4 + 3x^3 - x^2 - 2x + 1
Hmm. different problem, so disregard the above.
sum: x^4+3x^2-3
diff: -x^4 + 2x^3 - 3x^2 + 4x - 8
prod: x^7 - x^6 + 5x^5 - 9x^4 + 14x^3 - 19x^2 + 16x - 15
To find the sum, difference, and product of the given problem, let's break it down step by step.
The given problem is:
x^3 + 2x - 5 : x^4 - x^3 + 3x^2 - 2x + 3
1. To find the sum, we need to add the two expressions together.
x^3 + 2x - 5 + (x^4 - x^3 + 3x^2 - 2x + 3)
2. Combine like terms. Terms that have the same variable and exponent can be added or subtracted.
x^4 + (x^3 - x^3) + 3x^2 + (2x - 2x) + (2 + 3) - 5
Simplify:
x^4 + 3x^2 + 5 - 5
The sum of the two expressions is:
x^4 + 3x^2
3. To find the difference, we need to subtract one expression from the other.
(x^3 + 2x - 5) - (x^4 - x^3 + 3x^2 - 2x + 3)
4. Distribute the negative sign inside the parentheses:
x^3 + 2x - 5 - x^4 + x^3 - 3x^2 + 2x - 3
5. Combine like terms:
(-x^4 + x^4) + (x^3 + x^3) + (2x + 2x) + (-3x^2) + (-5 - 3)
Simplify:
0 + 2x^3 + 4x - 3x^2 - 8
The difference of the two expressions is:
2x^3 + 4x - 3x^2 - 8
6. To find the product, we multiply the two expressions together.
(x^3 + 2x - 5) * (x^4 - x^3 + 3x^2 - 2x + 3)
7. Distribute the terms using a distribution rule:
x^3 * (x^4 - x^3 + 3x^2 - 2x + 3) + 2x * (x^4 - x^3 + 3x^2 - 2x + 3) - 5 * (x^4 - x^3 + 3x^2 - 2x + 3)
8. Multiply each term by the corresponding term from the other expression:
x^7 - x^6 + 3x^5 - 2x^4 + 3x^3 + 2x^5 - 2x^4 + 6x^3 - 4x^2 + 6x^2 - 6x + 15x^4 - 5x^3 + 15x^2 - 10x + 15
9. Combine like terms:
x^7 - x^6 + 5x^5 + 6x^4 + 14x^3 + 21x^2 - 16x + 15
The product of the two expressions is:
x^7 - x^6 + 5x^5 + 6x^4 + 14x^3 + 21x^2 - 16x + 15
So, the sum of the expressions is x^4 + 3x^2, the difference is 2x^3 + 4x - 3x^2 - 8, and the product is x^7 - x^6 + 5x^5 + 6x^4 + 14x^3 + 21x^2 - 16x + 15.