Adding and subtracting polynomials.
Can someone help me solve this problem?
5x^3 . 2x^2 - 10x^4 + 3x^5 + 3x .(-2)x^4
. = The dot means to multiply. Thank you.
To add and subtract polynomials, you need to combine like terms. To solve this problem, follow these steps:
Step 1: Write down the given polynomials.
5x^3, 2x^2, -10x^4, 3x^5, and 3x.(-2)x^4
Step 2: Rearrange the polynomials in descending order of their exponents.
3x^5, -10x^4, 5x^3, 2x^2, and 3x.(-2)x^4
Step 3: Combine like terms.
The like terms in this case are the terms with the same exponent and variable part.
The terms with x^5: 3x^5
The terms with x^4: -10x^4 + (-2)x^4 = -12x^4
The terms with x^3: 5x^3
The terms with x^2: 2x^2
The terms with x: 3x
Step 4: Write the final expression.
The final expression is: 3x^5 - 12x^4 + 5x^3 + 2x^2 + 3x
Remember to combine like terms and ensure that the terms are in descending order of exponents to simplify polynomials.
5x^3 . 2x^2 - 10x^4 + 3x^5 + 3x .(-2)x^4
= 10x^5 - 10x^4 + 3x^5 - 6x^5
= 7x^5 - 10x^4
The word "solve" is usually used when dealing with equations, that is, we solve an equation.
You did not have an equation, so the instructions would be to "simplify" the expression.