Problem 92 - College Algebra

Question

Explain how to subtract polynomials.

Step-by-Step Solution

Answer

The subtraction of the polynomials \(5x^2 + 3x -2\) and \(3x^2 +2x -5\) results in \(2x^2+x-7\).

Step 1: Arrange the Polynomials

For subtracting polynomials, write the two polynomials one over the other in vertical alignment, with corresponding terms directly above or below each other. For example with polynomials \(5x^2 + 3x -2\) and \(3x^2 +2x -5\), arrange them as: \(5x^2 + 3x -2\) - \(3x^2 +2x -5\)

Step 2: Negate the Terms of the Second Polynomial

After arranging the polynomials, the next step is to distribute the negative sign to each term in the second polynomial. This would change the signs of each term in the second polynomial. \(5x^2 + 3x -2\) - \(3x^2 +2x -5\) becomes \(5x^2 + 3x -2\) - \(3x^2 - 2x + 5\)

Step 3: Combine Like Terms

Once the polynomials have been properly arranged and the second polynomial has been negated, the final step is to combine like terms. Terms in a polynomial are 'like terms' if they are multiples of the same powers of the variable. In our example, \(5x^2 + 3x -2\) - \(3x^2 - 2x + 5\) = \(5x^2 - 3x^2\) + \(3x - 2x\) + \(-2 - 5\), which simplifies to \(2x^2 + x - 7\).

Step 4: Final Answer

After combining like terms, the resulting expression is the answer to the subtraction of the two polynomials. In this example, the answer is \(2x^2+x-7\).