Which binomial is a factor of 3x^2+2x-5?
There are two monomial factors.
3x^2+2x-5 = (3x+5)(x-1)
To determine if a binomial is a factor of a given polynomial, we can use the concept of polynomial long division. Here's how you can find out if a binomial is a factor of 3x^2 + 2x - 5:
Step 1: Write the binomial you want to test as a factor, let's call it (ax + b).
Step 2: Set up the polynomial long division by dividing the given polynomial (3x^2 + 2x - 5) by the binomial (ax + b). Perform the division step by step, starting from the highest degree term.
Step 3: Divide the first term of the polynomial by the first term of the binomial. In this case, divide 3x^2 by ax. The result will be (3x / a).
Step 4: Multiply the (ax + b) by the result obtained in Step 3 (3x/a) and subtract it from the polynomial given. Write the result below the polynomial.
Step 5: Repeat the process for the remaining terms, bringing down the next term, and dividing it by the first term of the binomial. Continue until you reach the constant term.
Step 6: After all the terms have been divided and subtracted, examine the remaining polynomial below the line. If the degree of this polynomial is less than the degree of the binomial, then the binomial is a factor of the given polynomial.
Step 7: Compare the remaining polynomial after division (also known as the remainder) to zero. If the remainder is zero, then the binomial is a factor; otherwise, it is not a factor.
By following these steps, you can determine if a binomial is a factor of a given polynomial.