Questions: Divide. (x^2+2x-35) ÷ (x-5)

Transcript text: Divide. \[ \left(x^{2}+2 x-35\right) \div(x-5) \]

Solution

Solution Steps

To divide the polynomial \(x^2 + 2x - 35\) by \(x - 5\), we will use polynomial long division. The process involves dividing the first term of the dividend by the first term of the divisor, multiplying the entire divisor by this result, subtracting from the dividend, and repeating the process with the new polynomial formed. This continues until the degree of the remainder is less than the degree of the divisor.

Step 1: Set Up the Division

We are tasked with dividing the polynomial \(x^2 + 2x - 35\) by \(x - 5\). We set this up as a long division problem.

Step 2: Divide the Leading Terms

We divide the leading term of the dividend \(x^2\) by the leading term of the divisor \(x\): \[ \frac{x^2}{x} = x \]

Step 3: Multiply and Subtract

Next, we multiply the entire divisor \(x - 5\) by the result \(x\): \[ x(x - 5) = x^2 - 5x \] Now, we subtract this from the original polynomial: \[ (x^2 + 2x - 35) - (x^2 - 5x) = 2x - 35 + 5x = 7x - 35 \]

Step 4: Repeat the Process

Now we divide the leading term of the new polynomial \(7x\) by the leading term of the divisor \(x\): \[ \frac{7x}{x} = 7 \] We multiply the divisor \(x - 5\) by \(7\): \[ 7(x - 5) = 7x - 35 \] Subtracting this from \(7x - 35\) gives: \[ (7x - 35) - (7x - 35) = 0 \]

Final Answer

The quotient of the division is \(x + 7\) and the remainder is \(0\). Thus, we can express the result as: \[ \boxed{Q(x) = x + 7, R = 0} \]

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >