Question

divide.
\\((3x^2 + 15x + 16) \div (x + 4)\\)
your answer should give the quotient and the remainder.
quotient: \\(square\\)
remainder: \\(square\\)

Explanation:

Step1: Use polynomial long division

We divide \(3x^2 + 15x + 16\) by \(x + 4\). First, divide the leading term of the dividend \(3x^2\) by the leading term of the divisor \(x\), we get \(3x\).
Multiply the divisor \(x + 4\) by \(3x\): \(3x(x + 4)=3x^2+12x\)
Subtract this from the dividend: \((3x^2 + 15x + 16)-(3x^2+12x)=3x + 16\)

Step2: Divide the new leading term

Now, divide the leading term of \(3x + 16\) (which is \(3x\)) by the leading term of the divisor \(x\), we get \(3\).
Multiply the divisor \(x + 4\) by \(3\): \(3(x + 4)=3x+12\)
Subtract this from \(3x + 16\): \((3x + 16)-(3x + 12)=4\)

Answer:

Quotient: \(3x + 3\)
Remainder: \(4\)