Question

divide.
\\((15x^3 - 18x^2 - 19x - 5) \div (5x + 4)\\)
your answer should give the quotient and the remainder.
quotient: \\(square\\)
remainder: \\(square\\)

Explanation:

Step1: Divide the leading terms

Divide the leading term of the dividend \(15x^3\) by the leading term of the divisor \(5x\). So, \(\frac{15x^3}{5x} = 3x^2\).

Step2: Multiply and subtract

Multiply the divisor \(5x + 4\) by \(3x^2\) to get \(15x^3 + 12x^2\). Subtract this from the dividend:

$$
LATEXBLOCK0
$$

Step3: Divide the new leading term

Divide the leading term of the new dividend \(-30x^2\) by the leading term of the divisor \(5x\). So, \(\frac{-30x^2}{5x} = -6x\).

Step4: Multiply and subtract

Multiply the divisor \(5x + 4\) by \(-6x\) to get \(-30x^2 - 24x\). Subtract this from the new dividend:

$$
LATEXBLOCK1
$$

Step5: Divide the new leading term

Divide the leading term of the new dividend \(5x\) by the leading term of the divisor \(5x\). So, \(\frac{5x}{5x} = 1\).

Step6: Multiply and subtract

Multiply the divisor \(5x + 4\) by \(1\) to get \(5x + 4\). Subtract this from the new dividend:

$$
LATEXBLOCK2
$$

Answer:

Quotient: \(3x^2 - 6x + 1\)
Remainder: \(-9\)