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Question

# Divide and write the quotient and the remainder. (1) (y2 + 10y + 24) ÷ (y + 4) (2) (p2 + 7p − 5) ÷ (p + 3) (3) (3x + 2x2 + 4x3) ÷ (x − 4) (4) (2m3 + m2 + m + 9) ÷ (2m − 1) (5) (3x − 3x2 − 12 + x4 + x3) ÷ (2 + x2) (6) (a4 − a3 + a2 − a + 1) ÷ (a3 − 2) (7) (4x4 − 5x3 − 7x + 1) ÷ (4x − 1)

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Solution

## (1) (y2 + 10y + 24) ÷ (y + 4) So, quotient = y + 6 and remainder = 0 (2) (p2 + 7p − 5) ÷ (p + 3) So, quotient = p + 6 and remainder = $-$17. (3) (3x + 2x2 + 4x3) ÷ (x − 4) So, quotient = $4{x}^{2}+18x+75$ and remainder = 300. (4) (2m3 + m2 + m + 9) ÷ (2m − 1) So, quotient = ${m}^{2}+m+1$ and remainder = 10. (5) (3x − 3x2 − 12 + x4 + x3) ÷ (2 + x2) So, quotient = ${x}^{2}+x-5$ and remainder = x $-$ 2. (6) (a4 − a3 + a2 − a + 1) ÷ (a3 − 2) So, quotient = $a-1$ and remainder = ${a}^{2}+a-1$. (7) (4x4 − 5x3 − 7x + 1) ÷ (4x − 1) So, quotient = ${x}^{3}-{x}^{2}-\frac{x}{4}-\frac{29}{16}$ and remainder = $-\frac{13}{16}$.

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