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)

Answer 1

(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 = $4x^2+18x+75$ 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 = $-\frac{13}{16}$.