Question

1. find the quotient.

$(2x^2 - 3x - 5) div (x + 1)$
options:
$2x - 5$
$-2x + 5$
$2x^2 - 5x$
$2x$ remainder $-5$

1. find the quotient.

$(3x^3 + 17x^2 + 20x + 24) div (x + 4)$
options:
$-3x^2 - 5x - 6$
$3x^3 + 5x^2 + 6x$
$3x^2 + 5x + 6$
$3x + 5$ remainder $6$

1. find the quotient.

$(2x^3 + x^2 - 11x + 2) div (x - 2)$
options:
$-2x^2 - 5x + 1$
$2x^2 + 5x - 1$
$2x^3 + 5x^2 + x$
$2x + 5$ remainder $-1$

Explanation:

Step1: Solve question 7 (synthetic division)

Set up synthetic division for $(2x^2 - 3x - 5) \div (x+1)$:
Bring down 2. Multiply $2 \times (-1) = -2$, add to $-3$: $-3 + (-2) = -5$. Multiply $-5 \times (-1) = 5$, add to $-5$: $-5 + 5 = 0$.
Coefficients of quotient: $2, -5$, so quotient is $2x - 5$.

Step2: Solve question 8 (synthetic division)

Set up synthetic division for $(3x^3 + 17x^2 + 26x + 24) \div (x+4)$:
Bring down 3. Multiply $3 \times (-4) = -12$, add to $17$: $17 + (-12) = 5$. Multiply $5 \times (-4) = -20$, add to $26$: $26 + (-20) = 6$. Multiply $6 \times (-4) = -24$, add to $24$: $24 + (-24) = 0$.
Coefficients of quotient: $3, 5, 6$, so quotient is $3x^2 + 5x + 6$.

Step3: Solve question 9 (synthetic division)

Set up synthetic division for $(2x^3 + x^2 - 11x + 2) \div (x-2)$:
Bring down 2. Multiply $2 \times 2 = 4$, add to $1$: $1 + 4 = 5$. Multiply $5 \times 2 = 10$, add to $-11$: $-11 + 10 = -1$. Multiply $-1 \times 2 = -2$, add to $2$: $2 + (-2) = 0$.
Coefficients of quotient: $2, 5, -1$, so quotient is $2x^2 + 5x - 1$.

Answer:

1. $2x - 5$
2. $3x^2 + 5x + 6$
3. $2x^2 + 5x - 1$