Photo AI

What is the remainder when $P(x) = -x^3 - 2x^2 - 3x + 8$ is divided by $x + 2$? A - HSC - SSCE Mathematics Extension 1 - Question 3 - 2021 - Paper 1

Question 3

What is the remainder when $P(x) = -x^3 - 2x^2 - 3x + 8$ is divided by $x + 2$? A. -14 B. -2 C. 2 D. 14

Worked Solution & Example Answer:What is the remainder when $P(x) = -x^3 - 2x^2 - 3x + 8$ is divided by $x + 2$? A - HSC - SSCE Mathematics Extension 1 - Question 3 - 2021 - Paper 1

Step 1

Determine the function to evaluate

96%

114 rated

Answer

We start with the polynomial function defined as $P(x) = -x^3 - 2x^2 - 3x + 8$ . We need to find the remainder when this polynomial is divided by $x + 2$ .

Step 2

Apply the Remainder Theorem

99%

104 rated

Answer

According to the Remainder Theorem, the remainder of the division of a polynomial $P(x)$ by $x - c$ is $P(c)$ . In this case, since we are dividing by $x + 2$ , we set $c = -2$ .

Step 3

Evaluate $P(-2)$

96%

101 rated

Answer

Now we substitute $-2$ into the polynomial:

P(-2) &= -(-2)^3 - 2(-2)^2 - 3(-2) + 8 \\ &= -(-8) - 2(4) + 6 + 8 \\ &= 8 - 8 + 6 + 8 \\ &= 14. \end{align*}$$

Step 4

Conclude with the remainder

98%

120 rated

Answer

Thus, the remainder when $P(x)$ is divided by $x + 2$ is 14. According to the options provided, the correct answer is:

D. 14.

Join the SSCE students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;