MCQ
When $p(x) = x^3 - 3x^2 + 4x + 32$ is divided by $(x + 2),$ the remainder is:
- A$0$
- B$32$
- C$36$
- ✓$4$
✓
Answer
Correct option: D.
$4$
$p(x) = x^3 - 3x^2 + 4x + 32$
$x + 2 = 0 \Rightarrow x = -2$
By the renainder theorem, we know that when $p(x)$ is divided by
$(x + 2),$ the remainder is $p(-2).$
Now, $p(-2) = x^3 - 3x^2 + 4x + 32$
$= (-2)^3 - 3(-2)^2 + 4(-2) + 32$
$= -8 - 12 - 8 + 32$
$= 4$
$x + 2 = 0 \Rightarrow x = -2$
By the renainder theorem, we know that when $p(x)$ is divided by
$(x + 2),$ the remainder is $p(-2).$
Now, $p(-2) = x^3 - 3x^2 + 4x + 32$
$= (-2)^3 - 3(-2)^2 + 4(-2) + 32$
$= -8 - 12 - 8 + 32$
$= 4$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The sum of the length, breadth and depth of a cuboid is $19\ cm$ and its diagonal is $5\sqrt{5}\text{cm}.$ Its surface area is:
→The factors of $8a^3 + b^3 - 6ab + 1$ are:
→A, B and C are three collinear points. How many lines can be determined by them?
The weight of 10 students (in kg) are:
55, 40, 35, 52, 60, 38, 36, 45, 31, 44.
The median weight is.
55, 40, 35, 52, 60, 38, 36, 45, 31, 44.
The median weight is.
Axioms are assumed:
If one of the angles of a triangle is 130º then the angle between the bisectors of the other two angles can be:
- 50º
- 65º
- 90º
- 155º
In a histogram, each class rectangle is constructed with base as:
In the given figure, O is the centre of a circle. Then, $\angle\text{OAB}=?$
→- 50°
- 60°
- 55°
- 65°
If APB and CQD are two parallel lines, then the bisectors of $\angle\text{APQ},\angle\text{BPQ},\angle\text{CQP}$and $\angle\text{PQD}$ enclose a:
→- Square.
- Rhombus.
- Rectangle.
- Kite.
$(104 \times 96) = ?$
→