Question
Find the remainder when x3 - ax2 + 6x - a is divided by x - a.
✓
Answer
Let p(x) = x3 - ax2 + 6x - a
x - a = 0
⇒ x = a
$\therefore$ Remainder = (a)3 - a(a)2 + 6(a) - a
= a3 - a3 + 6a - a
= 5a
x - a = 0
⇒ x = a
$\therefore$ Remainder = (a)3 - a(a)2 + 6(a) - a
= a3 - a3 + 6a - a
= 5a
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
Look at the bar graph given below.
The linear equation that converts Fahrenheit (F) to Celsius (C) is given by the relation,
$\text{c}=\frac{5\text{F}-160}{9}$
If the temperature is 86°F, what is the temperature in Celsius?
→$\text{c}=\frac{5\text{F}-160}{9}$
If the temperature is 86°F, what is the temperature in Celsius?
ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal. Show that $\triangle \mathrm { ABE } \cong \triangle \mathrm { ACF },$ AB = AC i.e. $\triangle$ABC is an isosceles triangle.
→Calculate the value of x in the following figures.
Express the following in the form $\frac{\text{p}}{\text{q}},$ where p and q are integers and $\text{q}\neq0$:
0.888...
→0.888...
Identify the following as rational or irrational numbers. Give the decimal representation of rational numbers:
$\sqrt{100}$
→$\sqrt{100}$
Factorise:
16x4 - 1
16x4 - 1
Rationalise the denominator of the following:
$\frac{4}{\sqrt{11}-\sqrt{7}}$
→$\frac{4}{\sqrt{11}-\sqrt{7}}$
If $\text{x}=\text{a}^{\text{m}+\text{n}},\ \text{y}=\text{a}^{\text{n}+\text{l}}$ and $\text{z}=\text{a}^{\text{l}+\text{m}},$ prove that $\text{x}^\text{m}\text{y}^\text{n}\text{z}^\text{l}=\text{x}^\text{n}\text{y}^\text{l}\text{z}^\text{m}.$
→Factorise:
$7\text{x}^2+2\sqrt{14}\text{x}+2$
→$7\text{x}^2+2\sqrt{14}\text{x}+2$