[1 Mark Question Answer]

Question 11 Mark

Find the remainder (without division) when $2x^3 – 3x^2 + 7x – 8$ is divided by $x – 1 (2000)$

Answer

Let $x – 1 = 0,$ then $x = 1$
Substituting value of x in $f(x)$
$f(x) = 2x^3 – 3x^2 + 7x – 8$
$= 2(1)^3 – 3(1)^2 + 7(1) – 8$
$= 2 \times 1 – 3 \times 1 + 7 \times 1– 8$
$= 2 – 3 + 7 – 8$
$= -2$
$\therefore$ Remainder $= 2.$

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Question 21 Mark

Using remainder theorem, find the remainder on dividing $f(x)$ by $(x + 3)$ where $f(x) = 3x^3 + 7x^2 – 5x + 1$

Answer

Let $x + 3 = 0$
$⇒ x = -3$
Substituting the value of $x$ in $f(x),$
$f(x) = 3x^3 + 7x^2 – 5x + 1$
$= 3(–3)^3 + 7(–3)^2 – 5(–3) + 1$
$= –81 + 63 + 15 + 1$
$= –2$
Hence Reminder $= –2.$

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Question 31 Mark

Using remainder theorem, find the remainder on dividing $f(x)$ by $(x + 3)$ where $f(x) = 2x^2 – 5x + 1$

Answer

Let $x + 3 = 0$
$⇒ x = -3$
Substituting the value of $x$ in $f(x),$
$f(x) = 2x^2 – 5x + 1$
$\therefore f(-3) = 2(-3)^2 - 5(-3) + 1$
$= 18 + 15 + 1$
$= 34.$
Hence Reminder $= 34.$

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Question 41 Mark

Find the remainder (without divisions) on dividing $f(x)$ by $x – 2$, where $f(x) = 2x^3 – 7x^2 + 3$

Answer

Let $x – 2 = 0,$ then $x = 2$
Substituting value of $x$ in $f(x)$
$f(x) = 2x^3 – 7x^2 + 3$
$\therefore f(2) – 2(2)^3 – 7(2)^2 + 3 = 16 – 28 + 3$
Hence Reminnder $= –9.$

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Question 51 Mark

Find the remainder (without divisions) on dividing $f(x)$ by $x – 2,$ where $f(x) = 5x^2 – 1x + 4$

Answer

Let $x – 2 = 0,$ then $x = 2$
Substituting value of $x$ in $f(x)$
$f(x) = 5x^2 – 7x + 4$
$\Rightarrow f(2) = 5(2)^2 – 7(2) + 4$
$\Rightarrow f(2) = 20 - 14 + 4 = 10$
Hence Reminder $= 10.$

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Mathematics [1 Mark Question Answer]

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