[5 marks sum]

Question 15 Marks

The product of two numbers$-$is $16 x^4-1$. If one number is $2 x-1$, find the other.

Answer

Product of two numbers $=16 x^4-1$
One number $=2 x-1$
Then the second number $=\frac{16 \mathrm{x}^4-1}{2 \mathrm{x}-1}$
$=8 x^3+4 x^2+2 x+1$

View full question & answer→

Question 25 Marks

Find the quotient and the remainder when : $3 x^4+6 x^3-6 x^2+2 x-7$ is divided by $x-3$. verify your answer.

Answer

$\therefore$ Quotient $= 3x^3 + 15x^2 + 39x + 119$ and reminder $= 350$
Verification :
Dividend $=$ Quotient $\times$ Divisor $+$ Reminder
$= (3x^3 + 15x^2 + 39x + 119) (x − 3) + 350$
$= 3x^4 + 15x^3 + 39x^2 + 119x − 9x^3 − 45x^2 − 117x − 357 + 350$
$= 3x^4 + 6x^3 − 6x^2 + 2x − 7$
which is given

View full question & answer→

Question 35 Marks

Find the quotient and the remainder when : $a^3− 5a^2 + 8a + 15$ is divided by $a + 1$. verify your answer.

Answer

$\therefore$ Quotient $=a^2-6 a+14$ and reminder $=1$
Verification :
Dividiend $=$ Quotient $\times$ Divisor $+$ Reminder
$= (a2 − 6a + 14) \times (a + 1) + 1$
$= a^3 − 6a^2 + 14a + a^2 − 6a + 14 + 1$
$= a^3 − 5a^2 + 8a + 15$
which is given

View full question & answer→

Question 45 Marks

If $x = 6a + 86 + 9c\ ;\ y = 2b – 3a – 6c$ and $z = c – b + 3a$ ; find : $(i)\ x + y + z\ (ii)\ x – y + z\ (iii)\ 2x – y – 3z\ (iv)\ 3y – 2z – 5x$

Answer

$(i)\ x = 6a + 8b + 9c$
$y = − 3a + 2b − 6c$
$z = +3a − b + c$
Adding $x + y + z = 6a + 9b + 4c$
$(ii)\ x − y + z = (6a + 8b + 9c) − (2b − 3a − 6c) + (c − b + 3a)$
$= 6a + 8b + 9c − 2b + 3a + 6c + c − b + 3a$
$= 6a + 3a + 3a + 8b − 2b − b + 9c + 6c + c$
$= 12a + 5b + 16c$
$(iii)\ 2x − y − 3z = 2(6a + 8b + 9c) − (2b − 3a − 6c) − 3(c −b + 3a)$
$= 12a + 16b + 18c − 2b + 3a + 6c − 3c +3b − 9a$
$= 12a + 3a − 9a + 16b + 3b − 2b + 18c + 6c −3c$
$= 6a + 17b + 21c$
$(iv)\ 3y − 2z − 5x = 3(2b − 3a − 6c) − 2(c − b + 3a) − 5(6a + 8b + 9c)$
$= 6b − 9a − 18c − 2c + 2b − 6a − 30a − 40b − 45c$
$= − 9a − 6a − 30a + 6b + 2b − 40b − 18c − 2c − 45c$
$= − 45a − 32b − 65c$

View full question & answer→

MATHS [5 marks sum]

Test yourself on this topic