Question 12 Marks
Divide
$-4 a^3+4 a^2+a$ by $2 a$
Answer$\frac{-4\text{a}^3+4\text{a}^2+\text{a}}{2\text{a}}$
$=\frac{-4\text{a}^3}{2\text{a}}+\frac{4\text{a}^2}{2\text{a}}+\frac{\text{a}}{2\text{a}}$
$=-2\text{a}^{(3-1)}+2\text{a}^{(2-1)}+\frac{1}{2}$
$=-\text{2}\text{a}^2+2\text{a}+\frac{1}{2}$
View full question & answer→Question 22 Marks
Divide $x^5+x^4+x^3+x^2+x+1$ by $x^3+1$
View full question & answer→Question 32 Marks
Divide $4\text{z}^3+6\text{z}^3+6\text{z}^2-\text{z}\text{ by }-\frac{1}{2}\text{z}.$
View full question & answer→Question 42 Marks
Divide $4\text{y}^2+3\text{y}+\frac{1}{2}\text{ by }2\text{y}+1.$
View full question & answer→Question 52 Marks
Find whether, or not the first polynomial is a factor of the second:
$\frac{2\text{x}^2+5\text{x}+4}{\text{x+1}}$
Answer$\frac{2\text{x}^2+5\text{x}+4}{\text{x+1}}$
$=\frac{2\text{x}(\text{x}+1)+3(\text{x}+1)+1}{\text{x}+1}$
$=\frac{(\text{x}+1)(2\text{x}+3)+1}{\text{x}+1}$
Therefore,$(x + 1)$ is not a factor of $2x^2+ 5x + 4$
View full question & answer→Question 62 Marks
Simplify:$\frac{16\text{m}^3\text{y}^2}{4\text{m}^2\text{y}}$
Answer$\frac{16\text{m}^3\text{y}^2}{4\text{m}^2\text{y}}$ $=\frac{16\times\text{m}\times\text{m}\times\text{m}\times\text{y}\times\text{y}}{4\times\text{m}\times\text{m}\times\text{y}}$ $=4\text{m}^{(3-2)}\text{y}^{(2-1)}$ $=4\text{my}$
View full question & answer→Question 72 Marks
Divide $5 z^3-6 z^2+7 z$ by $2 z$
Answer$\frac{5\text{z}^3-6\text{z}^2+7\text{z}}{2\text{z}}$
$=\frac{5\text{z}^3}{2\text{z}}-\frac{6\text{z}^2}{2\text{z}}+\frac{7\text{z}}{2\text{z}}$
$=\frac{5}{2}\text{z}^{(3-1)}-3\text{z}^{(2-1)}+\frac{7}{2}$
$=\frac{5}{2}\text{z}^2-3\text{z}+\frac{7}{2}$
View full question & answer→Question 82 Marks
Divide $x^2+7 x+12$ by $x+4$
View full question & answer→Question 92 Marks
Divide$x+2 x^2+3 x^4-x^5$ by $2 x$
Answer$\frac{\text{x}+2\text{x}^2+3\text{x}^4-\text{x}^5}{2\text{x}}$
$=\frac{\text{x}}{2\text{x}}+\frac{2\text{x}^2}{2\text{x}}+\frac{3\text{x}^4}{2\text{x}}-\frac{\text{x}^5}{2\text{x}}$
$=\frac{1}{2}+\text{x}+\frac{3}{2}\text{x}^3-\frac{1}{2}\text{x}^4$
View full question & answer→Question 102 Marks
Divide $x^2-5 x+6$ by $(x-3)$
Answer$\frac{\text{x}^2-5\text{x}+6}{\text{x}-3}$
$=\frac{\text{x}^2-3\text{x}-2\text{x}+6}{\text{x}-3}$
$=\frac{\text{x}^2-3\text{x}-2\text{x}+6}{\text{x}-3}$
$=\frac{\text{x}(\text{x}-3)-2(\text{x}-2)}{\text{x}-3}$
$=\frac{(\text{x}-3)(\text{x}-2)}{\text{x}-3}=\text{x}-2$
View full question & answer→Question 112 Marks
Using division of polynomials, state whether.
$4x - 1$ is a factor of $4 x^2-13 x-12$
Answer
As the remainder is non zero. Hence $(4x - 1)$ is not a factor of $4 x^2-13 x-12$ View full question & answer→Question 122 Marks
Divide $m^3-14 m^2+37 m-26$ by $m^2-12 m+13$
View full question & answer→Question 132 Marks
Divide $14 x^2-53 x+45$ by $7 x-9$
View full question & answer→Question 142 Marks
Divide $\text{y}^4-3\text{y}^4+\frac{1}{2}\text{y}^2\text{ by }3\text{y}.$
Answer $\frac{\text{y}^4-3\text{y}^3+\frac{1}{2}\text{y}^2}{3\text{y}}$
$=\frac{\text{y}^4}{3\text{y}}-\frac{3\text{y}^3}{3\text{y}}+\frac{\frac{1}{2}\text{y}^2}{3\text{y}}$
$=\frac{1}{3}\text{y}^{(4-1)}-\text{y}^{(3-1)}+\frac{1}{6}\text{y}^{(2-1)}$
$=\frac{1}{3}\text{y}^3-\text{y}^2+\frac{1}{6}\text{y}$
View full question & answer→Question 152 Marks
Divide $3 x^3 y^2+2 x^2 y+15 x y$ by $3 x y$
View full question & answer→Question 162 Marks
Divide the first polynomial by the second polynomial in the following. Also write the quotient and remainder:
$\frac{\text{x}^4-\text{x}^3+5\text{x}}{\text{x}-1}$
Answer$\frac{\text{x}^4-\text{x}^3+5\text{x}}{\text{x}-1}$
$=\frac{\text{x}^3(\text{x}-1)+5(\text{x}-1)+5}{\text{x}-1}$
$=\frac{(\text{x}^3+5)(\text{x}-1)+5}{\text{x}-1}$
$=\Big(\text{x}^3+5\Big)+\frac{5}{\text{x}-1}$
Therefore, quotient $=x^3+5$ and remainder = 5
View full question & answer→Question 172 Marks
Divide $24 a^3 b^3$ by $-8 a b$.
Answer$\frac{24\text{a}^3\text{b}^3}{-8\text{ab}}$
$=\frac{24\times\text{a}\times\text{a}\times\text{a}\times\text{b}\times\text{b}\times{\text{b}}}{-8\times\text{a}\times\text{b}}$
$=-3\text{a}^{(3-1)}\text{b}^{(3-1)}$
$=-3\text{a}^2\text{b}^2$
View full question & answer→Question 182 Marks
Divide $a x^2-a y^2 b y(a x+a y)$
Answer$\frac{\text{ax}^2-\text{ay}^2}{\text{ax}+\text{ay}}$
$=\frac{\text{a}(\text{x}^2-\text{y}^2)}{\text{ax}+\text{ay}}$
$=\frac{\text{a}(\text{x}+\text{y})(\text{x}-\text{y})}{\text{a}(\text{x}+\text{y} )}=\text{x}-\text{y}$
View full question & answer→Question 192 Marks
Divide $72 a^4 b^5 c^8$ by $-9 a^2 b^2 c^3$.
Answer$\frac{72\text{a}^4\text{b}^5\text{c}^8}{-9\text{a}^2\text{b}^2\text{c}^3}$
$=\frac{72\times\text{a}\times\text{a}\times\text{a}\times\text{a}\times\text{b}\times\text{b}\times\text{b}\times\text{b}\times\text{b}\times\text{c}\times\text{c}\times\text{c}\times\text{c}\times\text{c}\times\text{c}\times\text{c}\times\text{c}}{-9\times\text{a}\times\text{a}\times\text{b}\times\text{b}\times\text{c}\times\text{c}\times\text{c}}$
$=8\text{a}^{(4-2)}\text{b}^{(5-2)}\text{c}^{(8-3)}$
$=8\text{a}^2\text{b}^3\text{c}^5$
View full question & answer→Question 202 Marks
Using division of polynomials, state whether.
$x + 6$ is a factor of $x^2-x-42$
Answer
Remainder is zero. Hence $(x + 6)$ is a factor of $x^2-x-42$. View full question & answer→Question 212 Marks
Divide $3 x^3+4 x^2+5 x+18$8 by $x + 2.$
View full question & answer→Question 222 Marks
Divide 6$6 x^3+11 x^2-39 x-65$ by $3 x^2+13 x+13$ and find the quotient and remainder.
Answer
Quotient $= 2x - 5$
Remainder $= 0$ View full question & answer→Question 232 Marks
Divide $5 x^3-15 x^2+25 x$ by $5 x$
View full question & answer→Question 242 Marks
Simplify:$\frac{32\text{m}^2\text{n}^3\text{p}^2}{4\text{mnp}}$
Answer$\frac{32\text{m}^2\text{n}^3\text{p}^2}{4\text{mnp}}$ $=\frac{32\times{\text{m}\times\text{m}\times\text{n}\times\text{n}\times\text{n}\times\text{p}\times\text{p}}}{4\times\text{m}\times\text{n}\times\text{p}}$ $=8\text{m}^{(2-1)}\text{n}^{(3-1)}\text{p}^{(2-1)}$ $=8\text{mn}^2\text{p}$
View full question & answer→Question 252 Marks
Divide $15 m^2 n^3$ by $5 m^2 n^2$
Answer$\frac{15\text{m}^2\text{n}^3}{5\text{m}^2\text{n}^2}$
$=\frac{15\times\text{m}\times\text{m}\times\text{n}\times\text{n}\times\text{n}}{5\times\text{m}\times\text{m}\times\text{n}\times\text{n}}$
$=3\text{m}^{(2-2)}\text{n}^{(3-2)}$
$=3\text{m}^0\text{n}^1$
$=3\text{n}$
View full question & answer→Question 262 Marks
Divide $x^4-y^4$ by $x^2-y^2$
Answer$\frac{\text{x}^4-\text{y}^4}{\text{y}^2-\text{y}^2}$
$=\frac{\big(\text{x}^2\big)^2-\big(\text{y}^2\big)^2}{\big(\text{x}^2-\text{y}^2\big)}$
$=\frac{\big(\text{x}^2-\text{y}^2\big)\times\big(\text{x}^2+\text{y}^2\big)}{\big(\text{x}^2-\text{y}^2\big)}=\text{x}^2+\text{y}^2$
View full question & answer→Question 272 Marks
Divide $x^4+x^2+1$ by $x^2+x+1$.
View full question & answer→Question 282 Marks
Divide $21abc^2$ by $ 7abc.$
Answer$\frac{-21\text{abc}^2}{7\text{abc}}$
$=\frac{-21\times{\text{a}}\times{\text{b}\times}\text{c}\times\text{c}}{7\times\text{a}\times\text{b}\times{\text{c}}}$
$=-3\text{a}^{(1-1)}\text{b}^{(1-1)}\text{c}^{(2-1)}$
$=-3\text{c}$
View full question & answer→Question 292 Marks
Divide $9\text{x}^2\text{y}-6\text{x}\text{y}+12\text{xy}^2\text{ by }-\frac{3}{2}\text{xy}.$
View full question & answer→Question 302 Marks
Divide $72 x y z^2$ by $-9 x z$
Answer$\frac{72\text{xyz}^2}{-9\text{xz}}$
$=\frac{72\times\text{x}\times\text{y}\times\text{z}\times\text{z}}{-9\times\text{x}\times\text{z}}$
$=8\text{x}^{(1-1)}\text{yz}^{(2-1)}$
$=-8\text{yz}$
View full question & answer→Question 312 Marks
Using division of polynomials, state whether.
$z^2+3$ is a factor of $z^5-9 z$
Answer
Remainder is zero. Therefore, $z^2+3$ is a factor of $z^5-9 z$. View full question & answer→