Soalan 1:
Senaraikan faktor sepunya dan FSTB bagi setiap sebutan berikut.
(a) 8y, 12y
(b) 2b, 3b
(c) 3w, 5w2
(d) 10m2, 15mk
(e) 5bc, 2c2, 3cd
(f) 4a2b, 8b2c, 6bcd
Penyelesaian:
(a)
$$ \begin{aligned} \mathrm{FSTB} & =(2)(2)(y) \\ & =4 y \end{aligned} $$
$$ \begin{aligned} & 8 y=1 \times 2 \times 2 \times 2 \times y \\ & 12 y=1 \times 2 \times 2 \times 3 \times y \end{aligned} $$
$$ \text { Faktor sepunya bagi } 8 y, 12 y \text { ialah } 1,2,4, y, 2 y \text { dan } 4 y \text {. } $$
(b)
$$ \mathrm{FSTB}=b $$
$$ \begin{aligned} 2 b & =1 \times 2 \times b \\ 3 b & =1 \times 3 \times b \end{aligned} $$
$$ \text { Faktor sepunya bagi } 2 b, 3 b \text { ialah } 1 \text { dan } b \text {. } $$
(c)
$$ \mathrm{FSTB}=w $$
$$ \begin{aligned} & 3 w=1 \times 3 \times w \\ & 5 w^2=1 \times 5 \times w \times w \end{aligned} $$
$$ \text { Faktor sepunya }=1 \text { dan } w . $$
(d)
$$ \begin{aligned} \mathrm{FSTB} & =(5)(m) \\ & =5 m \end{aligned} $$
$$ \begin{aligned} & 10 m^2=1 \times 2 \times 5 \times m \times m \\ & 15 m k=1 \times 3 \times 5 \times m \times k \end{aligned} $$
$$ \text { Faktor sepunya }=1,5, m \text { dan } 5 m . $$
(e)
$$ \mathrm{FSTB}=c $$
$$ \begin{aligned} & 5 b c=1 \times 5 \times b \times c \\ & 2 c^2=1 \times 2 \times c \times c \\ & 3 c d=1 \times 3 \times c \times d \end{aligned} $$
$$ \text { Faktor sepunya }=1 \text { dan } c . $$
(f)
$$ \begin{aligned} \mathrm{FSTB} & =(2)(b) \\ & =2 b \end{aligned} $$
$$ \begin{aligned} & 4 a^2 b=1 \times 2 \times 2 \times a \times a \times b \\ & 8 b^2 c=1 \times 2 \times 2 \times 2 \times b \times b \times c \\ & 6 b c d=1 \times 2 \times 3 \times b \times c \times d \end{aligned} $$
$$ \text { Faktor sepunya }=1,2, b \text { dan } 2 b $$
Senaraikan faktor sepunya dan FSTB bagi setiap sebutan berikut.
(a) 8y, 12y
(b) 2b, 3b
(c) 3w, 5w2
(d) 10m2, 15mk
(e) 5bc, 2c2, 3cd
(f) 4a2b, 8b2c, 6bcd
Penyelesaian:
(a)
$$ \begin{aligned} \mathrm{FSTB} & =(2)(2)(y) \\ & =4 y \end{aligned} $$
$$ \begin{aligned} & 8 y=1 \times 2 \times 2 \times 2 \times y \\ & 12 y=1 \times 2 \times 2 \times 3 \times y \end{aligned} $$
$$ \text { Faktor sepunya bagi } 8 y, 12 y \text { ialah } 1,2,4, y, 2 y \text { dan } 4 y \text {. } $$
(b)
$$ \mathrm{FSTB}=b $$
$$ \begin{aligned} 2 b & =1 \times 2 \times b \\ 3 b & =1 \times 3 \times b \end{aligned} $$
$$ \text { Faktor sepunya bagi } 2 b, 3 b \text { ialah } 1 \text { dan } b \text {. } $$
(c)
$$ \mathrm{FSTB}=w $$
$$ \begin{aligned} & 3 w=1 \times 3 \times w \\ & 5 w^2=1 \times 5 \times w \times w \end{aligned} $$
$$ \text { Faktor sepunya }=1 \text { dan } w . $$
(d)
$$ \begin{aligned} \mathrm{FSTB} & =(5)(m) \\ & =5 m \end{aligned} $$
$$ \begin{aligned} & 10 m^2=1 \times 2 \times 5 \times m \times m \\ & 15 m k=1 \times 3 \times 5 \times m \times k \end{aligned} $$
$$ \text { Faktor sepunya }=1,5, m \text { dan } 5 m . $$
(e)
$$ \mathrm{FSTB}=c $$
$$ \begin{aligned} & 5 b c=1 \times 5 \times b \times c \\ & 2 c^2=1 \times 2 \times c \times c \\ & 3 c d=1 \times 3 \times c \times d \end{aligned} $$
$$ \text { Faktor sepunya }=1 \text { dan } c . $$
(f)
$$ \begin{aligned} \mathrm{FSTB} & =(2)(b) \\ & =2 b \end{aligned} $$
$$ \begin{aligned} & 4 a^2 b=1 \times 2 \times 2 \times a \times a \times b \\ & 8 b^2 c=1 \times 2 \times 2 \times 2 \times b \times b \times c \\ & 6 b c d=1 \times 2 \times 3 \times b \times c \times d \end{aligned} $$
$$ \text { Faktor sepunya }=1,2, b \text { dan } 2 b $$
Soalan 2:
Faktorkan ungkapan algebra berikut.
(a) 5e + 10
(b) 2ab − 8a2
(c) 3abc + 6a2b
(d) 4x – 12x2
(e) ef + f2 + fg
(f) 2x2 – 4xy + 6wx
Penyelesaian:
(a)
$$ \begin{aligned} & 5 e+10 \\ & \text { FSTB }=5 \\ & =5(e+2) \end{aligned} $$
(b)
$$ \begin{aligned} & 2 a b-8 a^2 \\ & \text { FSTB }=2 a \\ & =2 a(b-4 a) \end{aligned} $$
(c)
$$ \begin{aligned} & 3 a b c+6 a^2 b \\ & \text { FSTB }=3 a b \\ & =3 a b(c+2 a) \end{aligned} $$
(d)
$$ \begin{aligned} & 4 x-12 x^2 \\ & \text { FSTB }=4 x \\ & =4 x(1-3 x) \end{aligned} $$
(e)
$$ \begin{aligned} & e f+f^2+f g \\ & \text { FSTB }=f \\ & =f(e+f+g) \end{aligned} $$
(f)
$$ \begin{aligned} & 2 x^2-4 x y+6 w x \\ & \text { FSTB }=2 x \\ & =2 x(x-2 y+3 w) \end{aligned} $$
Faktorkan ungkapan algebra berikut.
(a) 5e + 10
(b) 2ab − 8a2
(c) 3abc + 6a2b
(d) 4x – 12x2
(e) ef + f2 + fg
(f) 2x2 – 4xy + 6wx
Penyelesaian:
(a)
$$ \begin{aligned} & 5 e+10 \\ & \text { FSTB }=5 \\ & =5(e+2) \end{aligned} $$
(b)
$$ \begin{aligned} & 2 a b-8 a^2 \\ & \text { FSTB }=2 a \\ & =2 a(b-4 a) \end{aligned} $$
(c)
$$ \begin{aligned} & 3 a b c+6 a^2 b \\ & \text { FSTB }=3 a b \\ & =3 a b(c+2 a) \end{aligned} $$
(d)
$$ \begin{aligned} & 4 x-12 x^2 \\ & \text { FSTB }=4 x \\ & =4 x(1-3 x) \end{aligned} $$
(e)
$$ \begin{aligned} & e f+f^2+f g \\ & \text { FSTB }=f \\ & =f(e+f+g) \end{aligned} $$
(f)
$$ \begin{aligned} & 2 x^2-4 x y+6 w x \\ & \text { FSTB }=2 x \\ & =2 x(x-2 y+3 w) \end{aligned} $$