Page 32 - PWR UP TG2 MATHS

Matematik Tingkatan 2 Bab 2
11. Faktorkan setiap ungkapan berikut. SP 2.2.2 TP3
Factorise each of the following expression.

Pendaraban silang / Cross multiplication Faktor sepunya dalam empat sebutan algebra
Common factor in four algebraic terms
y – 8y + 15 Pendaraban faktor 15:
2
2
Factor multiplication of 15: xy – y – 4x + 4y Gabungkan sebutan dengan faktor
(–1) × (–15) → (–1) + (–15) = –16 2 sepunya dalam satu kurungan.
(–3) × (–5) → (–3) + (–5) = –8 = (xy – y ) + (–4x + 4y) Combine the terms with common factor
= y(x – y) – 4(x – y) in one brackets.
Pendaraban y –3 –3y = (x – y)(y – 4)
silang: (×) y –5 –5y (+)
Cross Faktor sepunya. Faktorkan.
multiplication: y 2 +15 –8y Common factor. Factorise.

y – 8y + 15 = (y – 3)(y – 5)
2

(a) p – 4p – 12 (f) ab + ac + bd + cd
2
= (p + 2)(p – 6) = (ab + ac) + (bd + cd)
= a(b + c) + d(b + c)
p +2 +2p
(×) (+) = (b + c)(a + d)
p –6 –6p
p 2 –12 –4p

(b) 6m – m – 2 (g) pq – p + 3q – 3p
2
2
= (3m – 2)(2m + 1) = (pq – p ) + (3q – 3p)
2
3m –2 –4m = p(q – p) + 3(q – p)
(×) (+)
2m +1 +3m = (q – p)(p + 3)
6m 2 –2 –m

(c) –6x – 7x + 5 (h) bm – bn + cm – cn
2
= (–3x – 5)(2x – 1) = (bm – bn) + (cm – cn)
–3x –5 –10x
(×) (+) = b(m – n) + c(m – n)
2x –1 +3x = (m – n)(b + c)
–6x 2 +5 –7x

(d) k – 12k + 36 (i) wp – hp – wq + hq
2
= (k – 6) 2 k –6 –6k = (wp – hp) – (wq – hq)
(×) (+)
k –6 –6k = p(w – h) – q(w – h)
k 2 +36 –12k = (w – h)(p – q)

2
2
(e) 8t + 29t – 12 (j) 3h + 12h – 2hk – 8k
= (8t – 3)(t + 4) 8t –3 –3t = (3h + 12h) – (2hk + 8k)
2
(×) (+)
t +4 +32t = 3h(h + 4) – 2k(h + 4)
8t 2 –12 29t = (h + 4)(3h – 2k)

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