WS2 Mixed factorisation - thefinneymathslab.weebly.com · 1 Factorise –25x(a – 3n) – 15xy(a...
Transcript of WS2 Mixed factorisation - thefinneymathslab.weebly.com · 1 Factorise –25x(a – 3n) – 15xy(a...
© John Wiley & Sons Australia, Ltd Page 1
WS2 Mixed factorisation 1 Factorise –25x(a – 3n) – 15xy(a – 3n).
I like Finney’s way better … watch my video if you have forgotten my easy way to do this *** The text book makes it look harder than it actually is! HCF = −5x(a – 3n) Divide each term by HCF. −25x(a – 3n) ÷ −5x(a – 3n) = 5 −15xy(a – 3n) ÷ −5x(a – 3n) = 3y Complete the factorisation. –25x(a – 3n) – 15xy(a – 3n) = −5x(a – 3n)(5 + 3y)
2 Factorise 8x2 – 12xy –2px + 3py.
I like Finney’s way better … watch my video if you have forgotten my easy way to do this *** The text book makes it look harder than it actually is! There are no common factors in all 4 terms. Group terms in pairs. The common factor of 8x2 and −12xy is 4x. 8x2 – 12xy = 4x(2x – 3y) The common factor of –2px and 3py is −p. –2px + 3py = −p(2x – 3y) Complete the factorisation.
)4)(32()32()32(432128 2
pxyxyxpyxxpypxxyx
−−=
−−−=+−−
3 Factorise (x + 1)2 – y2.
Factorise, using the rule for difference of two squares. (x + 1)2 – y2 = (x + 1 + y)(x + 1 – y)
4 Factorise 36x2 – 25y2.
Factorise, using the rule for difference of two squares.
)56)(56()5()6(
253622
22
yxyxyx
yx
−+=
−=
−
© John Wiley & Sons Australia, Ltd Page 2
5 Factorise a2 + 24a – 25.
Find all the factor pairs of −25 and their sum. Factors: 1, −25 : sum = −24 5, −5 : sum = 0 −1, 25 : sum = 24* Find the pair (marked *) whose sum equals the coefficient of the middle term (24). Factorise, using the rule for quadratic trinomials. a2 + 24a – 25 = (a – 1)(a + 25)
6 Factorise 6x2 – 5x – 6.
Find all the factor pairs of –36 and their sum.
0 sum :6 6,5 sum :9 4,
*5 sum :9 4,9 sum :21 3,
9 sum : 21 3,61 sum :81 2,
61 sum :81 2,35 sum : 63 1,
35sum :63 1,:Factors
=−
=−
−=−
=−
−=−
−=−
=−
=−
−=−
The factor pairs 4 and –9 multiply to give –36 and add to give –5 (marked *).
( ) ( )( )( )3223
2332326946656 22
−+=
+−+=
−−+=−−
xxxxx
xxxxx
© John Wiley & Sons Australia, Ltd Page 3
7 Complete the square for each of the following expressions: (a) xx 82 + (b) mm 62 −
(a) x2 + 2× (4)x
= x2 + 2× (4)x +16−16
= x + 4( )2 −16 (b) m2 − 2× (3)m
= m2 − 2× (3)x + 9− 9
= m−3( )2 − 9
8 Factorise the following by completing the square:
158)a( 2 ++ xx
2012)b( 2 +− xx
I like Finney’s way better … My way is done in the previous question! … watch my video if you have forgotten my easy way to do this *** The text book makes it look harder than it actually is!
)3)(5()14)(14(
1)4(1516)168(
158218
218
158)a(
2
2
222
2
++=
−+++=
−+=
+−++=
+⎟⎠
⎞⎜⎝
⎛ ×−⎟⎠
⎞⎜⎝
⎛ ×++=
++
xxxx
xxx
xx
xx
)10)(2()46)(46(
16)6(2036)3612(
20122112
2112
2012)b(
2
2
222
2
−−=
−−+−=
−−=
+−+−=
+⎟⎠
⎞⎜⎝
⎛ −×−⎟⎠
⎞⎜⎝
⎛ −×+−=
+−
xxxx
xxx
xx
xx
© John Wiley & Sons Australia, Ltd Page 4
9 Factorise the following by completing the square:
52)a( 2 −− xx
36)b( 2 −+ xx
*** I like “Finney’s way” better J ***
)61)(61(
6)1(51)12(
52212
212
52)a(
2
2
222
2
−−+−=
−−=
−−+−=
−⎟⎠
⎞⎜⎝
⎛ −×−⎟⎠
⎞⎜⎝
⎛ −×+−=
−−
xx
xxx
xx
xx
)323)(323(
)123)(123(
12)3(39)96(
36216
216
36)b(
2
2
222
2
−+++=
−+++=
−+=
−−++=
−⎟⎠
⎞⎜⎝
⎛ ×−⎟⎠
⎞⎜⎝
⎛ ×++=
−+
xx
xx
xxx
xx
xx
10 Factorise each of the following: (a) 20x2 – 4x (b) x2 – 13 (c) 3x2 + 14x – 5
(a) 20x2 – 4x
= 4x(5x – 1) (b) x2 – 13
= (x + 13 )(x – 13 ) (c) 3x2 + 14x – 5
= 3x2 + 15x – x – 5 = 3x(x + 5) – (x + 5) = (3x – 1)(x + 5)