polynomials(form 4) 15點ga

1) -5a2 + 18 – 27a
= -5a2 – 27a + 18
= -5a2 – 30a + 3a + 18
= -5a(a + 6) + 3(a + 6)
= (a + 6)(3 – 5a)
2) x4 – y4
= (x2)2 – (y2)2
= (x2 – y2)(x2 + y2)
= (x – y)(x + y)(x2 + y2)
3) a3 – 125
= a3 – 53
= (a – 5)(a2 + 5a + 25)
4) 8r3 + 343
= (2r)3 + 73
= (2r + 7)(4r2 – 14r + 49)
5) (s + 2)3 – 23
= (s + 2 – 2)[(s + 2)2 + 2(s + 2) + 4]
= s(s2 + 4s + 4 + 2s + 4 + 4)
= s(s2 + 6s + 12)
6) 2bx3 – 16by3
= 2b(x3 – 8y3)
= 2b([x3 – (2y)3]
= 2b(x – 2y)(x2 + 2xy + 4y2)
7) -x2 + 4x + 12
= -x2 + 6x – 2x + 12
= -x(x – 6) – 2(x – 6)
= (6 – x)(x + 2)
8) -6 + 16p – 8p2
= -2(3 – 8p + 4p2)
= -2(3 – 2p – 6p + 4p2)
= -2[(3 – 2p) – 2p(3 – 2p)]
= -2(3 – 2p)(1 – 2p)
= 2(2p – 3)(1 – 2p)
9) a2 – 3ab – 18b2
= a2 – 6ab + 3ab – 18b2
= a(a – 6b) + 3b(a – 6b)
= (a + 3b)(a – 6b)
10) 16h2 + 4kh – 30k2
= 2(8h2 + 2kh – 15k2)
= 2(8h2 + 12kh – 10kh – 15k2)
= 2[4h(2h + 3k) – 5k(2h + 3k)]
= 2(4h – 5k)(2h + 3k)
11) x3 – 8
= x3 – 23
= (x – 2)(x2 + 2x + 4)

1. -5a^2+18-27a
= -5a^2-30a+3a+18
=-5a(a+6)+3(a+6)
=(-5a+3)(a+6)

2. x^4-y^4
= (x^2-y^2) (x^2+y^2)
=(x-y) (x+y) (x^2+y^2)

3. a^3-125
= a^3- 5 ^3
=(a-5) (a^2+5a +5^2)
=(a-5) (a^2+5a +25)

4. 8r^3+343
= (2^3) (r^3) + 7^3
= (2r + 7) [( 2^2)(r^2) - 2r(7) + 7^2]
= (2r + 7) ( 4r^2 - 14r + 49)

5. (s+2)^3-2^3
=(s+2 -2) [(s+2)^2 +(s+2) (2) +2^2]
=s (s^2 +4s +4 +2s+4+4)
=s(s^2+6s +12)

6. 2bx^3-16by^3
=2b (x^3-8y^3)
=2b [ (x^3-(2^3)y^3 ]
= 2b (x-2y) [x^2 + x(2y) + (2^2)y^2 ]
=2b(x-2y) (x^2 + 2xy + 4y^2 )

7. -x^2+4x+12
=-x^2+6x - 2x +12
=x(-x+6)+2(-x+6)
= (x+2)(-x+6)

8. -6+16p-8p^2
= -6 +4p + 12p -8p^2
=-6 +4p - 2p(-6 +4p)
=(1-2p) (-6+4p)

9. a^2-3ab-18b^2
=a^2+3ab -6ab-18b^2
=a (a+3b)-6b (a+3b)
= (a -6b) (a+3b)

10. 16h^2=4kh-30k^2
如果 是 16h^2 +4kh-30k^2
則 =2( 8h^2 -2kh -15k^2)
=2( 8h^2 +10kh -12kh -15k^2)
= 2 [ 2h (4h +5k) -3 k (4h +5k) ]
= 2(2h-3k) (4h +5k)

11. x^3-8
= x^3-2^3
= (x-2) ( x^2 +2x + 2^2)
= (x-2) ( x^2 +2x + 4)

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