Maths 天才請進!!!!

首先，我不是數學天才。

1.
3a2 + 4a + 2 = 7

12a2 + 16a + 1
= 4(3a2 + 4a) + 1
= 4(3a2 + 4a + 2 - 2) + 1
= 4(3a2 + 4a + 2) - 4x2 + 1
= 4(7) - 4(2) + 1
= 28 - 8 + 1
= 21

=====
2.
-(x2+3)-[(x+m)-(5-x-2x2)]
= -(x2+3)-[x+m-5+x+2x2]
= -(x2+3)-[2x2+2x+m-5]
= -x2-3-2x2-2x-m+5
= -3x2-2x+(2-m)

constant term:
2-m = 6
-m = 4
m = -4

=====
3.
The answer is b.

(4x3+x2-9)+(2x3+3x2+5x-1)=ax3+bx2+cx+d
4x3+x2-9+2x3+3x2+5x-1=ax3+bx2+cx+d
6x3+4x2+5x-10 = ax3+bx2+cx+d

Compare x3 terms: a = 6
Compare x2 terms: b = 4
Compare x terms: c = 5
Compare constant terms: d = -10

Therefore, a > c > b > d

=====
4.
(6x2-2x+8)+(-5x2+kx-7) = x2+4x+1
6x2-2x+8-5x2+kx-7 = x2+4x+1
x2+(k-2)x+1 = x2+4x+1

Compare the x terms:
k-2 = 4
k = 6

======
5.
6x2+6x+5=50

There is no “k” in the question.

However,
2x2+2x+1+(12x2+12x-13)
= 2x2+2x+1+12x2+12x-13
= 10x2+10x-12
= (5/3)(6x2+6x)-12
= (5/3)( 6x2+6x+5-5)-12
= (5/3)( 6x2+6x+5)-(5/3)(5)-12
= (5/3)(50)-(25/3)-12
= (250/3)-(25/3)-12
= 189/3

======
6.
The original polynomial
= (4x3-2x2+3x-2)+(-x4+2x3+3x2-5xy)
= 4x3-2x2+3x-2-x4+2x3+3x2-5xy
= -x4+6x3+x2+3x-5xy-2
=

1. Polynominal 3a^2+4a+2=7, 咁 polynomial 12a^2+16a+1
嘅value係=?

3a^2+4a+2=7
3a^2+4a=7-2
3a^2+4a=5
(3a^2+4a)乘4=5乘4
12a^2+16a=20 similar 12a^2+16a+1=?
12a^2+16a+1=20+1 both side just +1
12a^2+16a+1= 21

2.After simplicfication化簡, the constant term 常數項 of the
polynomial -(x^2+3)-[(x+m)-(5-x-2x^2)] 係 6, 咁請問個
value of m 係?

-(x^2+3)-[(x+m)-(5-x-2x^2)]-----constant term = 6
= -x^2-3-x-m-5+x+2x^2
= x^2-3-5-m------- -3-5-m係constant term
so -3-5-m=6
-8-m=6
m= -14

3. Polynomial : (4x^3+x^2-9)+(2x^3+3x^2+5x-1)=ax^3+
bx^2+cx+d, 咁請問以下邊個係 correct order?

a. a>b>c>d
b. a>c>b>d answer is (a)
c. c>b>a>d
d. c>d>b>a

4. If the sum of polynomial 6x^2-2x+8 and -5x^2+kx-7 is
x^2+4x+1, 咁請問 what is the value of k?

-2x+kx=4x
kx=6x
k=6

5. 6x^2+6x+5=50, 咁請問2x^2+2x+1+(12x^2+12x-13)之中,
k 嘅value 係?

where is the k in both equation???

6.Polynomial 4x^3-2x^2+3x-2 is subtracted from another
polynomial, if the difference is -x^4+2x^3+3x^2-5xy, 咁請問
原來條polynomial 係?

4x^3-2x^2+3x-2-( -x^4+2x^3+3x^2-5xy)
=4x^3-2x^2+3x-2+x^4-2x^3-3x^2-5xy
=x^4+2x^3-5x^2-5xy+3x-2

Hint for Q1:
3a^2+4a=5,
So,
12a^2+16a=20
see?