a: \(10x^3-90x^5\)

\(=10x^3\cdot1-10x^3\cdot9x^2\)

\(=10x^3\left(1-9x^2\right)=10x^3\left(1-3x\right)\left(1+3x\right)\)

b: \(3a^2-6a^2b+5a-10ab\)

=3a^2(1-2b)+5a(1-2b)

=(1-2b)(3a^2+5a)

=a(3a+5)(1-2b)

c: \(7a^3-28a^2+28a\)

\(=7a\left(a^2-4a+4\right)\)

\(=7a\left(a-2\right)^2\)

d: \(45a^3-30a^2+5a-500\)

\(=5\left(9a^3-6a^2+5a-100\right)\)

e:Sửa đề: \(a^2b-49b+14b^2-b^3\)

\(=b\left(a^2-49+14b-b^2\right)\)

\(=b\left\lbrack a^2-\left(b-7\right)^2\right\rbrack\)

=b(a-b+7)(a+b-7)

f: \(x^4+4\)

\(=x^4+4x^2+4-4x^2\)

\(=\left(x^2+2\right)^2-4x^2=\left(x^2+2-2x\right)\left(x^2+2+2x\right)\)

a) 10x³-90x⁵=10x³(1-9x²)=10x³(1-3x)(1+3x)

b)3a²-6a²b+5a-10ab=(3a²-6a²b)+(5a-10ab)=3a²(1-2b)+5a(1-b)=(3a²+5a)(1-2b)=a(3a+5)(1-2b)

c) 7a³-28a²+28a=7a(a²-4a+4)

d) 45a³-30a²+5a-500=5(9a³-6a²+a-100)

a) Kết quả - 2 x 4   +   3 x 2  + 5.          b) Kết quả - 4 x 3   + 1 2 x − 1.

= 2x ( x² - 25 )

= 2x ( x + 5 ) ( x - 5 )

1/ Đặt x²+x=t

=>(x²+x)²+4(x²+x)-12=t²+4t-12=t²+6t-2t-12=t(t+6)-2(t+6)=(t-2)(t+6)=(x²+x-2)(x²+x+6)=(x²-x+2x-2)(x²+x+6)

=[x(x-1)+2(x-1)](x²+x+6)=(x-1)(x+2)(x²+x+6)

2/ Đặt x²+x=t 

=>(x²+x)²+9x²+9x+14=(x²+x)²+9(x²+x)+14=t²+9t+14=t²+2t+7t+14=t(t+2)+7(t+2)=(t+2)(t+7)=(x²+x+2)(x²+x+7)

3/ Đặt x²+5x=t

=>(x²+5x)²+10x²+50x+24=(x²+5x)²+10(x²+5x)+24=t²+10t+24=t²+4t+6t+24=t(t+4)+6(t+4)=(t+4)(t+6)=(x²+5x+4)(x²+5x+6)

=(x²+x+4x+4)(x²+2x+3x+6)=[x(x+1)+4(x+1][x(x+2)+3(x+2)]=(x+1)(x+4)(x+2)(x+3)=(x+1)(x+2)(x+3)(x+4)

\(7x^2+50x+7=\left(7x^2+49x\right)+\left(x+7\right)=7x\left(x+7\right)+\left(x+7\right)=\left(x+7\right)\left(7x+1\right)\)

7x² + 50x + 7

= 7x² + 49x + x + 7

= ( 7x² + 49x ) + ( x + 7 )

= 7x( x + 7 ) + ( x + 7 )

= ( 7x + 1 )( x + 7 )

hok tốt

x 4  + 2 x 3  +  x 2  =  x 2 ( x 2  + 2x + 1) =  x 2 x + 1 2