\(3x^4-20x^3+35x^2+10x-48=0\)

\(\Leftrightarrow\left(x^2-2x-3\right)\left(3x^2-14x+16\right)=0\)

\(\Leftrightarrow\left(x+1\right)\left(x-3\right)\left(3x-8\right)\left(x-2\right)=0\)

\(\Rightarrow x=\left\{-1;3;\frac{8}{3};2\right\}\)

cảm ơn bạn

bạn có thể giải chi tiết hơn dc ko

           15 ⋮ \(x\); 20 ⋮ \(x\); 35 ⋮ \(x\) (\(x\) lớn nhất)

     ⇒ \(x\) \(\in\) ƯCLN(15; 20; 35) 

         15 = 3.5;   20 = 2².5;    35 =  5.7

       ƯCLN(15; 20; 35) = 5 ⇒ \(x\) = 5

\(E=5x^7+10x^6-20x^5-35x^4+20x^3-5x^2+40x+105\)

\(=\left(5x^7+10x^6-20x^5-35x^4+20x^3-5x^2+40x\right)+105\)

\(=5x\left(x^6+2x^5-4x^4-7x^3+4x^2-x+8\right)+105\)

Thay \(x^6+2x^5-4x^4-7x^3+4x^2-x+8=0\)vào đa thức ta được:

\(E=5x.0+105=105\)

a: Ta có: \(-3x^4+20x^3-35x^2-10x+48\)

\(=-\left(3x^4-20x^3+35x^2+10x-48\right)\)

\(=-\left(3x^4-9x^3-11x^3+33x^2+2x^2-6x+16x-48\right)\)

\(=-\left(x-3\right)\left(3x^3-11x^2+2x+16\right)\)

\(=-\left(x-3\right)\left(3x^3-6x^2-5x^2+10x-8x+16\right)\)

\(=-\left(x-3\right)\left(x-2\right)\left(3x^2-5x-8\right)\)

\(=-\left(x-3\right)\left(x-2\right)\left(3x-8\right)\left(x+1\right)\)

b: Ta có: \(-\left(2x^4+7x^3+x^2-7x-3\right)\)

\(=-\left(2x^4-2x^3+9x^3-9x^2+10x^2-10x+3x-3\right)\)

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

\(=-\left(x-1\right)\left(2x^3+2x^2+7x^2+7x+3x+3\right)\)

\(=-\left(x-1\right)\left(x+1\right)\left(2x^2+7x+3\right)\)

\(=-\left(x-1\right)\left(x+1\right)\cdot\left(x+3\right)\left(2x+1\right)\)

1)  =\(-3x^4+9x^3+11x^3-33x^2-2x^2+6x-16x+48\)

    =\(-3x^3\left(x-3\right)+11x^2\left(x-3\right)-2x\left(x-3\right)-16\left(x-3\right)\)

=  \(\left(x-3\right)\left(-3x^3+11x^2-2x-16\right)\)

= \(\left(x-3\right)\left(-3x^3+6x^2+5x^2-10x+8x-16\right)\)

=\(\left(x-3\right)\left(-3x^2\left(x-2\right)+5x\left(x-2\right)+8\left(x-2\right)\right)\)

=  \(\left(x-3\right)\left(x-2\right)\left(-3x^2+5x+8\right)\)

= \(\left(x-3\right)\left(x-2\right)\left(x-\frac{8}{3}\right)\left(x+1\right)\)

Ý b lm theo ý tưởng tương tự nha bn :D 

a) 5x²y² + 20x²y⁴ - 35x⁵y³ 

= \(5x^2y^2\left(1+4y-7x^3y\right)\)

b) 2x ( x + y ) - 7x - 7y

\(=2x\left(x+y\right)-7\left(x+y\right)=\left(2x-7\right)\left(x+y\right)\)

c) 5x^2 ( x - 1 ) + 5 ( 1 - x )

\(5x^2\left(x+1\right)+5\left(1-x\right)=5x^2\left(x-1\right)-5\left(x-1\right)=\left(5x^2-5\right)\left(x-1\right)=5\left(x^2-1\right)\left(x+1\right)\)

= 5(x+1)(x-1)(x-1) = 5(x+1)(x-1)^2

lỗi ah

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