c: \(x^4+x^3-4x^2+x+1\)

\(=x^4-x^3+2x^3-2x^2-2x^2+2x-x+1\)

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

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

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

Phương trình 18 x 2 + 23x + 5 = 0 có a – b + c = 18 – 23 + 5 = 0  nên phương trình có hai nghiệm phân biệt là x 1 = − 1 ;   x 2 = − 5 18 . Khi đó A = 18 (x + 1) x + 5 18

Đáp án: A

8x²-23x-3=8x²-24x+x-3

=8x(x-3)+(x-3)

=(x-3)(8x+1)

\(8x^2-23x-3=8x^2+x-24x-3\)

                            \(=\left(8x^2+x\right)-\left(24x+3\right)\)

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

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

Ta có: \(-8x^2+23x+3\)

\(=\left(-8x^2+24x\right)-\left(x-3\right)\)

\(=-8x\left(x-3\right)-\left(x-3\right)\)

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

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

\(-8x^2+23x+3\)

\(=-\left(8x^2-23x-3\right)\)

\(=-\left(8x^2-24x+x-3\right)\)

\(=-\left[8x\left(x-3\right)+\left(x-3\right)\right]\)

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

-8x² + 23x + 3

= -8x² - x + 24x + 3

= -x( 8x + 1 ) + 3( 8x + 1 )

= ( 8x + 1 )( 3 - x )

\(9a^3-13a+6=\left(9a^3-6a^2\right)+\left(6a^2-4a\right)-\left(9a-6\right)=3a^2\left(3a-2\right)+2a\left(3a-2\right)-3\left(3a-2\right)=\left(3a-2\right)\left(3a^2+2a-3\right)\)

\(x^4-4x^3+8x+3=\left(x^4+x^3\right)-\left(5x^3+5x^2\right)+\left(5x^2+5x\right)+\left(3x+3\right)=x^3\left(x+1\right)-5x^2\left(x+1\right)+5x\left(x+1\right)+3\left(x+1\right)=\left(x+1\right)\left(x^3-5x^2+5x+3\right)=\left(x+1\right)\left[\left(x^3-3x^2\right)-\left(2x^2-6x\right)-\left(x-3\right)\right]=\left(x+1\right)\left(x-3\right)\left(x^2-2x-1\right)\)

\(a^4-9a^3+81a-81\)

\(=\left(a^2-9\right)\left(a^2+9\right)-9a\left(a^2-9\right)\)

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

=x³+3x²+3x+1+27x³

=(x+1)³ +(3x)³

=(x+1+3x) ( (x+1)²-(x+1).3x+(3x)²)

=(4x+1) (x²+2x+1-3x²-3x+9x²)

=(4x+1)(7x²-x+1)