a)\(x^3-x^2-14x+24=x^3-3x^2+2x^2-6x-8x+24\)

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

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

=\(\left(x-3\right)\left(x^2+4x-2x-8\right)=\left(x-3\right)\left(x-2\right)\left(x+4\right)\)

b)Tương tự câu a

c)\(x^3-7x+6=x^3-x^2+x^2-x-6x+6\)

=\(x^2\left(x-1\right)+x\left(x-1\right)-6\left(x+1\right)=\left(x+1\right)\left(x^2+x-6\right)\)

=\(\left(x+1\right)\left(x^2+3x-2x-6\right)\)

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

d;e thương tự câu c

Vì mình mới họ định lí mới nên minhfm uốn làm thử nếu cậu không hiểu tì hỏi mình để mình làm cách bình thường .

a ) Áp dụng định lí Bezout :
Đặt \(f\left(x\right)=x^3-7x-6,\) ta thấy \(f\left(-1\right)=0\) nên \(-1\) là một ước của \(f\left(x\right)\).

Vậy \(f\left(x\right)\) chia hết cho \(\left(x+1\right)\). Ta có : \(f\left(x\right)=\left(x+1\right)\left(x^2-x-6\right)\)

\(x^2-x-6=\left(x+2\right)\left(x-3\right)\).

Kết quả \(f\left(x\right)=\left(x+1\right)\left(x+2\right)\left(x-3\right)\)

b ) Áp dụng định lí Bezout :

Đặt \(f\left(x\right)=x^3-19x-30.\)Xét một số ước của 30 , ta được \(f\left(-2\right)=0\).

Ta chia \(f\left(x\right)\) cho \(\left(x+2\right);f\left(x\right)=\left(x+2\right)\left(x^2-2x-15\right)\)

\(x^2-2x-15\) nhận \(x=5\) làm nghiệm .

Do vậy \(f\left(x\right)=\left(x+2\right)\left(x+3\right)\left(x-5\right)\)

Chúc bạn học tốt

a) \(x^3-7x-6\)

\(=\left(x^3+2x^2\right)-\left(2x^2+4x\right)-\left(3x+6\right)\)

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

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

b)\(x^3-19x-30\)

\(=\left(x^3-5x^2\right)+\left(5x^2-25x\right)+\left(6x-30\right)\)

\(=\left(x-5\right)\left(x^2+5x+6\right)\)

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

c) \(a^3-6a^2+11a-6\)

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

\(=\left(a-1\right)\left(a^2-5a+6\right)\)

\(=\left(a-1\right)\left(a-2\right)\left(a-3\right)\)

a) a⁴ + a² - 2

a⁴ + 2a² - a² - 2

a².( a² + 2 ) - ( a² + 2 )

( a² - 1 ).( a² + 2 )

( a + 1 ).( a - 1 ).( a² +2 )

b) x⁴ + 4x² - 5

x⁴ + 5x² - x² - 5

x².( x² + 5 ) - ( x² + 5 )

( x² - 1 ).( x² + 5 )

( x + 1 ).( x - 1 ).( x² + 5 )

c) x³ - 19x - 30

x³ + 2x² - 2x² + 4x - 15x - 30

x²( x + 2 ) - 2x.( x + 2 ) - 15.( x + 2 )

( x + 2 ).( x² - 2x - 15 )

d) x³ - 7x - 6

x³ - 3x² + 3x² - 9x + 2x - 6

x².( x - 3 ) + 3x.( x - 3 ) + 2.( x - 3 )

( x - 3 ).( x² + 3x +2 )

( x - 3 ).( x² + 2x + x + 2 )

( x - 3 ).( x.( x + 2 ) + ( x + 2 )

( x + 1 ).( x + 2 ).( x - 3 )

e) x³ - 5x² - 14x

x³ - 7x² + 2x² - 14x

x².( x - 7 ) + 2x.( x - 7 )

( x - 7 ).( x² + 2x )

x.( x + 2 ).( x - 7 )

\(x^2-x-6=x^2+2x-3x-6=x\left(x+2\right)-3\left(x+2\right)=\left(x-3\right)\left(x+2\right)\)

\(x^3-19x-30=x^3+6x-25x-30=x\left(x^2-25\right)+6x-30=x\left(x^2-25\right)+6\left(x-5\right)\)

\(=x\left(x-5\right)\left(x+5\right)+6\left(x-5\right)=\left(x-5\right)\left[\left(x\right)\left(x+5\right)+6\right]\)

\(x^3-5x^2-14x\)

\(=x^3+2x^2-7x^2-14x\)

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

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

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

\(x^3-7x-6\)

\(=x^3+x^2-x^2-x-6x-6\)

\(=x^2\left(x+1\right)-x\left(x+1\right)-6\left(x+1\right)\)

\(=\left(x+1\right)\left(x^2-x-6\right)\)

\(=\left(x+1\right)\left(x^2+2x-3x-6\right)\)

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

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

\(x^3-19x-30\)

\(=x^3-5x^2+5x^2-25x+6x-30\)

\(=x^2\left(x-5\right)+5x\left(x-5\right)+6\left(x-5\right)\)

\(=\left(x-5\right)\left(x^2+5x+6\right)\)

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

\(=\left(x-5\right)\left[x\left(x+2\right)+3\left(x+2\right)\right]\)

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

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

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

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

b) \(x^3-19x-30==x^3+2x^2-2x^2-4x-15x-30=x^2\left(x+2\right)-2x\left(x+2\right)-15\left(x+2\right)\)

\(=\left(x+2\right)\left(x^2+2x-15\right)=\left(x+2\right)\left(x-3\right)\left(x+5\right)\)

c) \(x^3-6x^2+11x-6=x^3-x^2-5x^2+5x+6x-6=x^2\left(x-1\right)-5x\left(x-1\right)+6\left(x-1\right)=\left(x-1\right)\left(x-2\right)\left(x-3\right)\)

a)x²-x-2=x²-2x+x-2=x(x-2)+(x-2)=(x-2)(x+1)

b)x³-19x-30=x³+2x²-2x²-4x-15x-30=x²(x+2)-2x(x+2)-15(x+2)=(x²-2x-15)(x+2)=(x²+3x-5x-15)(x+2)=[x(x+3)-5(x+3)](x+2)=(x-5)(x+3)(x+2)=(x-5)(x+2)(x+3)

c)x³-6x²+11x-6=x³-x²-5x²+5x+6x-6=x²(x-1)-5x(x-1)+6(x-1)=(x²-5x+6)(x-1)=(x²+x-6x+6)(x-1)=[x(x+1)-6(x+1)](x-1)=(x-6)(x+1)(x-1)=(x-6)(x-1)(x+1)

a) x³ - 7x - 6 = x³ + x² - x² - x - 6x - 6

= x²(x + 1) - x(x + 1) - 6(x + 1)

= (x + 1)(x² - x - 6)

= (x + 1)(x² + 2x - 3x - 6)

= (x + 1)[x(x + 2) - 3(x + 2)]

= (x + 1)(x + 2)(x - 3)

a)  = x² - 3x + 2x - 6

    = x(x -3) + 2(x - 3)

    = (x - 3)(x + 2)

b)  = x² - x + 5x - 5

    = x(x - 1) + 5(x - 1)

    = (x - 1)(x + 5)

c)  = x³ - 5x² + 5x² - 25x + 6x - 30

    = x²(x - 5) + 5x(x - 5) +6(x - 5)

    = (x - 5)(x² + 5x + 6)

    = (x - 5)(x² + 2x + 3x + 6)

    = (x - 5)[x(x + 2) + 3(x + 2)]

    = (x - 5)(x + 2)(x + 3)

a)  = x² - 3x + 2x - 6

    = x(x -3) + 2(x - 3)

    = (x - 3)(x + 2)

b)  = x² - x + 5x - 5

    = x(x - 1) + 5(x - 1)

    = (x - 1)(x + 5)

c)  = x³ - 5x² + 5x² - 25x + 6x - 30

    = x²(x - 5) + 5x(x - 5) +6(x - 5)

    = (x - 5)(x² + 5x + 6)

    = (x - 5)(x² + 2x + 3x + 6)

    = (x - 5)[x(x + 2) + 3(x + 2)]

    = (x - 5)(x + 2)(x + 3)