Find the factors of x^3−7x−6

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To find the factors of x3-7x-6, a method called equating coefficients can be used.

Firstly, set the equation to zero and find a suitable number which satisfies the equation, in this case x=-1 satisfies the equation, therefore one factor is (x+1), therefore the cubic equation can be represented by:

(x+1)(Ax2+Bx+C)

Expanding this polynomial gives:

x(Ax2+Bx+C)+(Ax2+Bx+C)

Ax3+Bx2+Cx+Ax2+Bx+C

Ax3+(A+B)x2+(C+B)x+C

Equating the coefficients looks at the number before the variable and comparing it with the predicted equation.

Ax3=1x................................(1)

(A+B)x2=0x2...........................(2)

(C+B)x=-7x ............................(3)

C=-6 ......................................(4)

therefore A=1, C=-6, and B=-1

(x-1)(x2-x-6)

and this is a matter of factorising (x2-x-6) which is (x-3)(x-2)

and so the factorised form becomes:

(x-1)(x-3)(x-2)

Michael W. GCSE Maths tutor, IB Maths tutor, A Level Maths tutor, GCS...

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