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# The Factors Of X3 − 7x + 6 Are - Mathematics

MCQ

The factors of x3 − 7x + 6 are

#### Options

• x (x − 6) (x − 1)

• (x2 − 6) (x − 1)

• (x + 1) (x + 2) (x + 3)

• (x − 1) (x + 3) (x − 2)

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#### Solution

The given expression to be factorized is  x3 − 7x + 6

This can be written in the form

x3 − 7x + 6  = x^3 - (1 + 6) x + 6

 = x^3 -x -6x +6

Take common x from the first two terms and -6from the last two terms. Then we have

x3 − 7x + 6 = x(x^2 -1) -6 (x-1)

 = x{(x)^2 - (1)^2 } -6 (x-1)

 = x(x+1)(x-1) -6 (x-1)

Finally, take common(x-1)from the above expression,

x3 − 7x + 6 = (x-1){x(x+1) - 6}

= (x - 1)(x^2 + x - 6)

 = (x -1) (x^2 + 3x - 2x - 6)

 = (x-1){x (x+3) -2 (x+3)}

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

Is there an error in this question or solution?
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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 5 Factorisation of Algebraic Expressions
Q 11 | Page 26
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