Question

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Answer 1

Answer:

1)

Step-by-step explanation:

1) 1+8x³

=8x³+1

= (2x)³+1³

= (2x + 1)(4x²-2x+1)

2) 3x³-x²-3x+1

=3x³-3x-x²+1

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

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

Answer 2

Answer:

(i)(1+2x) and(1-2x+4x^2)

(ii)(x + 1) , (x - 1) , (3x - 1)

Step-by-step explanation:

(i) 1 + 8x³    

can be written as

    1^3+2x^3                 {using the identity a^3+b^3=(a+b)(a^2-ab+b^2)}

where,

    a=1  , b=2x

so by equating we get,

   (1+2x)(1-2x+4x^2)=1+8x^3

Hence the factors of it are,

(1+2x) and(1-2x+4x^2)

(ii) 3x³ - x² - 3x + 1

    see attachment for this answer.