Factorise: $3 x^{3} + 5 x^{2} + 3 x + 5$

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Solution

The equation $3 x^{3} + 5 x^{2} + 3 x + 5$ can be factorised as follows:

$3 x^{3} + 5 x^{2} + 3 x + 5 = (3 x^{3} + 3 x) + (5 x^{2} + 5) = 3 x (x^{2} + 1) + 5 (x^{2} + 1) = (3 x + 5) (x^{2} + 1)$

Hence, $3 x^{3} + 5 x^{2} + 3 x + 5 = (3 x + 5) (x^{2} + 1)$

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Using the FActor theroem, show that:
(i) (x-2) is a factor fo $x^{3} - 2 x^{2} - 9 x + 18$ Hence factories the expression
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Q. Factorise:

3 x^{3} - x^{2} - 3 x + 1

\lim_{x \to 1} \frac{x^{4} - 3 x^{3} + 2}{x^{3} - 5 x^{2} + 3 x + 1}

Q. Simplify:
12x − [3x³ + 5x² − {7x² − (4 − 3x − x³) + 6x³} − 3x]

{lim}_{x \to 1} \frac{x^{4} - 3 x^{3} + 2}{x^{3} - 5 x^{2} + 3 x + 1}

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Factorise: 3x3+5x2+3x+5

The equation 3x3+5x2+3x+5 can be factorised as follows:3x3+5x2+3x+5=(3x3+3x)+(5x2+5)=3x(x2+1)+5(x2+1)=(3x+5)(x2+1)Hence, 3x3+5x2+3x+5=(3x+5)(x2+1)

Factorise: $3 x^{3} + 5 x^{2} + 3 x + 5$

The equation $3 x^{3} + 5 x^{2} + 3 x + 5$ can be factorised as follows:

$3 x^{3} + 5 x^{2} + 3 x + 5 = (3 x^{3} + 3 x) + (5 x^{2} + 5) = 3 x (x^{2} + 1) + 5 (x^{2} + 1) = (3 x + 5) (x^{2} + 1)$

Hence, $3 x^{3} + 5 x^{2} + 3 x + 5 = (3 x + 5) (x^{2} + 1)$