factor 4x^3-13x^2+4x-3 — step-by-step solution

Let's factorize in

ℝ

4 x^{3}

- 13 x^{2}

+ 4 x

- 3

Try the obvious solution first:

x = 3

Let's evaluate the value of:

4 \cdot 3^{3}

- 13 \cdot 3^{2}

+ 4 \cdot 3

- 3

ℹ

3^{3}

27

‖

3^{2}

9

‖

4 \cdot 3

12

4 \cdot 27

- 13 \cdot 9

+ 12

- 3

ℹ

4 \cdot 27

108

‖

- 13 \cdot 9

-117

‖

12 - 3

9

108 - 117 + 9

- 9 + 9

0

Root found:

x = 3

Compute the quotient and remainder of

(4 x^{3}

- 13 x^{2}

+ 4 x

- 3)

(x - 3)

Expression in progress	Divide leading terms	Quotient	Quotient × divisor	Remainder after subtracting
$4 x^{3}$ $- 13 x^{2}$ $+ 4 x$ $- 3$	$\frac{4 x^{3}}{x}$	$4 x^{2}$	$4 x^{2} \cdot (x - 3) = 4 x^{3} - 12 x^{2}$	$(4 x^{3}$ $- 13 x^{2}$ $+ 4 x$ $- 3) - (4 x^{3} - 12 x^{2}) = - x^{2} + 4 x - 3$
$- x^{2} + 4 x - 3$	$- \frac{x^{2}}{x}$	$- x$	$- x \cdot (x - 3) = - x^{2} + 3 x$	$(- x^{2} + 4 x - 3) - (- x^{2} + 3 x) = x - 3$
$x - 3$	$\frac{x}{x}$	$1$	$x - 3 = x - 3$	$(x - 3) - (x - 3) = 0$

So the result of the euclidean division is:

4 x^{2} - x + 1

▶Factored expression:

(x - 3) \cdot (4 x^{2} - x + 1)