Question
Factorize: $x^3-2 x^2-x+2$
✓
Answer
$x^3-2 x^2-x+2$
We need to consider the factors of $2 ,$ which are $\pm 1, \pm 2$
Let us substitute $1$ in the polynomial $x^3-2 x^2-x+2$ to get
$(1)^3-2(1)^2-(1)+2=1-2-1+2=0$
Thus, according to factor theorem, we can conclude that $(x-1)$ is a factor of the polynomial
$x^3-2 x^2-x+2$
Let us divide the polynomial $x^3-2 x^2-x+2$ by $(x-1)$,to get
$x^3-2 x^2-x+2$
$=(x-1)\left(x^2-x-2\right) .$
$=(x-1)\left(x^2+x-2 x-2\right)$
$=(x-1)[x(x+1)-2(x+1)]$
$=(x-1)(x-2)(x+1) .$
Therefore, we can conclude that on factorizing the polynomial $x^3-2 x^2-x+2$,
we get $(x-1)(x-2)(x+1)$
We need to consider the factors of $2 ,$ which are $\pm 1, \pm 2$
Let us substitute $1$ in the polynomial $x^3-2 x^2-x+2$ to get
$(1)^3-2(1)^2-(1)+2=1-2-1+2=0$
Thus, according to factor theorem, we can conclude that $(x-1)$ is a factor of the polynomial
$x^3-2 x^2-x+2$
Let us divide the polynomial $x^3-2 x^2-x+2$ by $(x-1)$,to get
$x^3-2 x^2-x+2$
$=(x-1)\left(x^2-x-2\right) .$
$=(x-1)\left(x^2+x-2 x-2\right)$
$=(x-1)[x(x+1)-2(x+1)]$
$=(x-1)(x-2)(x+1) .$
Therefore, we can conclude that on factorizing the polynomial $x^3-2 x^2-x+2$,
we get $(x-1)(x-2)(x+1)$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
In the given figure, $O$ is the centre of a circle in which chords $AB$ and $CD$ intersect at $P$ such that $PO$ bisects $\angle\text{BPD}.$ Prove that $AB$ $= CD$.
→In parallelogram $A B C D$, two points $P$ and $Q$ are taken on diagonal $B D$ such that $D P=B Q$.
Show that
i. $\triangle APD \cong \triangle C Q B$
ii. $A P=C Q$
iii. $\triangle A Q B \cong \triangle C P D$
iv. $A Q=C P$
v. $APCQ$ is a parallelogram.
→Show that
i. $\triangle APD \cong \triangle C Q B$
ii. $A P=C Q$
iii. $\triangle A Q B \cong \triangle C P D$
iv. $A Q=C P$
v. $APCQ$ is a parallelogram.
What length of tarpaulin $3 \ m$ wide will be required to make conical tent of height $8 \ m$ and base radius $6 \ m$? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately $20 \ cm$. $\left( \text{Use }\pi \text{ = 3}\text{.14} \right)$
→In the given figure, $PQ$ is a diameter of a circle with centre $O$. If $\angle\text{PQR}=65^\circ,\angle\text{SPR}=40^\circ$ and $\angle\text{PQM}=65^\circ,$ find $\angle\text{QPR},\angle\text{QPM}$ and $\angle\text{PRS}.$
→In the given figure, a circle with centre $O$ is given in which a diameter $A B$ bisects the chord $C D$ at a point $E$ such that $C E=E D=8 cm$ and $E B=4 cm$. Find the radius of the circle.
→How many cubic centimetres of iron are there in an open box whose external dimension are $36\ cm, 25\ cm$ and $16.5\ cm$, the iron being $1.5\ cm$ thick throughout? If $1cm^3$ of iron weighs $15g$, find the weight of the empty box in kilograms.
→In the adjoining figure, $O$ is the centre of a circle. If $AB$ and $AC$ are chords of the circle such that $AB = AC$, $\text{OP}\perp\text{AB}$ and $\text{OQ}\perp\text{AC},$ prove that $PB = QC$.
→Find the values of $a$ and $b$ if $\frac{7+3 \sqrt{5}}{3+\sqrt{5}}-\frac{7-3 \sqrt{5}}{3-\sqrt{5}}=a+b \sqrt{5}$.
→In the given figure, $O$ is the centre of a circle. If $\angle\text{AOC}=140^\circ$ and $\angle\text{CAB}=50^\circ,$ calculate
$i. \angle\text{EDB}$
$ii. \angle\text{EBD}$
→$i. \angle\text{EDB}$
$ii. \angle\text{EBD}$
The path of a train $A$ is given by th equation $3x + 4y - 12 = 0$ and the path or another train $B$ is given by the equation $6x + 8y - 48 = 0.$ Represent this situation graphically.
→