Question
Determine which of the following polynomials has $x - 2$ a factor:
$i. 3x^2 + 6x - 24$
$ii. 4x^2+ x – 2$
$i. 3x^2 + 6x - 24$
$ii. 4x^2+ x – 2$
✓
Answer
Given $x - 2 = 0$
$\Rightarrow x = 2$
Now, we have two equations
$i. 3x^2 + 6x – 24$
Put $x = 2$ in this equation
$3(2)^2 + 6 \times 2 - 24$
$3 \times 4 + 12 - 24$
$12 + 12 - 24 = 0$
$X - 2$ is a polynomial factor for this equation.
$ii. 4x^2+ x – 2$
Put $x = 2$ in this equation
$4(2)^2 + 2 - 2$
$4 \times 4 + 2 - 2 = 16$
$X - 2$ is a not a polynomial factor for this equation.
Hence, the equation $3x^2 + 6x – 24$ is an equation which has a polynomial factor of $x - 2.$
$\Rightarrow x = 2$
Now, we have two equations
$i. 3x^2 + 6x – 24$
Put $x = 2$ in this equation
$3(2)^2 + 6 \times 2 - 24$
$3 \times 4 + 12 - 24$
$12 + 12 - 24 = 0$
$X - 2$ is a polynomial factor for this equation.
$ii. 4x^2+ x – 2$
Put $x = 2$ in this equation
$4(2)^2 + 2 - 2$
$4 \times 4 + 2 - 2 = 16$
$X - 2$ is a not a polynomial factor for this equation.
Hence, the equation $3x^2 + 6x – 24$ is an equation which has a polynomial factor of $x - 2.$
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
If a sphere is inscribed in a cube, find the ratio of the volume of cube to the volume of the sphere.
Factorise: $2 x^3-3 x^2-17 x+30$
→In $\triangle\text{ABC},\angle\text{A}=50^{\circ}$ and $\angle\text{B}=60^{\circ}$ Determine the longest and shortest sides of the triangle.
→ Evaluate:
$\Big(\frac{64}{125}\Big)^{-\frac{2}{3}}+\Big(\frac{256}{625}\Big)^{-\frac{1}{4}}+\Big(\frac{3}{7}\Big)^0$
→$\Big(\frac{64}{125}\Big)^{-\frac{2}{3}}+\Big(\frac{256}{625}\Big)^{-\frac{1}{4}}+\Big(\frac{3}{7}\Big)^0$
A hemispherical bowl is made of steel $0.5\ cm$ thick. The inside radius of the bowl is $4\ cm$. Find the volume of steel used in making the bowl. $\big(\text{Take}\ \pi=\frac{22}{7}\big).$
→Two angle of a triangle are equal and the third angle is greater than each one of them by $18^\circ.$ Find the angles.
→The following bar graph shows the results of an annual examination in a secondary school. Read the bar graph and choose the correct alternative in each of the following:
$i.$ The pair of classes in which the results of boys and girls are inversely proportional are:
$a. VI, VIII$
$b. VI, IX$
$c. VII, IX$
$d. VIII, X$
$ii.$ The class having the lowest failure rate of girls is:
$a. VI$
$b. X$
$c. IX$
$d. VIII$
$iii.$ The class having the lowest pass rate of students is:
$a. VI$
$b. VII$
$c. VIII$
$d. IX$
→$i.$ The pair of classes in which the results of boys and girls are inversely proportional are:
$a. VI, VIII$
$b. VI, IX$
$c. VII, IX$
$d. VIII, X$
$ii.$ The class having the lowest failure rate of girls is:
$a. VI$
$b. X$
$c. IX$
$d. VIII$
$iii.$ The class having the lowest pass rate of students is:
$a. VI$
$b. VII$
$c. VIII$
$d. IX$
In the given figure, $O$ is the center of the circle. If $\angle\text{BOD}=160^\circ,$ find the value of $x$ and $y$. 
→Determine $(8\text{x})^\text{x},$ if $9^{\text{x}+2}=240+9^\text{x}. $
→Simplify: $\frac{3\sqrt2-2\sqrt3}{3\sqrt2+2\sqrt3}+\frac{\sqrt{12}}{\sqrt3-\sqrt2}$
→