Factorise: 4 x^4+7 x^2-2 - Vidyadip

Question

Factorise: $4 x^4+7 x^2-2$

✓

Answer

Let $x^2 = y$ Then, $4x^4 + 7x^2 - 2$
$= 4y^2 + 7y - 2$
$= 4y^2 + 8y - y - 2$
$= 4y(y + 2) - 1(y + 2)$
$= (y + 2)(4y - 1)$
Now replacing $y$ by $x^2,$
we get $4x^4 + 7x^2 - 2 = (x^2 + 2)(4x^2 - 1)$
Since $a^2 - b^2 = (a - b)(a + b) = (x^2 + 2)(2x + 1)(2x - 1)$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Factorisation of Polynomials→Factorisation of Polynomials — all question types→Maths STD 9 question papers→Gujarat Board STD 9 question papers→Gujarat Board question paper generator→

Similar questions

A rectangular container, whose base is a square of side $5\ cm$, stands on a horizontal table, and holds water up to $1\ cm$ from the top.
When a solid cube is placed in the water it is completely submerged, the water rises to the top and $2$ cubic cm of water overflows.
Calculate the volume of the cube and also the length of its edge.

A cylinder of same height and radius is placed on top of a hemisphere. Find the curved surface area of the shape if the length of the shape is $7\ cm$.

If $\text{x}=3+2\sqrt{2},$ check whether $\text{x}+\frac{1}{\text{x}}$ is rational or irrational.

Solve the equation $2y - 1 = y + 1$ and represent it graphically on the coordinate plane.

If $3 x-2 y=11$ and $x y=12$, find the value of $27 x^3-8 y^3$

Eleven bags of wheat flour, each marked $5\ kg$, actually contained the following weights of flour (in Kg).

Find the probability that any of these bags chosen at random contains more than $5\ kg$ of flour.

Prove that:
$\frac{(\text{x}^{\text{a}+\text{b}})^2(\text{x}^{\text{b}+\text{c}})^2(\text{x}^{\text{c}+\text{a}})^2}{(\text{x}^\text{a}\text{x}^\text{b}\text{x}^\text{c})}=1$

The following table shows the number of students participating in various games in school.

Game	Cricket	Football	Basketball	Tennis
Number of students	$27$	$36$	$18$	$12$

Draw a bar graph to represent the above data.

Find the measure of all the angles of a parallelogram, if one angle is $24^\circ$ less than twice the smallest angle.

Prove that: $\sqrt{\frac{1}{4}}+(0.01)^{-\frac{1}{2}}-(27)^{\frac{2}{3}}=\frac{3}{2}$