RS Aggarwal Solutions Class 9 Mathematics Solutions for Factorization of Polynomials Exercise 3F in Chapter 3 - Factorization of Polynomials

Question 5 Factorization of Polynomials Exercise 3F

16𝑥^4 + 54𝑥


16𝑥^4 + 54𝑥

We can write the given question as,

16𝑥^4 + 54𝑥 = 2𝑥(8𝑥^3 + 27)

According to the equation,

𝑎^3 + 𝑏^3 = (𝑎 + 𝑏)(𝑎^2 − 𝑎𝑏 + 𝑏^2)

So we get,

2𝑥(8𝑥^3 + 27)

= 2𝑥 ((2𝑥)^3 + 3^3)

Using the equation,

= 2𝑥 ((2𝑥) + 3)((2𝑥)^2 − (2𝑥)(3) + (3)^2)

= 2𝑥(2𝑥 + 3)(4𝑥^2 − 6𝑥 + 9)

Video transcript
"hi students welcome to leader learning here i am your leader tutor to help you solve the question the question we have is 16 x to the power 4 plus 54 x now to solve it first we'll take 2 as a common and we can also take x as a common so in the bracket it will be 8 x cube plus 27 just 27. now we can write this 8 as a 2 cube x cube plus 27 as 3q now further we can apply this 2x whole cube plus 3q now here this numbers are in the form of a cube plus b cube so we can apply the formula a plus b in bracket a square minus a b plus b square so we'll apply this formula to x in bracket to 2 x whole square minus 2 multiplied by x multiplied by 3 plus 3 square now on further simplification 2x will be as it is the a plus b part is left 2 x plus 3 so in the bracket it's 2 x plus 3 and this bracket the next bracket will be 4 x square minus 6 x plus 9 so this way we simplify the question now we cannot do any more simplification out of this so this we will consider it as a our final answer any more simplification will further we will get back to the question so this is our final answer i hope you understood the question we just used only one formula aq plus b cube for any doubt you can write in the comment section for regular updates do subscribe to the video channel thank you "
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