divide 27x³ - 64 by 3x-4 with solution.pls
Answers
Answer:
The answer is in the attachment.
Step-by-step explanation:
The explanation is in the attachment.
Answer:
9x2 + 12x + 16
Step-by-step explanation:
Theory : A difference of two perfect cubes, a3 - b3 can be factored into
(a-b) • (a2 +ab +b2)
Proof : (a-b)•(a2+ab+b2) =
a3+a2b+ab2-ba2-b2a-b3 =
a3+(a2b-ba2)+(ab2-b2a)-b3 =
a3+0+0-b3 =
a3-b3
Check : 27 is the cube of 3
Check : 64 is the cube of 4
Check : x3 is the cube of x1
Factorization is :
(3x - 4) • (9x2 + 12x + 16)
Factoring 9x2 + 12x + 16
The first term is, 9x2 its coefficient is 9 .
The middle term is, +12x its coefficient is 12 .
The last term, "the constant", is +16
Step-1 : Multiply the coefficient of the first term by the constant 9 • 16 = 144
Step-2 : Find two factors of 144 whose sum equals the coefficient of the middle term, which is 12 .
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Cancel out (3x-4) which appears on both sides of the fraction line.
Final result :
9x2 + 12x + 16
Hope you get it!
Please mark as Brainliest :)
Note- You can also solve this question by Long Division Method, but this is the method I prefer because there are many cases where long division doesnt help, but factorisation does help, thus learning this method is necessary!
Good luck