divide x^3-64;x-4 by synthetic method
Answers
Step-by-step explanation:
I hope this answer is very helpful to you
and thank you for giving this question because I have learned yesterday itself this method
Answer:
hope this helps you please mark it as the brainliest and please follow me if you want to.
Step-by-step explanation:
STEP
1
:
x3 - 64
Simplify ———————
x + 4
Trying to factor as a Difference of Cubes:
1.1 Factoring: x3 - 64
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 : 64 is the cube of 4
Check : x3 is the cube of x1
Factorization is :
(x - 4) • (x2 + 4x + 16)
Trying to factor by splitting the middle term
1.2 Factoring x2 + 4x + 16
The first term is, x2 its coefficient is 1 .
The middle term is, +4x its coefficient is 4 .
The last term, "the constant", is +16
Step-1 : Multiply the coefficient of the first term by the constant 1 • 16 = 16
Step-2 : Find two factors of 16 whose sum equals the coefficient of the middle term, which is 4 .
-16 + -1 = -17
-8 + -2 = -10
-4 + -4 = -8
-2 + -8 = -10
-1 + -16 = -17
1 + 16 = 17
2 + 8 = 10
4 + 4 = 8
8 + 2 = 10
16 + 1 = 17
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Polynomial Long Division :
1.3 Polynomial Long Division
Dividing : x-4
("Dividend")
By : x+4 ("Divisor")
dividend x - 4
- divisor * x0 x + 4
remainder - 8
Quotient : 1
Remainder : -8
Final result :
(x - 4) • (x2 + 4x + 16)
————————————————————————
x + 4
See results of polynomial long division:
1. In step #01.03