Accountancy, asked by lili4168, 4 days ago

f(x)=16(x⁴-64x) solution​

Answers

Answered by kabirajsahu2468
0

Answer:

Trying to factor as a Difference of Cubes:

2.2 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

2.3 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

Equation at the end of step

2

:

x - 16x • (x - 4) • (x2 + 4x + 16) = 0

STEP

3

:

STEP

4

:

Pulling out like terms

4.1 Pull out like factors :

1025x - 16x4 = -x • (16x3 - 1025)

Trying to factor as a Difference of Cubes:

4.2 Factoring: 16x3 - 1025

Check : 16 is not a cube !!

Ruling : Binomial can not be factored as the difference of two perfect cubes

Polynomial Roots Calculator :

4.3 Find roots (zeroes) of : F(x) = 16x3 - 1025

Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient

In this case, the Leading Coefficient is 16 and the Trailing Constant is -1025.

The factor(s) are:

of the Leading Coefficient : 1,2 ,4 ,8 ,16

of the Trailing Constant : 1 ,5 ,25 ,41 ,205 ,1025

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