45x^6 by 5√3x^4 solve it proprely
Answers
Answer:
Step by step solution :
STEP
1
:
Equation at the end of step 1
((3•(x4))-(6•(x3)))-(32•5x2) = 0
STEP
2
:
Equation at the end of step
2
:
((3 • (x4)) - (2•3x3)) - (32•5x2) = 0
STEP
3
:
Equation at the end of step
3
:
(3x4 - (2•3x3)) - (32•5x2) = 0
STEP
4
:
STEP
5
:
Pulling out like terms
5.1 Pull out like factors :
3x4 - 6x3 - 45x2 = 3x2 • (x2 - 2x - 15)
Trying to factor by splitting the middle term
5.2 Factoring x2 - 2x - 15
The first term is, x2 its coefficient is 1 .
The middle term is, -2x its coefficient is -2 .
The last term, "the constant", is -15
Step-1 : Multiply the coefficient of the first term by the constant 1 • -15 = -15
Step-2 : Find two factors of -15 whose sum equals the coefficient of the middle term, which is -2 .
-15 + 1 = -14
-5 + 3 = -2 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and 3
x2 - 5x + 3x - 15
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-5)
Add up the last 2 terms, pulling out common factors :
3 • (x-5)
Step-5 : Add up the four terms of step 4 :
(x+3) • (x-5)
Which is the desired factorization
Equation at the end of step
5
:
3x2 • (x + 3) • (x - 5) = 0
STEP
6
:
Theory - Roots of a product
6.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation:
6.2 Solve : 3x2 = 0
Divide both sides of the equation by 3:
x2 = 0
When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:
x = ± √ 0
Any root of zero is zero. This equation has one solution which is x = 0
Step-by-step explanation:
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Answer: