Solving Polynomials by factorizing
Not what you're looking for?
Factor
1. x^2 + 12x +36 - y^6
2.9y^2 + 12y + 4 - x^2
solve each equation
n^2 + n = 72
(4x + 9)(x - 4)(x + 1) = 0
m^3 = m^2 + 12m
(x + 4)(5x - 1 ) = 0
x^ + 6x - 7 = 0
A stereo system installer needs to run speaker wire along the two diagonals of a rectangular room whose dimensions are 40 feet by 75 feet. Find how much speaker wire she needs.
The longer leg of a right triangle is 4 feet longer than the other leg. Find the length of the two legs if the hypotenuse is 20 feet.
After t seconds, the height h(t) of a model rocket lauched from the ground into the air is given by the function h(t) = -16t^2 + 80t. Find how long it takes the rocket to reach a height of 96 feet.
The function W (x) = 0.5x^2 gives the number of servings of wedding cake that can be obtained from a two-layer x-inch square wedding cake tier. What size square wedding cake tier is needed to serve 50 people?
Purchase this Solution
Solution Summary
The solution describes the steps in factorizing the given polynomials. It also shows step by step method to convert given word problem into algebraic form and then finding the solutions.
Solution Preview
Solutions
30.x^2 + 12x +36 - y^6
first we can factorize
x^2+12x+36
On splitting middle term we get
x^2+6x+6x+36
=x(x+6)+6(x+6)
=(x+6)*(x+6)
Now put this value in original polynomial
x^2 + 12x +36 - y^6
=(x+6)^2-y^6
y^6 may be written as (y^3)^2
we get
=(x+6)^2-(y^3)^2
We know that (a^2-b^2) =(a+b)(a-b)
Comparing above relation with our polynomial we can write
(x+6)^2-(y^3)^2 = {(x+6)+y^3}*{(x+6)-y^3}=(x+6-y^3)(x+6+y^3)
34.9y^2 + 12y + 4 - x^2
First we can factorize
9y^2 + 12y + 4
On splitting middle terms we get
=9y^2+6y+6y+4
=3y(3y+2)+2(3y+2)
=(3y+2)(3y+2)
Now put this value in original polynomial
9y^2 + 12y + 4 - x^2
=(3y+2)^2-x^2
We know that (a^2-b^2) =(a+b)(a-b)
Comparing above relation with our polynomial we can write
(3y+2)^2-x^2 ={(3y+2)+x}*{(3y+2)-x}=(3y+2+x)(3y+2-x)
Solve each equation
Problem: n^2 + n = 72
Solution:
n^2+n-72=0
Split middle terms in such as a way that their product is -72n^2 and sum is +n
n^2+9n-8n-72=0
n(n+9)-8(n+9)=0
(n+9)(n-8)=0
meaning (n+9)=0 or (n-8)=0 or both
n+9=0 i.e. ...
Education
- BEng (Hons) , Birla Institute of Technology and Science, India
- MSc (Hons) , Birla Institute of Technology and Science, India
Recent Feedback
- "Thank you"
- "Really great step by step solution"
- "I had tried another service before Brain Mass and they pale in comparison. This was perfect."
- "Thanks Again! This is totally a great service!"
- "Thank you so much for your help!"
Purchase this Solution
Free BrainMass Quizzes
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Probability Quiz
Some questions on probability
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts