Simplify.6 x^2-5 x-[3 x-(4 x^2-9)]

Name: Problem 47, Chapter 5: Intermediate Algebra for College Students
Uploaded: 2021-07-29T16:38:51-08:00
Duration: 6 min 58 s
Channel: Anas Venkitta
Description: Simplify.6 x^2-5 x-[3 x-(4 x^2-9)]

Key Concepts

Order of Operations

This concept involves evaluating expressions in a specific sequence, typically following the PEMDAS/BODMAS rules. It ensures that operations inside parentheses/brackets are handled first, followed by exponents, then multiplication and division, and finally addition and subtraction, which is essential when simplifying algebraic expressions.

Distributive Property and Handling of Negative Signs

The distributive property allows one to multiply a single term by each term inside a parenthesis, an important step in removing brackets. Special attention is paid to negative signs when distributing, as they affect the signs of the terms inside the parentheses, making this concept crucial in the simplification process.

Combining Like Terms

This concept involves adding or subtracting coefficients of terms that have the same variable raised to the same power. Through identifying and combining these like terms, an expression is simplified into its most concise form.

Transcript

00:01 So in the given question we are told to find the roots of the polynomial x to the power 4 minus x cube minus 3x square minus 3x square plus 5x minus 2 and what we can do over here is when we substitute a value a root of this equation as the value of x over here the value of the polynomial would be equal to 0.

00:32 So considering this, the first method that we can do with the we are going to use is we are going to substitute the values like 0, 1, 2, 3 etc.

00:45 In this polynomial and find one of the roots of this equation.

00:49 Right.

00:50 So what we can do is let's take x equal to 1 first and what we would have is 1 minus 1 minus 3 plus plus minus 2 which is equal to 1.

01:02 1 minus 1 is equal to 0 minus 3 minus 2 is equal to minus 5 so we have 5 minus 5 which is equal to 0.

01:13 So what we have found is that one of the roots of this equation is 1 the corresponding factor is then x minus 1 and to find the other factors of this polynomial we can divide the polynomial with x minus 1 right? so when we divide the given polynomial x to the power 4 minus x cube minus 3x square plus 5x plus 2 with x minus 1, what we get as the quotient is x cubed times x minus 1 is x to the power 4 minus x cube which is equal to 0, then we have minus 3x square plus 5x plus 2 which we can.

02:04 Take in the question we can take minus 3x and we would have minus 3x square minus 3x minus 1 times 3x is plus 3x so when we subtract these two terms we have 0 plus 2x plus 2 and in the next step what we can do is we can take the expression 5x minus 3x is equal to 5x minus 5x minus 3x is equal to 2x and we have over here it is minus 2 right it is not plus 2 it is minus 2 so we can make this change over here and what we would get when we subtract is 2x minus 2 and now when we multiply x minus 1 with 2 we get 2 x minus 2 and this gives us a reminder of 0 and now we can write the given polynomial as the product of its factors x minus 1 and the cociant x cube minus 3x plus 2 so over here also we have to factorize x cube minus 3x plus 2...

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