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Question
Note: Enter your answer and show all the steps that you use to solve this problem and write your final answer in factored form in the space provided.
Simplify: (9x3+2x2−5x+4)−(5x3−7x+4)
pls:)
To simplify the expression (9x^3 + 2x^2 - 5x + 4) - (5x^3 - 7x + 4), we can combine like terms:
= 9x^3 + 2x^2 - 5x + 4 - 5x^3 + 7x - 4
Now, let's group the like terms:
= (9x^3 - 5x^3) + (2x^2) + (-5x + 7x) + (4 - 4)
Simplifying further:
= 4x^3 + 2x^2 + 2x
So, the simplified expression is 4x^3 + 2x^2 + 2x.
Great- final answer needs to be in factored form (hint- each term has a common factor you can take out.)
Apologies for that oversight. Let's factor out the common terms:
= 2x(2x^2 + x + 1)
So, the simplified expression in factored form is 2x(2x^2 + x + 1).
can you show a step by step
Certainly! Here is the step-by-step process to factor the expression:
1. Start with the simplified expression: 4x^3 + 2x^2 + 2x.
2. Look for the common factors in each term. In this case, we see that there is a common factor of 2x in each term.
3. Factor out the common factor of 2x from each term:
2x(2x^2 + x + 1).
4. The expression is now factored as 2x(2x^2 + x + 1).
Note: Factoring involves identifying the common factor(s) in an expression and then dividing each term by those common factor(s) to simplify the expression. In this case, the common factor was 2x, which when factored out, leaves us with the expression 2x multiplied by the remaining terms inside the parentheses.