Polynomials
स्टोरीबोर्ड पाठ
- Introducing Factoring Polynomials
- I am so glad you asked, you can factor a polynomial by using the ‘greatest common factor method’. This is because it is one of the most efficient yet easiest ways of factoring a polynomial.
- What about factoring, how do you factor a polynomial?
- Examples of Factoring Polynomials
- Should we do a few examples? I think I know how to factor a polynomial and would love to try to do so.
- Absolutely, practicing will most definitely help us become better in understanding polynomials and how to factor them. Let’s try factoring 5 x 4 + 40x. Factor the sum of the two cubes.
- Factoring using the GCF
- I began with factoring the GCF which is 5x then rewrote it as the sum of cubes which then used that method to solve. Is this correct?
- 5x^4+40x5x(x^3+8)5x(x^3+2^3)5x(x+2)(x^2-x(2+2^2))5x(x+2)(x^2-2x+4)
- Maddie - What about factoring, how do you factor a polynomial? Anna - I am so glad you asked, you can factor a polynomial by using the ‘greatest common factor method’. This is because it is one of the most efficient yet easiest ways of factoring a polynomial.
- Anna provides an Expression
- x^3+3x^2-4x-12
- Julie - Should we do a few examples? I think I know how to factor a polynomial and would love to try to do so. Anna - Absolutely, practicing will most definitely help us become better in understanding polynomials and how to factor them. Let’s try factoring 5 x 4 + 40x. Factor the sum of the two cubes.
- Example of Factoring Polynomials
- x^3+3x^2-4x-12 (x^3+3x^2) + (-4x-12) x^2(x+3) - 4(x+3) (x+3)(x^2-4) (x+3)(x+2)(x-2)
- Julie - I began with factoring the GCF which is 5x then rewrote it as the sum of cubes which then used that method to solve. Is this correct?
- A Factoring tip from Anna
- x^3+3x^2-4x-12(x^3+3x^2) + (-4x-12)x^2(x+3) - 4(x+3)(x+3)(x^2-4)(x+3)(x+2)(x-2)
- Wow, okay, thank you for teaching us!
- Anna - Yes, that is correct, great job! I will now show you both how to factor polynomials by grouping with the equation x^3+3x^2-4x-12.
- Yes, that is correct, great job! I will now show you both how to factor polynomials by grouping with the equation x^3+3x^2-4x-12.
- Maddie - How do you factor that? Anna - I first started off by grouping the terms of the expression and then continued to factor common monomials from each group. After that, I factored out the common binomial which is (x+3). Lastly, I factored the difference of squares to get the final answer.
- How do you factor that?
- I first started off by grouping the terms of the expression and then continued to factor common monomials from each group. After that, I factored out the common binomial which is (x+3). Lastly, I factored the difference of squares to get the final answer.
- Anna - Finally, something to remember is that you can also use a graph to help you factor a polynomial. By understanding the Factor Theorem, you can determine the corresponding factors of the polynomial but only if you can determine the zeros of a polynomial function from its graph. Julie and Maddie- Wow, okay, thank you for teaching us!
- Finally, something to remember is that you can also use a graph to help you factor a polynomial. By understanding the Factor Theorem, you can determine the corresponding factors of the polynomial but only if you can determine the zeros of a polynomial function from its graph.
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