S5 Pol 2 Operations with polynomials
Success Criteria
Use operations of addition, subtraction and multiplication with polynomials
Open Ended Task
Open Ended Task
Damien performed an operation on two polynomial expressions and obtained an answer of 6x6+2x4+8x2. He can't remember the two polynomials or the operation that he used. Write down three different mathematical statements (one with addition, one with subtraction and one with multiplication), that would give the answer Damien obtained.
Enabling Prompt
1. Write down two polynomials that would add to give 5x4.
2. Write down two polynomials that would subtract to give 4x3.
3. Write down two polynomials that would multiply to give 12x8.
Extending Task
The polynomial P(x)=x3+4x2−9x−36 can be written in the form
P(x)=(x−a)(x−b)(x−c), where
a,b,c are non-zero integers. What are the values of
a,b,c ?
Solution
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Consolidating Task
Damien performed another operation on two polynomial expressions and obtained an answer of 8x5+6x2+8x. He can't remember the two polynomials or the operation that he used. Write down three different mathematical statements (one with addition, one with subtraction and one with multiplication), that would give the answer Damien obtained.
Consolidating Task Solution
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Check Your Understanding