S5 Pol 2 Operations with polynomials

Stage 5 Mathematics 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 LaTeX: 6x^6+2x^4+8x^26x6+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 LaTeX: 5x^45x4.

2. Write down two polynomials that would subtract to give LaTeX: 4x^34x3.

3. Write down two polynomials that would multiply to give LaTeX: 12x^812x8.

Extending Task

The polynomial LaTeX: P(x)=x^3+4x^2-9x-36P(x)=x3+4x29x36 can be written in the form LaTeX: P(x)=(x-a)(x-b)(x-c)P(x)=(xa)(xb)(xc), where LaTeX: a,b,ca,b,c are non-zero integers. What are the values of LaTeX: a,b,ca,b,c ?

Solution

Panel Content

Consolidating Task

Damien performed another operation on two polynomial expressions and obtained an answer of LaTeX: 8x^5+6x^2+8x8x5+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

Panel Content

Check Your Understanding