Grade 9 Polynomials

Definitions

100

How many terms does this polynomial have?

3x² + 7x - 4

3

200

How do we represent 2n² + n - 5 with algebra tiles?

2 shaded large boxes, one shaded rectangle, 5 unshaded small squares

300

What type of polynomial is this expression?

9b - 13 + b²

Trinomial

400

What are the coefficients in this expression?

-4x⁴ + x - 1

-4 and 1

500

What is the degree of this expression?

12m⁵n²

5

Adding

100

(3x + 2) + (x + 5)

4x + 7

200

(x² + 4x) + (4x² - x)

With algebra tiles

5x² + 3x

5 shaded large squares

3 shaded rectangles

300

(6x² + 2x - 1) + (2x² - x + 4)

Algebraically

8x² + x + 3

400

(-7n² -3n + 7) + (-2n² + 4n + 1)

-9n² + n + 8

500

(3y² - 4xy + 2x²) + (2xy + y² - 5x²)

4y² - 2xy - 3x²

Subtracting

100

(x - 5) - (x + 2)

With algebra tiles

-7

7 small unshaded squares

200

(2m + 4) - (3m - 5)

Algebraically

-m + 9

300

(4x² + 3x -5) - (3x² + x + 2)

x² + 2x - 7

400

(7g² - 4g + 6) - (-2g² + g - 12)

5g² - 5g + 18

500

(-3x² + 5x - 8) - (-x² - 2x - 4)

-2x² + 7x - 4

Multiplying

100

2(3x + 1)

6x + 2

200

2(5x² + x - 3)

10x² + 2x - 6

300

5x(x - 3)

With algebra tiles

5x² - 15x

400

(-3r)(4r + 3)

Algebraically

-12r² - 9r

500

2x(7x - 3y)

14x² - 6xy

Dividing

100

(4x - 12) ÷ 4

x - 3

200

(21x + 14) ÷ 7

Algebraically

3x + 2

300

(4x² - 12x + 24) ÷ 4

x² - 3x + 6

400

(6x² - 3x) ÷ 3x

With algebra tiles

3x - 1

500

(3x² - xy) ÷ x

3x - y