Polynomials

Writing equations

100

Name the polynomial by its degree and no. of terms

7x⁴- 3x+2x-1

Quartic and 4 term polynomial

200

Give an example for cubic trinomial

ax³+bx+c

Or whatever with cube in its degree and should have 3 terms.

300

Give the equation

Translated 10 units down, and 3 units to left

y= (x+3)³-10

400

What is called the number in front of the term with the highest co-efficient

Leading coefficient

500

Write the equation of the cubic function

Stretched vertically by 3 which is shifted right by 4 units and then up to 1 point and reflected over x axis.

y= -3 (x-4)³ +1

Addition/ Subtraction

100

Subtract

(x² - 8) - (3x³ - 6x - 4 + 9x²)

-3x³ - 8x²  +6x - 4

200

Add

(2x² -7x + 5x⁴ +4x³ - 11)+( 6x³ + x⁴ -3x² + 10x)

6x⁴ + 10x³ - x² +3x - 11

300

Subtract the polynomial

(-x²-5)-(-3x² - x-8)

2x² +x+3

400

Subtract the polynomial

(2x - 3x) - (x² -2x + 4)

-x² + x - 4

500

Add the following

(-1 + x² + 2x) + (1 -2x + 2x²)

3x²

Multiply

100

Find out the factors for 

x³ +x² -12x

x (x+4) (x-3)

200

(3x) (2y)

6xy

300

Factor

6x²+ 5x - 4

(2x - 1) (3x + 4)

400

Multiply

4x (x-2)²

4x³−16x²+16x

500

Multiply 

(d+3) (d²-4d+1)

d³-d² -11d +3

Factoring

100

Factor

x²-9

(x+3) (x-3)

200

Factor 

x³ + x²  - 2x

x (x-1) (x+2)

300

Factor the following binomial bu using suitable method

5y²-22y+8

(5y - 2) (y - 4)

400

Factor the following

(8x⁴ + 8x³ +27x+27)

(3x+4) (9x² +12x +16) (x+1)

500

Factor the following

12x³ - 9x²+32x - 24

(3x²+8) (4x - 3)

Long/ Synthetic division

100

Use synthetic division

3x^3- - 4x² + x - 16 / x-2

3x² + 2x + 5 + (-6)/ X-2

200

Solve the following

(3x² +3x -12) / (x  + 2)

3x - 3 + (-6)/ x+2

300

Use long division to find the remainder and quotient

Divisor : x-3

Dividend: x² +2x +6

 Quotient : x+5

Remainder : 21 or 21/x-3

400

Is (x+5) a factor of (2x² -6x -1). If yes find the other factor for that

 NO

500

Divide the following by long division method

x⁴-10x²+11

x³ - x² -9x +9 +2/(x+1)