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Names & Exponent Rules
Sums & Differences
Products
Factoring GCF & 4-terms
Factoring Quadratics & Difference of 2 Squares
100
Give the complete two-word name of this polynomial: (½)x⁴
A QUARTIC MONOMIAL
100
Think of a number. Add one. Multiply by three. Subtract nine. Divide by three. Subtract the number first thought of. What is the result?
-2
100
4x²•7x³ =?
28x⁵
100
What's the difference of the LCM and the GCF? You can use the given numbers 12 and 8 as an example for your answer.
While the GCF is the LARGEST DIVISOR of two or more numbers, the LCM is the SMALLEST of all their MULTIPLES. The GCF of 12 and 8 is 4, and their LCM is 24.
100
Factor 64x² – 224x + 196
(8x – 14)²
200
What are the result of these sums 1) 15xᵏ + 3xᵖ and 2) 15xᵏ + 3xᵏ ?
1) The same; and 2) 18xᵏ
200
What are the results of these sums 1)4x³ - 7x³ and 2) 4x² - 7x³ ?
1) –3x³ and 2) is impossible to simplify.
200
–x•6x⁴ = ?
–6x⁵
200
Factor 12x⁶ – 20x⁴ + 24x²
12x⁶ – 20x⁴ + 24x² = 4x²(3x⁴ – 5x² + 6)
200
Factor: 2x² + 9x – 45
(2x + 15)(x – 3)
300
What are the products of these monomials 1) 15xᵏ • 3xᵖ and 2)15xᵏ • 3yᵖ ?
Products: 1) 45xᵏ˖ᵖ and 2) 45xᵏyᵖ
300
If a square has a side of 7x - 5 cm, what is its perimeter?
28x - 20 cm
300
If a square has a side of 7x - 5 cm, what is its area?
49x² – 70x + 25 square cm
300
Factor 3 – x⁴ + y²(x⁴– 3)
3 – x⁴ + y²(x⁴– 3) =1(3 – x⁴) – y²(3 – x⁴); therefore => (3 – x⁴)(1 – y²)
300
Factor x² + 11x – 26
(x + 13)(x – 2)
400
What are the quotients of 1) 15xᵏ ÷ 3xᵖ and 2) 15xᵏ ÷ 3yᵖ ?
Answers: 1) 5xᵏ˗ᵖ and 2) 5xᵏ / yᵖ
400
If a rectangle has a length of (12x - 9y) in. and a width of (5x + y) in., what is its perimeter?
34x - 16y inches
400
If a rectangle has a length of (12x - 9y) in and a width of (5x + y) in, what is its area?
60x² – 33xy – 9y² square inches
400
Factor 55x³ – 33x² – 35x + 21
55x³ – 33x² – 35x + 21 = 11x²(5x – 3) – 7(5x – 3) => (5x – 3)(11x² – 7)
400
Factor 361x⁸ – 289y⁴
(13x⁴ + 17y²)(13x⁴ – 17y²)
500
What is the result of this power? (15xᵏ)ᵖ
15ᵖ•xᵏᵖ
500
If the altitude of a right triangle is 3x + 2 cm, the base is 4x - 2 cm, and the perimeter is 3x² + 6x cm, what is the length of the hypotenuse?
Hypotenuse = P -(a + b) => 3x² + 6x – (7x) = 3x² – x
500
If the altitude of a right triangle is 14x³ – 18x² ft, and the base is 14x³ + 18x² ft, what's its area?
Area = (ab/2) =>(196x⁶ – 324x⁴)/2 = 98x⁶ – 162x⁴square feet
500
Factor 120ab³ – 10a + 96b³ – 8
120ab³ – 10a + 96b³ – 8 =>10a(12b³ – 1) + 8(12b³ – 1) => (12b³ – 1)(10a + 8)
500
Factor 162b⁶ – 450c²
2(81b⁶ – 225c²) => 2(9b³ + 15c)(9b³ – 15c)