1. A polynomial is a finite series of terms in the form ax^m where is a(n)------ and m is a(n)---------
Real number
Irrational number
whole number
rational number
2. Classify each expression below as either a polynomial or not.
Polynomial
Not a Polynomial
x-3+ \sqrt{ }x
-4x^8
X^4+2y^2+z-w^2
X^-3-x+1
3. Explain why 2x^3y and 2yx^2 are not like terms
4. Which two polynomials have a sum of 4x−6?
A. 4x^2+x−3) +(4x^2+3x+3)
B. (−4x^2+x−3) +(4x^2−5x−3)
C. (−4x^2+x−3) +(4x^2+3x−3)
D. (−4x^2+x−3) +(−4x^2+3x+3)
5. Subtract (2x^2+5x−3) −(x^2−2x+4)
A. 3x^2+3x+1
B. X^2+3x+1
C. X^2+7x-1
D. X^2+7x-7
6. Multiply (x−4)(x−5)
A. X^2-9x+20
B. X^2+9x-20
C. x2−9x-20
D. x^2+9x+20
7. Multiply (x-4)^2
A. X^2+16
B. X^2-8x+16
C. X^2+8x-16
D. X^2-8x-16
8. Given the expression)(−2x^2)(3x)(x) Jose says that you will get different results if you change the order that you multiply the quantities. Is Jose correct? Explain.
A. No because multiplication is commutative.
B. Yes, because multiplication is not associative.
C. Yes, because multiplication is not commutative.
D. No becuase multiplication is associative.
9. Completely factor the following expression ab^3+2a^2b^2
A. ab(b^2+2ab)
B. b^2(ab+2a^2
C. a(b^3+2ab^2)
D. ab^2(b+2a)
10. Completely factor the following expression: x^2+x−6
A. (x+6)(x−1)
B. (x−3)(x+2)
C. (x−3)(x-2)
D. (x−6)(x+1)
11. Completely factor the following expression x^2−7x+12
A. (x−4)(x−3)
B. (x+4)(x-3)
C. (x−4)(x+4
D. (x+4)(x+3)
12. Factor the following expression completely: X^2+6x+9
A. (x−3)(x+3)
B. (x+3)^2
C. (x+6)(x+9)
D. (x-3)^2
13. Factor the following expression completely 4x^2+5x−21
A. (4x−3)(x+7)
B. (2x+3)(2x−7)
C. (4x−7)(x+3)
D. (2x+7)(2x−3)
14. Factor the following expression completely 3x^2-75
A. (3x+15)(x−5)
B. (3x−15)(x+5)
C. 3(x−5)(x+5)
D. 3(x−5)(x−5)
15. Factor the following expression completely: 9x^2−16
A. 9(x−4)(x+4)
B. (3x−4)(3x+4)
C. (3x−4)(3x−4)
D. (3x+4)(3x+4)
1. a) Real number b) Whole number
1. A polynomial is a finite series of terms in the form ax^m where a is a real number and m is a whole number.
2. Classify each expression below as either a polynomial or not:
- x - 3 + √x is not a polynomial because the term √x is not in the form ax^m.
- -4x^8 is a polynomial because it is in the form ax^m.
- x^4 + 2y^2 + z - w^2 is a polynomial because it is in the form ax^m.
- x^-3 - x + 1 is not a polynomial because the term x^-3 is not in the form ax^m.
3. 2x^3y and 2yx^2 are not like terms because they have different exponents. In like terms, the variable must have the same exponent in each term. Since one term has an exponent of 3 and the other has an exponent of 2, they are not considered like terms.
4. The two polynomials that have a sum of 4x - 6 are:
B. (-4x^2 + x - 3) + (4x^2 - 5x - 3)
C. (-4x^2 + x - 3) + (4x^2 + 3x - 3)
5. Subtract (2x^2 + 5x - 3) - (x^2 - 2x + 4):
B. x^2 + 3x + 1
6. Multiply (x - 4)(x - 5):
A. x^2 - 9x + 20
7. Multiply (x - 4)^2:
B. x^2 - 8x + 16
8. Given the expression (-2x^2)(3x)(x), Jose is correct. Changing the order in which you multiply the quantities will give different results. This is because multiplication is not commutative.