1. A polynomial is a finite series of terms in the form ax^m where is a(n)------ and m is a(n)---------

Question

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)
please answer all of them

Answer 1

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.
a) x-3+ \sqrt{ }x - Not a Polynomial (due to the square root term)
b) -4x^8 - Polynomial
c) X^4+2y^2+z-w^2 - Polynomial
d) X^-3-x+1 - Not a Polynomial (due to negative exponent)

3. 2x^3y and 2yx^2 are not like terms because the exponent of x in 2x^3y is 3, whereas the exponent of x in 2yx^2 is 2. Like terms must have the same variables raised to the same power.

4. The two polynomials that have a sum of 4x−6 are:
B. (−4x^2+x−3) +(4x^2−5x−3)

5. Subtracting (2x^2+5x−3) −(x^2−2x+4) gives
C. x^2+7x-1

6. Multiplying (x−4)(x−5) gives
A. x^2-9x+20

7. Multiplying (x-4)^2 gives
B. x^2-8x+16

8. Jose is correct. The order of multiplying the quantities does matter. Multiplication is not commutative.

9. Completely factoring the expression ab^3+2a^2b^2 gives
C. a(b^3+2ab^2)

10. Completely factoring the expression x^2+x−6 gives
B. (x−3)(x+2)

11. Completely factoring the expression x^2−7x+12 gives
A. (x−4)(x−3)

12. Factoring the expression completely: X^2+6x+9 gives
B. (x+3)^2

13. Factoring the expression completely 4x^2+5x−21 gives
A. (4x−3)(x+7)

14. Factoring the expression completely 3x^2-75 gives
C. 3(x−5)(x+5)

15. Factoring the expression completely: 9x^2−16 gives
A. 9(x−4)(x+4)

Answer 2

1. isaac was asked to factor the following expression completely: 8x^2−20x−12 Isaac got (8x+4) (x−3) as their answer and claims it is correct because when multiplying the factors it simplifies to the original polynomial expression. Is Isaac correct? Why or why not?
2. Classify each of the following polynomials as factorable or not factorable.
Factorable
Not Factorable
X^2−2x−15
X^2+5x+2
X^2+6x+8
X^2+-5x+3
3. Explain why we know that 3x^2+4x−2 is not factorable.

Answer 3

1. Isaac is incorrect. The correct factored form of 8x^2−20x−12 is (2x-6)(4x+2), not (8x+4)(x−3). When multiplying the factors (2x-6)(4x+2), it simplifies to the original polynomial expression.

2. Classify each of the following polynomials as factorable or not factorable.
a) X^2−2x−15 - Factorable
b) X^2+5x+2 - Factorable
c) X^2+6x+8 - Factorable
d) X^2+-5x+3 - Not factorable

3. We know that 3x^2+4x−2 is not factorable because it cannot be written as the product of two binomials with integer coefficients. It does not have any integer factors that can be multiplied to obtain the original polynomial.