Question

1. find the degree of the monomial 6p^3q^2

a. 2
b. 3
c. 5
d.6
2. simplify (7t^2+9) + (6t^2+8)
a. t^2 + 1
b. 13t^2+17
c. 13t^4+17
d.42t^2+72
3. simplify 3n(4n^2+5n)
a. 12n^3+15n^2
b.7n^2+8n
c.12n^2+15n
d.12n^2+8n
4. factor 18s-63
a.9(2s+7)
b.6(3s-11)
c.18(s-3)
d.9(2s-7)
5. what is the simpler form of (5x^3+2)(5x^3-2)
a.25x^6+20x^3-4
b.25x^6-20x^3-4
c.25x^9-4
d.25x^6-4
6. simplify (x+7)(x+5)
a. x^2+12x+35
b. x^2+35
c. x^2+12x+12
d. x^2+12x+2
7. simplify (2z-3)^2
a.4z^2-9
b.4z^2-9z
c.4z^2-12x-9
d.4z^2-12x+9

Answer 1

Part 1: 5

Part 2:
`13t^2+17`

Part 3:
`12n^3+15n^2`

Part 4:9(2s-7)

Part 5:
`25x^6-4`

Part 6:
`(x^2+12x+35)`

Part 7:
`4z^2-12z+9`

Explanation:

Part 1: we have to find the degree of monomial
`6p^3q^2`

The degree of a polynomial is the highest degree of its monomials (individual terms) with non-zero coefficients.

The degree of monomial= 3+2=5

Option c is correct.

Part 2: simplify
`(7t^2+9) + (6t^2+8)`

`(7t^2+9) + (6t^2+8)`

`(7t^2+6t^2)+(9+8)`

`13t^2+17`

Option b is correct.

Part 3: simplify
`3n(4n^2+5n)`

`3n(4n^2+5n)`

By distributive property

`12n^3+15n^2`

Option a is correct.

Part 4: . factor 18s-63

18s-63

Taking 9 common from both terms

9(2s-7)

Option d is correct.

Part 5: simpler form of
`(5x^3+2)(5x^3-2)`

`(a-b)(a+b)=a^2-b^2`

`(5x^3+2)(5x^3-2)=(5x^3)^2-2^2=25x^6-4`

Option d is correct.

Part 6: simplify (x+7)(x+5)

`(x+7)(x+5)=(x^2+5x+7x+35)=(x^2+12x+35)`

Option a is correct.

Part 7: simplify
`(2z-3)^2`

`(a-b)^2=a^2+b^2-2ab`

`(2z-3)^2=(4z^2+9-2(2z)(3)=4z^2-12z+9`

Option d is correct.