Download 1.Simplify by factoring.Assume that all expressions under radicals

1.Simplify by factoring.Assume that all expressions under radicals represent non negative
numbers.^50a^b.
=
50a^ b  25  2a^ b  5 2a^ b
2.Television sets. what does it mean to refer to a 20in. tv set or a 25in. tv set? such units refer to the
diagnal of the screen. A 35in. tv set also has width of 28inches. what is its height. what is the height of a
35in.tv?
Ans = 21 inch height
3.this is a fraction r^-9 over (r+3)^2 simplify by removing factors of 1.
r^-9/(r+3)^2
= 1/r^9(r+3)^2 = 1/r^9(r^2+6r+9) = 1/(r^11 + 6 r^10 + 9 r^9)
4.Identify the degree of each term of the polynomial and the degree of the polynomial.-7x^3+4x^2+6x+9
first term is, second term is,third term is, fourth term is, and polynomial is.
Degree is defined as the maximum power of x. here
first term is .-7x^3 so degree is 3
second term is 4x^2, so degree is 2
third term is 6x , so degree is 1
fourth term is 9, so degree is 0
and polynomial is.-7x^3+4x^2+6x+9 so degree is 3 (highest power remember)
5.Find the x-intercepts for the graph of the equation y=x^2+2x-3.
X- intercept is when the function value becomes 0 , that is y=0, so x^2+2x-3 =0
So factoring x^2+3x-x -3 =0, so x(x+3) -1(x-3) =0
So (x+3)(x-1) = 0 , hence x =-3,1
So x-intercepts are (-3,0) and (1,0)
6.Factor out completely 49m^2+64-112m.
49m^2+64-112m
= 49m^2-112m +64
For factoring we see 112 = 56+56, so we get
49m^2-56m -56m +64
= 7m(7m-8) -8(7m-8)
=(7m-8)(7m-8)
=(7m=8)^2
7.Rationalize the denominator. Assume that all expressions under radicals represent positive numbers.
this is a fraction also ^x-^y over ^x+^y.
For rationalizing, we multiply numerator and denominator by
x y
x y

x y
x y

8. Solve 10x^4-19x^2+6=0.
x y
x y

( x  y )2
( x )2  ( y )2

x y
x y2 x y
x y
Factorizing , we get
10x^4-15x^2- 4x^2+6=0.
= 5x^2(2x^2-3) -2(2x^2-3) =0
(5x^2-2)(2x^2-3) =0
So (5x^2-2)=0 or (2x^2-3) =0
So, x^2 = 2/5 or x^2 = 3/2 so x =
2 / 5 or - 2 / 5 or 3 / 2 or - 3 / 2
9.Factor completely 9v^2-121.
9v^2-121.
= (3v)^2 – (11)^2
= (3v-11)(3v+11)
As the formula (a-b)(a+b ) = a^2-b^2
10.Find the greatest common factor for the group of terms. -18a^4,3a^5
-18a^4 and 3a^5 we first consider numbers, 18 and 3, clearly 3 is the gcd of 18 and 3.
Now consider polynomial a^4 and a^5 , since a^4 is the lesser degree of the two, we have to choose this,
So gcd = 3a^4
.11.Factor the trinomial v^3-3v^2-54v.
v^3-3v^2-54v.
= v(v^2 -3v-54)
= v( v^2 – 9v+6v-54)
=v[v(v-9) +6(v-9)
=v(v-6)(v-9)