Factoring is aided by having the equations in standard form. The first step in each case is to put the equations in that form. The zero product property tells you that a product is zero when a factor is zero. The solutions are the values of x that make the factors zero.

1. x^2 -x = 0

x(x -1) = 0 . . . . . x = 0 or 1

2. 16x^2 +1 = 0

This is the "difference of squares" ...

(4x)^2 - (i)^2 = 0

(4x -i)(4x +i) = 0 . . . . . x = -i/4 or i/4 (zeros are complex)

3. x^2 +10x +25 = 0

(x +5)(x +5) = 0 . . . . . x = -5 with multiplicity 2

5 0

2 years ago

If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) has how many different positive factors greater than 1?

harina [27]

Answer:

d. 15

Step-by-step explanation:

List the exponents of each of the prime factors. Here, they are 3, 1, 1.

Add 1 to each of these values and form the product of these sums:

(4)(2)(2) = 16

This is the number of divisors of the number. Since 1 is included in this count, 15 of the divisors are greater than 1.

3 0

3 years ago

Solve the inequality state your answer algebraicly and in interval notation<br> 4(n-3)-2n<-10+2n

AlexFokin [52]

Answer:

See below

Step-by-step explanation:

Expand L side to get

4n -12 -2n < -10 + 2n simplify L side

2n -12 < -10 +2n subtract 2n from both sides

<u>-12 < -10 </u> <===== so the equation is true for ALL n

(-∞ , + ∞ )

4 0

1 year ago