factor x squared-7x-30 completely

Question

a. (x-1)(x+30)

b. (x-5)(x+6)

c. (x-10)(x+3)

d. (x+2)(x-15)

Answer 1

x² - 7x - 30 = (x-10)(x+3) since -30 = -10*3, and -10+3 = -7, the coefficient of x.

Answer: c. (x-10)(x+3)

Answer 2

just testing this site

Answer 3

X²-10X+3X-30

= X(X-10)+3(X-10)

= (X-10) (X+3)

Answer 4

The easiest way to factor a quadratic equation   ax² + b x + c is to use the quadratic formula. What you are doing is assuming the equation is set equal to zero and then solving for the different values of x that would make this a true statement. This will then give you the factors of the quadratic equation

So if ax² + b x + c = 0, and the quadratic equation

x₁ =(-b + sqrt(b² - 4ac))/2a 

x₂ =(-b - sqrt(b² - 4ac))/2a

Which would give us the factoring of (x-x₁)(x-x₂)

 

In the polynomial x² - 7x -30

a =1.   b = -7, and c = -30

if we substitute those values we get

x₁ = (-b + sqrt(b² - 4ac))/2a = (-(-7) + sqrt((7² - 4 * (1)*(-30))/(2*1) = (7+sqrt(49+120))/2 = (7+sqrt(169))/2 = (7+13)/2 = 20/2 = 10

x₂ = (-b - sqrt(b² - 4ac))/2a = (-(-7) - sqrt((7² + 4 * (1)*(-30))/(2*1)= (7 - sqrt(169))/2 = (7-13)/2 = (-6)/2 = -3

Now, if we substitute in the values for x₁ and x₂, we get

(x-x₁)(x-x₂) = (x-10)(x-(-3)) = (x-10)(x+3) -- Which is ANSWER C

Note: you can verify your answer by multiplying out the factored answer

(x-10)(x+3) = x²+ 3x -10x - 30 = x² -7x -30