What is x^2-19x+60 factored? Can someone help me with factoring polynomials?

Question

Please help me, If you just give me this one i might be able to do it i just need help!

Answer 1

x^2 - 19x + 60 = (x-15)(x-4)

All you need are two numbers that multiply to 60 and add to 19. The numbers are 15 and 4. Because the 19x term is negative, both signs have to be negative.

Answer 2

Here's what I do when I have to factor polynomials.

basic polynomial ax^2 +bx + c

1) look at the sign of c. if c is positive you know that x factors into an (x+n)(x+m) or (x-n)(x-m). if c is negative then it can only be (x+n)(x-m).

2) look at the sign of b. if c is positive and b is negative you know that it has to factor into a (x-n)(x-m) form.

3) factor c. knowing the basic form of the factor, see which ones add up or subtract to b.

so for this one, since it's +60 and -19, we know that it has to be (x-n)(x-m). The factors of 60 are (1,60), (2,30), (3,20), (4,15), (5,12), and (6,10). We can see that 4 and 15 add up to 19. so -4 + -15 equals -19 and -4 * -15 equals +60

so our factored polynomial is (x-4)(x-15)

Answer 3

60 = 5*3*2*2

x^2-19x+60
x^2-15x-4x+60
x(x-15)-4(x-15)
(x-4)(x-15)

Answer 4

x^2-19x+60
=x^2-15x-4x+60
=X(x-15) -4(x-15)
=(x-15)(x-4)

Answer 5

(x - 4)(x - 15)

x = 4, 15

Answer 6

(x-15)(x-4)=0

for quadratic equations, you could always find the roots by using the following equation, given ax^2+bx+c=0:

x = (-b) +/- (sqrt(b^2 - 4ac) / 2a)

so in your case, a=1, b = -19, c=60

Answer 7

(x-4)times (x-15)

Answer 8

(19 +/- root (361-120)) / 2
(19 +/- root 241 )/ 2
then just do both sides