How do I convert the equation to intercept form by factoring y=x^2-4x-21

Question

How do I convert the equation to intercept form by factoring y=x^2-4x-21

Answer 1

x^2 - 4x - 21

can be factored as:

(x-7)(x+3)

Giving us the zero's/roots/INTERCEPTS of x. *These points are where the graph crosses the X axis.

given this,

y = (x-7)(x+3)

is our intercept form.

TIPS:

the best way to factor is to look at the two values on the right (in this example: -4 and -21)

and look at the factors of 21: (1*21) , (3*7)

we know since 21 is negative, one of these numbers must be negative, so which of the factors added together- keeping in mind that one must be negative - will add up to -4? This is the best way to factor when x^2 does not have a constant in front.

Answer 2

x²- 4x -21 has 2 factors

=(x-7)(x+3)

which by the FOIL method is x² +3x -7x -21

when y=0, the x-intercepts are x=7 and x=-3

just set each factor equal to zero: x-7=0, so x=7; x+3=0, so x=-3

factoring is trial and error, but if there are easy integer factors, they will involve factors of the constant term which is 21. There are only two factors, 7 and 3. Then just make sure the signs are right. Since -4x has a negative coefficient, you want the larger number, the 7 to be negative and the 3 positive.

Answer 3

What numbers hold true if you start factoring?

(x-7)(x+3)

check answer

x^2 +3x -7x - 21

simplify,

x^2 -4x - 21