What are the factors for the trinomial x2 plus 2x-24?

Answer 1

Assuming x**2+2x-24:

Factoring:

ax**2 + bx + c

Step 1: Multiply coefficients of first and third terms

a∗c

Step 2: Factor product of coefficient of first and third term (a*c), choose 2

factors whose sum is the coefficient of the second term (b)

a∗c=d∗e

d+e=b

Step 3: Rewrite equation

ax2 + dx + ex + c

Step 4: Factor sets of terms (first and second, third and fourth)

gx(hx + i) + j(hx + i)

where: g is the greatest common factor of a and d

where: j is the greatest common factor of e and c

where: h = a ÷ g, e ÷ j

where: i = d ÷ g, c ÷ j

Step 5: Combine Like terms:

(gx + j)(hx + 1)

Example:

Step 1: Multiply coefficients of first and third terms

1*-24 = -24

Step 2: Factor product of coefficient of first and third term (a*c), choose 2

factors whose sum is the coefficient of the second term (b)

-24=2*2*2*3*-1

-24=

-2*12, 2*-12

-4*6, 4*-6

-3*8, 3*-8

-4+6=2

Step 3: Rewrite equation

x**2-4x+6x-24

Step 4: Factor sets of terms (first and second, third and fourth)

gx(hx + i) + j(hx + i)

where: g is the greatest common factor of a and d

where: j is the greatest common factor of e and c

where: h = a ÷ g, e ÷ j

where: i = d ÷ g, c ÷ j

x(x-4)+6(x-4)

Step 5: Combine Like terms:

(x+6)(x-4)

Answer 2

(x + 6)(x - 4)