Question

factor $x^2 - 3x - 28$. $ax^2 + bx + c$ identify the values that should be written to complete the x diagram. on the top: on the bottom: on the sides: rewrite the expression using the numbers on the sides of the x diagram. use double grouping to factor the four terms. $x^2 - 3x - 28 = $

Explanation:

Step1: Find $ac$ and $b$

For $x^2-3x-28$, $a=1$, $b=-3$, $c=-28$.
$ac = 1\times(-28) = -28$

Step2: Find side values (sum to $b$)

Find two numbers that multiply to $-28$ and add to $-3$: $4$ and $-7$, since $4\times(-7)=-28$ and $4+(-7)=-3$.

Step3: Rewrite the trinomial

Split the middle term using the side values:
$x^2 + 4x - 7x - 28$

Step4: Group and factor terms

Group first/second and third/fourth terms:
$(x^2 + 4x) + (-7x - 28)$
Factor out GCF from each group:
$x(x + 4) - 7(x + 4)$
Factor out the common binomial:
$(x + 4)(x - 7)$

Answer:

On the top: $-28$
On the bottom: $-3$
On the sides: $4$ and $-7$
Rewritten expression: $x^2 + 4x - 7x - 28$
$x^2 - 3x - 28 = (x + 4)(x - 7)$