Question

factor the following trinomial.
$8x^2 - 29x - 12$
$(x - ?)(8x + )$

Explanation:

Step1: Set up equation for constants

Let the missing constants be $a$ and $b$, so:
$$(x - a)(8x + b) = 8x^2 - 29x - 12$$

Step2: Expand left-hand side

$$8x^2 + (b - 8a)x - ab = 8x^2 - 29x - 12$$

Step3: Match coefficients

We get two equations:

1. $b - 8a = -29$
2. $-ab = -12 \implies ab = 12$

Step4: Solve for $a$ and $b$

Test positive integer values for $a$ (since $ab=12$):
If $a=4$, then $b=\frac{12}{4}=3$.
Check: $3 - 8(4) = 3 - 32 = -29$, which matches.

Answer:

The missing constants are 4 and 3, so the factored form is $(x - 4)(8x + 3)$