Question

The expression $12y^2-65y+42$ can be written as $(Ay-14)(By-3),$ where $A$ and $B$ are integers. What is $AB + A$?

Answer 1

Answer:

$AB + A = 16$

Step-by-step explanation:

Given

$12y^2 - 65y + 42 = (Ay -14)(By - 3)$

Required

Find $AB + A$

$12y^2 - 65y + 42 = (Ay -14)(By - 3)$

Expand

$12y^2 -56y -9y + 42 = (Ay - 14)(By -3)$

Factorize

$4y(3y -14) -3(3y - 14) = (Ay - 14)(By -3)$

Factor out 3y- 14

$(3y - 14)(4y -3) = (Ay - 14)(By -3)$

By comparison:

$Ay - 14 = 3y - 14$

and

$By - 3 = 4y - 3$

So, we have:

$Ay - 14 = 3y - 14$

Add 14 to both sides

$Ay = 3y$

Divide both sides by y

$A = 3$

$By - 3 = 4y - 3$

Add 3 to both sides

$By = 4y$

Divide both sides by y

$B = 4$

So, the expression $AB + A$ is:

$AB + A = 3 * 4 + 4$

$AB + A = 12 + 4$

$AB + A = 16$