When the expression $$ 7(x-3)^{2}-4(x-3)-3 $$ is fully factored, it ca be expressed in the form $$ (a x-b)(x-c) $$. The values of a , b , and c are:

Question

UpStudy AI · Accepted Answer

Let $$ u = x - 3 $$. Then the expression becomes

$$
7u^2 - 4u - 3.
$$

We look for two numbers whose product is $$7(-3) = -21$$ and whose sum is $$-4$$. We observe that

$$
-7 \times 3 = -21 \quad \text{and} \quad -7 + 3 = -4.
$$

Rewrite the quadratic:

$$
7u^2 - 7u + 3u - 3.
$$

Factor by grouping:

$$
7u(u - 1) + 3(u - 1) = (7u + 3)(u - 1).
$$

Recall that $$ u = x - 3 $$. Substitute back:

$$
(7(x-3)+3)(x-3-1) = (7x-21+3)(x-4) = (7x-18)(x-4).
$$

This is in the form $$(ax - b)(x - c)$$ where

$$
a = 7,\quad b = 18,\quad c = 4.
$$
$$ a = 7 $$, $$ b = 18 $$, and $$ c = 4 $$.

When the expression is fully factored, it ca
be expressed in the form . The values of a , b , and c are: