of actorise $$ 6 a^{2}-36 a+48 $$

Question

UpStudy AI · Accepted Answer

Certainly! Let's factorize the quadratic expression:

$$ 6a^{2} - 36a + 48 $$

**Step 1: Factor Out the Greatest Common Factor (GCF)**

First, identify the greatest common factor of all the terms. The GCF of 6, 36, and 48 is **6**.

$$ 6a^{2} - 36a + 48 = 6(a^{2} - 6a + 8) $$

**Step 2: Factor the Quadratic Expression**

Now, focus on factoring the quadratic inside the parentheses:

$$ a^{2} - 6a + 8 $$

We need to find two numbers that multiply to **8** (the constant term) and add up to **-6** (the coefficient of the middle term).

Let's list the factor pairs of 8:

- 1 and 8
- 2 and 4

Now, considering the signs, since the product is positive and the sum is negative, both numbers should be negative:

- $$-2$$ and $$-4$$

Check:

$$ (-2) + (-4) = -6 $$
$$ (-2) \times (-4) = 8 $$

**Step 3: Write the Factored Form**

Using these numbers, we can write the factored form of the quadratic:

$$ a^{2} - 6a + 8 = (a - 2)(a - 4) $$

**Step 4: Combine with the GCF**

Don't forget to include the GCF we factored out earlier:

$$ 6(a^{2} - 6a + 8) = 6(a - 2)(a - 4) $$

**Final Factored Form:**

$$ 6a^{2} - 36a + 48 = 6(a - 2)(a - 4) $$
The expression $$ 6a^{2} - 36a + 48 $$ can be factored as $$ 6(a - 2)(a - 4) $$.

of actorise \( 6 a^{2}-36 a+48 \)