Question

How do you factor #3x^2 - 10x + 3?

Answer 1

3x^2-10x+3

3x^2-9x-x+3

3x(x-3) -1(x-3)

(3x-1) (x-3)

Answer 2

Factorising 3x² - 10x + 3

We can factorise this quadratic polynomial (as it's degree is 2) by using splitting the middle term.

Step 1: First of all, we've to multiply the co-efficient of x² and the constant term.

Here, the co-efficient of x² is 3 and constant term is also 3.

Multiplying 3 and 3, we obtain, 9.

Step 2: Now we've to find two factors of 9 which would give us the sum as the co - efficient of x.

Here, the co-efficient of x is - 10.

Factors of 9 are $\mathsf{\pm 1 \pm 3 \pm 9}$

So, the two factors of 9 which would give us the sum as - 10 are - 1.

Step 3: We've to substitute - 1 and - 9 along with the respective variable. You can write - 1 first or - 9 or vice versa. It won't be a problem.

3x² - 10x + 3

(or) 3x² - 9x - x + 3

Step 4: Group the terms.

(3x² - 9x) - (x + 3)

Step 5: Take common outside.

3x(x - 3) - 1(x - 3)

Step 6: You'll observe that both the terms inside the bracket will be same as the other. Now as they both arw common, take them out. Write the uncommon terms inside the bracket after the common terms.

(x - 3)(3x - 1)

So, x - 3 and 3x - 1 are the factors of 3x² - 10x + 3.

$\fbox{\bold{\mathsf{Note:}}}$

There can be no factor, one factor or maximum two factors for a quadratic polynomial.

For example: x² - 1

It has no factor since it is a quadratic polynomial.

Example 2: x² - 2x + 1

It has only one factor since it is a quadratic polynomial.