Factorise the following quadratic:3𝑥2−17𝑥+10

To factorise the quadratic equation 3x² - 17x + 10, we need to find two numbers that multiply to give 30 (3*10) and add up to -17.

The numbers that satisfy these conditions are -15 and -2 because -15*-2 = 30 and -15 + -2 = -17.

So, we can write the middle term (-17x) as the sum of -15x and -2x.

The equation becomes: 3x² - 15x - 2x + 10.

Now, we can factor by grouping:

3x(x - 5) - 2(x - 5)

Now, you can see that (x - 5) is a common factor. So, we can write the equation as:

(3x - 2)(x - 5)

So, the factorised form of the quadratic equation 3x² - 17x + 10 is (3x - 2)(x - 5).