I had to factor 5x^3-10x^2+43x-6. I got 5x(x^2+-2x)+3(x-2). My teacher said this was half right. What did I do wrong then? Thank you!!

CHECK THIS Ihh.tutor

Your answer expands to

5*x^3-10*x^2+3*x-6
Could you check the question if the coefficient is not 3x instead of 43x.

The expression as in the qustion has no rational factors, so there is probably a typo somewhere.

Yes, your answer is half-way, if not more, to factorizing completely.

Yes, it is supposed to be a three, not a fourty three.

If it is a 3x and not 43x, then you only have to continue your factorization:

5x(x^2+-2x)+3(x-2)
=5x(x^2-2x)+3(x-2)
=5x²(x-2) + 3(x-2)
=(5x²+3)(x-2)
which is the correct answer.
Check:
(5x²+3)(x-2)
=5x³ -10² + 3x -6 OK

To factor the expression 5x^3 - 10x^2 + 43x - 6, you need to follow a specific method such as factoring by grouping or using the rational root theorem. Let's go through the steps one by one:

1. Look for the greatest common factor (GCF) among all terms in the expression. In this case, the GCF is 1, so we can move on to the next step.

2. Check for a possible rational root by using the rational root theorem. The rational root theorem states that any rational root of the polynomial equation must be in the form of a fraction, where the numerator is a factor of the constant term (-6), and the denominator is a factor of the leading coefficient (5). The factors of -6 are ±1, ±2, ±3, and ±6, while the factors of 5 are ±1 and ±5. By testing these possible fractions, we can find the roots of the equation, if any.

After checking the possible rational roots, we find that x = 1/5 is a root of the equation. This means that (5x - 1) is a factor of the polynomial.

Now, we need to divide the polynomial by (5x - 1) and find the remaining factors:

3. Perform long division or synthetic division to divide the polynomial by (5x - 1). The quotient obtained will be a quadratic polynomial.

When you perform the division, you should get a quotient of x^2 - 2x + 3. Note that your attempt mentioned 5x(x^2 - 2x) as the quotient. However, this is incorrect because once you divide (5x - 1) into 5x^3, the resulting term should be x^2, not x.

So, the correct division should give you (x^2 - 2x + 3) as the quotient.

Finally, we can write the factored form of the polynomial as follows:

5x^3 - 10x^2 + 43x - 6 = (5x - 1)(x^2 - 2x + 3)

Therefore, the correct factorization of the expression is (5x - 1)(x^2 - 2x + 3).