Question

Consider the following polynomiat function. f(x)=x^4−5x^3+x^2+25x−30 Step 1 of 4 : Factor the polynomial completely.

Answer 1

To factor the polynomial completely, we can use various methods such as factoring by grouping, synthetic division, or using the rational root theorem. For the given polynomial, x⁴ - 5x³ + x² + 25x - 30, factoring by grouping yields x(x - 5)(x² + 25) - 30 as the complete factorization.

Step-by-step explanation:

To factor the polynomial completely, we can use various methods such as factoring by grouping, synthetic division, or using the rational root theorem. Considering the given polynomial, x⁴ - 5x³ + x² + 25x - 30, we can try factoring it by grouping.

Grouping terms, we have: (x⁴ - 5x³) + (x² + 25x) - 30.

Factoring each group further, we get x³(x - 5) + x(x + 25) - 30.

Now, we can factor out common terms and simplify further: x³(x - 5) + x(x + 25) - 30 = x(x - 5)(x² + 25) - 30.

So, the polynomial x⁴ - 5x³ + x² + 25x - 30 can be completely factored as x(x - 5)(x² + 25) - 30.