Answer:
Final factored form is y = (x - 2)(x + 2)(x - 1)(x + 1)
Explanation:
y = x^4 - 5x^2 + 4
First step is to separate the first term into something that looks like (x^2)^2. Everything stays the same in this step. Hence:
= (x^2)^2 - 5(x^2) + 4
(x^2)^2 is the same as x^4 because powers inside brackets are multiplied by the power outside the brackets (2 × 2 = 4).
Next step is to replace all x^2 in our equation with just x. Hence:
= (x)^2 - 5x + 4
We can the factor it like a quadratic, making the two numbers inside the brackets multiply to give us 4 and add to give -5. Hence:
x^2 - 5x + 4 = (x - 4)(x - 1)
Now we can reverse a previous step, replacing all x's in the equation with x^2. Hence:
= (x^2 - 4)(x^2 - 1)
Difference of perfect squares states that if we have two squared numbers in our brackets, and one is subtracted from the other (a^2 - b^2), this can be factorised as (a - b)(a + b). Hence:
= (x - √4)(x + √4)(x - √1)(x + √1)
= (x - 2)(x + 2)(x - 1)(x + 1)
And this is now the final factored form, with each bracket corresponding to an x intercept.
Hope that helps!