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HI guys can you help me?​

HI guys can you help me?​-example-1
User LeslieM
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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!

User Logan Capaldo
by
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