How do you factor #p^4+5p^2+6#?

Answer 1

(p^2 + 2)(p^2 + 3)

Call #x = p^2#, the trinomial transforms to: #f(x) = x^2 + 5x + 6.# Factor f(x). Find 2 numbers knowing sum (5) and product (6). They are 2 and 3. #f(x) = (x + 2)(x + 3)# #f(p) = (p^2 + 2)(p^2 + 3)#

If being asked, you can continue factoring with complex numbers. #f(p) = (p - isqrt2)(p + isqrt2)(x - isqrt3)(x + isqrt3)#

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Answer 2

Ethan Adkins

To factor the expression (p^4 + 5p^2 + 6), we can treat it as a quadratic equation in terms of (p^2). Let (x = p^2), then the expression becomes (x^2 + 5x + 6). We can factor this quadratic expression by finding two numbers that multiply to (6) and add to (5). These numbers are (2) and (3). So, we can rewrite the expression as ((x + 2)(x + 3)). Substituting back (x = p^2), we get ((p^2 + 2)(p^2 + 3)). Therefore, the factored form of (p^4 + 5p^2 + 6) is ((p^2 + 2)(p^2 + 3)).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.