Question

factorize x^4+3x^2+4​

Answer 1

$\huge\mathfrak Explanation$

Because the$x^4$ coefficient is 1

we know the coefficient for the$x^2$terms in the factor will also be 1 :

$(x^2)(x^2)$

Because the constant is a negative and the coefficient for the x term is a negative we know the sign for the constants in the factors will have one positive and one negative:

$(x^2+)(x^2-)$

Now we need to determine the factors which multiply to -4 and also add to -3:

1*(-4)=(-4);1-4=(-3)《 this IS the factor

$(x^2+1)(x^2-4)$

The factor$(x^2-4)$ is a special form of the quadratic:

$x^2-y^2=(x+y)(x-y)$

We can factor this term as:

$(x^2+1)(x+2)(x-2)$

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