Questions: Factor the higher degree polynomial. Select "Prime" if the polynomial cannot be factored. 4 x^4+5 x^2-6 4 x^4+5 x^2-6= Prime

Transcript text: Factor the higher degree polynomial. Select "Prime" if the polynomial cannot be factored. \[ 4 x^{4}+5 x^{2}-6 \] \[ 4 x^{4}+5 x^{2}-6= \] $\square$ Prime

Solution

Solution Steps

Step 1: Substitute to simplify the polynomial

Let $ y = x^2 $. Substitute $ y $ into the polynomial: \[ 4x^4 + 5x^2 - 6 = 4y^2 + 5y - 6. \]

Step 2: Factor the quadratic in terms of $ y $

Factor the quadratic expression $ 4y^2 + 5y - 6 $: \[ 4y^2 + 5y - 6 = (4y - 3)(y + 2). \]

Step 3: Substitute back $ y = x^2 $

Replace $ y $ with $ x^2 $ in the factored form: \[ (4y - 3)(y + 2) = (4x^2 - 3)(x^2 + 2). \]

Final Answer

\[ 4 x^{4}+5 x^{2}-6 = (4x^{2}-3)(x^{2}+2) \]

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