Simplify. 24 x 4 + 55 x 2 − 24

Question

Simplify.   24      x          4        +  55      x          2        −  24

Zayden Dorsey · Accepted Answer

Let   u  =      x          2      , then we have:  24      u          2        +  55  u  −  24We see that 24*-24=-576, and since 64*(-9)=-576, and that 64+(-9)=55, and so  24      u          2        +  55  u  −  24  =  24      u          2        +  64  u  −  9  u  −  24...=8u(3u+8)-3(3u+8)...=(3u+8)(8u-3)Thus in the end we have  24      x          5        +  55      x          2        −  24  =  (  3      x          2        +  8  )  (  8      x          2        −  3  )

excefebraxp · Accepted Answer

we apply the middle term factorization technique to solve this.

24 x^{4} + 55 x^{2} - 24

= 24 x^{4} + 64 x^{2} - 9 x^{2} - 24

= 8 x^{2} * (3 x^{2} + 8) - 3 * (3 x^{2} + 8)

= (3 x^{2} + 8) * (8 x^{2} - 3)

[taking

(3 x^{2} + 8)

as the common factor]
Answer:-

(3 x^{2} + 8) * (8 x^{2} - 3)

Simplify. 24x^4 +55x^2 -24

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