Find the value of 'a' and 'b; if $x^{2} - 4$ is a factor of ${a x}^{4} + {2 x}^{3} - {3 x}^{2} + b x + 4$

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Solution

Let $f (x) = a x^{4} + 2 x^{3} - 3 x^{2} + b x - 4$ and $g (x) = x^{2} - 4$
We have $g (x) = x^{2} - 4 = (x - 4) (x + 4)$
Given: $g (x)$ is a factor of $f (x)$

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Respected Sir,

Please help me in solving my below mentioned doubt:

Find the values of a and b, if x² - 4 is a factor of ax⁴ + 2x³ - 3x² + bx - 4.

{(a x)}^{4} + 2 x - {3 x}^{2} + b x - 4

x^{2} - 4

2 x^{3} + a x^{2} + b x + 12

Find the value of a for which (x - 4) is a factor of $(2 x^{3} - 3 x^{2} - 18 x + a)$ .

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