Question

Find the value of a, if x+2 is a factor of
${4x}^{4} + {2x}^{3} - {3x}^{2} - 48x + 5a$
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Answer 1

Answer:

Let p(x)= 4x^4+2x^3-3x^2-48x+5a

since x+2 is a factor of p(x)

therefore p(-2)=0

p(-2)=4×(-2)^4+2(-2)^3-3(-2)^2-48(

-2)+5a= 0

=4096-64+36+96+5a=0

=4164+5a=0

=5a=-4164

=-4164/5

=832•8

Answer 2

Hey there!

When x+2 is factor of given polynomial.,

x + 2 = 0

x = -2

Now,

$p(x) = 4x^4 + 2x^3 - 3x^2-48x + 5a\\p(-2) = 4(-2)^4 + 2(-2)^3 - 3(-2)^2 - 48\times2 + 5a\\0 = 4 \times 16 +2(-8) - 3\times4 - 96 + 5a\\0=64 - 16 -12 -96 + 5a\\0 = 64 - 124 + 5a\\0=-60 + 5a\\5a = 60 a \\ a = 60 \div 5\\\boxed{a = 12}$