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Is $x − 2$ a factor of the polynomial $p (x) = 4 x 2 + x − 2$ ?

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True

False

answer is B.

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Detailed Solution

The given polynomial is,

p (x) = 4 x 2 + x − 2

We know by Factor theorem that if

x − k

is a factor of the given polynomial

p (x),

then

p (k) = 0

Since to check whether

x − 2

is a factor of the polynomial

p (x) = 4 x 2 + x − 2,

we check whether

p 2 = 0.

Substitute the value

x = 2

p (x),

we get

p 2 = 422 + 2 − 2 = 4 × 4 + 0 = 16 ≠ 0

Since

p 2 ≠ 0,

therefore

x − 2

isn’t a factor of the polynomial

p (x) = 4 x 2 + x − 2.

Thus, the given statement is not true.
Hence, option (2) is correct.

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