Question

. Is it true that (x – 2) is a factor of the polynomial x 4 – 8x 3 + 17x 2 + 2x – 24? explain​

Answer 1

Answer:

true

Step-by-step explanation:

Answer 2

True,  (x – 2) is a factor of the polynomial x⁴ – 8x³ + 17x² + 2x – 24

Given :  polynomial x⁴ – 8x³ + 17x² + 2x – 24

To Find :   (x – 2) is a factor of the polynomial  or not

Solution:

Factor Theorem.

x – a is a factor of the polynomial p(x), if p(a) = 0.  

Also, if x – a is a factor of p(x), then p(a) = 0,  

where a is any real number.  

This is an extension to remainder theorem where remainder is 0, i.e. p(a) = 0.

Let say P(x) = x⁴ – 8x³ + 17x² + 2x – 24

 (x – 2) is a factor of the polynomial   P(x) = x⁴ – 8x³ + 17x² + 2x – 24

iff P(2) = 0

 P(x) = x⁴ – 8x³ + 17x² + 2x – 24

Substitute x = 2

=> P(2) =  2⁴ – 8(2)³ + 17(2)² + 2(2) – 24

=> P(2) =  16 – 64 + 68 + 4 – 24

=> p(2) = 88 - 88

=> p(2) = 0

Hence   (x – 2) is a factor of the polynomial   P(x) = x⁴ – 8x³ + 17x² + 2x – 24

True, (x – 2) is a factor of the polynomial    x⁴ – 8x³ + 17x² + 2x – 24

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