Question

From the following polynomials, fmd out which of them has (x — 1) as a factor :
(1) 2x³ - 3x² + 3x - 2
(2) 4x³ + x⁴ - x + 1
(3) 5x⁴ - 4x³ - 2x + 1
(4) 3x³ + x² + x + 11

Answer 1

Answer:

only the first one has the factor (x-1)

Answer 2

Answer:

$1)2x^{3}-3x^{2}+3x-2$

$3)5x^{4}-4x^3-2x+1$

Step-by-step explanation:

(x-1) is a factor if and only if 1 satisfies the given equation

putting value of x as 1 in all the given equation

$1)2x^{3}-3x^{2}+3x-2=2(1)^{3}-3(1)^{2}+3(1)-2=0$ hence it satisfies the given equation

$2)4x^{3}+x^{4}-x+1=4(1)^{3}+(1)^{4}-1+1$≠0hence it does not satisfies the given equation

$3)5x^{4}-4x^{3}-2x+1=5(1)^{4}-4(1)^{3}-2(1)+1=0$ hence it satisfies the given equation

$4)3x^{3}+x^{2}+x+11=3(1)^{3}+(1)^2+1+11$≠0 hence it does not satisfies the given equation