Which has X-1 as a factor?

Which has X-1 as a factor?

x³+x²+x+1 Let p(x)= x³+x²+x+1 The zero of x+1 is -1. On putting x= -1p(−1)=(−1)³+(−1)²+(−1)+1=−1+1−1+1=0Hence, by factor theorem, x+1 is a factor of x³+x²+x+1.

How do you know if X-1 is a factor?

1 Expert Answer By the factor theorem, if P(1)=0, then x-1 is a factor.

Is X-1 a factor of this polynomial?

(b) Let assume (x + 1) is a factor of x3 + x2 + x+1. (-1)3 + (-1)2 + (-1) + 1 = 0 ⇒ -1+1-1 + 1 = 0 ⇒ 0 = 0 Hence, our assumption is true.

Is a 1 a factor?

The number 1 is the smallest factor of every number. Every number will have a minimum of two factors, 1 and the number itself. A number that has only two factors, 1 and the number itself, is called a prime number.

Is Xa factor in math?

q(x) +0 = (x-a). Thus, x-a is a factor of p(x) when the remainder is zero. If the (x-a) is a factor of polynomial p(x), then the remainder must be zero. So, we can say that x-a exactly divides p(x).

How do you find zeros using factor theorem?

Using the Factor Theorem to Solve a Polynomial Equation It tells us how the zeros of a polynomial are related to the factors. Recall that the Division Algorithm. If k is a zero, then the remainder r is f ( k ) = 0 f ( k ) = 0 and f ( x ) = ( x − k ) q ( x ) + 0 f ( x ) = ( x − k ) q ( x ) + 0 or.

Can a polynomial have no zeros?

A polynomial function may have zero, one, or many zeros. All polynomial functions of positive, odd order have at least one zero, while polynomial functions of positive, even order may not have a zero.

Is 1 a factor of every number Yes or no?

We know that a number multiplied by 1 is the number itself. So, 1 is a factor of every number.

Is X-1 a factor?

If you’re comfortable with the link between factors and zeros of a polynomial, it’s enough to see that x=1 is a zero of x n -1, hence x-1 is a factor. You’ve got the right start for a proof by induction.

Is 1 a root of x – 1?

Since the root of x − 1 is 1, we simply have to check that 1 is a root of x n − 1. Plugging in x = 1 gives 1 n − 1 = 0. So, 1 is indeed a root.

What is the $X -R$ is a factor of?

†: Factor Theorem: $x -r$ is a factor of $f(x)$ if and only if $f(r) = 0$. abstract-algebrapolynomialsalternative-proof Share Cite Follow edited Jan 26 ’15 at 9:07 Lord_Farin 17k99 gold badges4444 silver badges117117 bronze badges asked Jan 25 ’15 at 21:08 FlipFlip 72811 gold badge88 silver badges2222 bronze badges $\\endgroup$ 4 1