(i) Let p(x) = x³ + x² + x + l Putting x + l = 0, we get, x = -1 Using remainder theorem, when p(x) = x³ + x² + x + l is divided by x + 1, remainder is given by p(-1) = (-1)³ + (-1)² + (-1) + 1 = -1 + 1 – 1 + 1 = 0 Since, remainder p(-1) = 0, hence x + 1 is a factor of x³ + x² + x + l.
(i) Let p(x) = x³ + x² + x + l
Putting x + l = 0, we get, x = -1
Using remainder theorem, when p(x) = x³ + x² + x + l is divided by x + 1, remainder is given by p(-1)
= (-1)³ + (-1)² + (-1) + 1
= -1 + 1 – 1 + 1 = 0
Since, remainder p(-1) = 0, hence x + 1 is a factor of x³ + x² + x + l.
Determine which of the following polynomials has (x + 1) a factor: x³ + x² + x + 1
(i) Let p(x) = x³ + x² + x + l Putting x + l = 0, we get, x = -1 Using remainder theorem, when p(x) = x³ + x² + x + l is divided by x + 1, remainder is given by p(-1) = (-1)³ + (-1)² + (-1) + 1 = -1 + 1 – 1 + 1 = 0 Since, remainder p(-1) = 0, hence x + 1 is a factor of x³ + x² + x + l.
(i) Let p(x) = x³ + x² + x + l
See lessPutting x + l = 0, we get, x = -1
Using remainder theorem, when p(x) = x³ + x² + x + l is divided by x + 1, remainder is given by p(-1)
= (-1)³ + (-1)² + (-1) + 1
= -1 + 1 – 1 + 1 = 0
Since, remainder p(-1) = 0, hence x + 1 is a factor of x³ + x² + x + l.
Use the Factor Theorem to determine whether g(x) is a factor of p(x) in the following cases: p(x) = 2x³ + x² – 2x – 1, g(x) = x + 1
(i) p(x) = 2x³ + x² - 2x - 1 and g(x) = x + 1 putting x + 1 = 0, we get, x = -1 Using remainder theorem, when p(x) = 2x³ + x² - 2x - 1 is divided by g(x) = x + 1, remainder is given by p(-1) = (-1)³ + (-1)² + (-1) + 1 = -1 + 1 - 1 + 1 = 0 Since, remainder p(-1) = 0, hence g(x) is factor of p(x).
(i) p(x) = 2x³ + x² – 2x – 1 and g(x) = x + 1
See lessputting x + 1 = 0, we get, x = -1
Using remainder theorem, when p(x) = 2x³ + x² – 2x – 1 is divided by g(x) = x + 1, remainder is given by p(-1)
= (-1)³ + (-1)² + (-1) + 1
= -1 + 1 – 1 + 1 = 0
Since, remainder p(-1) = 0, hence g(x) is factor of p(x).
Write the coefficients of x² in each of the following: 2 + x² + x.
In 2 + x² + x the coefficients of x² is 1. You can see here video explanation of this question 😁✌
In 2 + x² + x the coefficients of x² is 1.
You can see here video explanation of this question 😁✌
See lessWrite the coefficients of x² in each of the following: 2 – x² + x³
In 2 - x² + x³ the coefficients of x² is -1.
In 2 – x² + x³ the coefficients of x² is -1.
See lessWrite the coefficients of x² in the following: (π/2).x²+x.
In (π/2)x² + x the coefficients of x² is π/2.
In (π/2)x² + x the coefficients of x² is π/2.
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