Trying to find the right answer to this..

p(x) = x 3 - 4x 2 + x + 6, g(x) = x - 3 g(x) = 0 ⇒ x - 3 = 0 ⇒ x = 3 ∴ Zero of g(x) is 3. Now, p( 3) = (3) 3 - 4(3) 2 + 3 + 6 = 27 - 36 + 3 + 6 = 0 ∴ By factor theorem, g(x) is a factor of p{x).

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Polynomials

Short Answer Type

101. If the polynomial p(x) = x⁴- 2x³ + 3x² - ax + 8 is divided by (x - 2), it leaves a remainder 10. Find the value of a.

167 Views

102. The polynomials ax³+ 3x² - 3 and 2x³ - 5x + a when divided by x - 4 leave the same remainder in each case. Find the value of a.

139 Views

103. Determine which of the following polynomials has (x + 1) a factor:

x³ + x² + x + 1

235 Views

104. Determine which of the following polynomials has (x + 1) a factor:

x⁴ + x³ + x² + x + 1

111 Views

105. Determine which of the following polynomials has (x + 1) a factor:

x⁴ + 3x³ + 3x² + x + 1

129 Views

106. Determine which of the following polynomials has (x + 1) a factor:

left parenthesis straight x cubed minus straight x squared minus left parenthesis 2 plus square root of 2 right parenthesis straight x plus square root of 2 right parenthesis

133 Views

107. Use the factor theorem to determine whether g(x) is a factor ofp(x) in each of the following cases:

p(x) = 2x³ + x² - 2x - 1, g(x) = x + 1

146 Views

108. Use the factor theorem to determine whether g(x) is a factor ofp(x) in each of the following cases:

p(x) = x³ + 3x² + 3x + 1,g(x) = x + 2

238 Views

109. Use the factor theorem to determine whether g(x) is a factor ofp(x) in each of the following cases:

p(x) = x³ - 4x² + x + 6, g(x) = x - 3

p(x) = x³ - 4x² + x + 6, g(x) = x - 3
g(x) = 0
⇒ x - 3 = 0 ⇒ x = 3
∴ Zero of g(x) is 3.
Now, p( 3)
= (3)³ - 4(3)² + 3 + 6
= 27 - 36 + 3 + 6 = 0
∴ By factor theorem, g(x) is a factor of p{x).

129 Views