Chapter 12: Q3. (page 800)

Which of the following is not a factor of $x^{4} - 6 x^{2} - 27$ ?
role="math" localid="1648185076360" $A$ $x^{2} + 3$ $C$ $x + 3$
$B$ $x - 3$ $D$ $x^{2} - 3$

Short Answer

Expert verified

$x^{2} - 3$ is not a factor of the given expression.

Step by step solution

Step 1. Substitution.

Substitute $z$ for $x^{2}$ into the given expression.

$z^{2} - 6 z - 27$

Step 2. Factor.

Factor the above obtained expression.

$\begin{array}{l} z^{2} + 3 z - 9 z - 27 = z (z + 3) - 9 (z + 3) \\ = (z - 9) (z + 3) \end{array}$

Step 3. Substitution.

Substitute $x^{2}$ for $z$ into $(z - 9) (z + 3)$ .

$(x^{2} - 9) (x^{2} + 3) = (x + 3) (x - 3) (x^{2} + 3)$

Therefore, $x^{2} - 3$ is not a factor of given expression. Option $D$ is the required answer.

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Which of the following is not a factor of $x^{4} - 6 x^{2} - 27$ ?
role="math" localid="1648185076360" $A$ $x^{2} + 3$ $C$ $x + 3$
$B$ $x - 3$ $D$ $x^{2} - 3$

Short Answer

Step by step solution

Step 1. Substitution.

Step 2. Factor.

Step 3. Substitution.

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Which of the following is not a factor of x4−6x2−27?role="math" localid="1648185076360" Ax2+3 Cx+3Bx−3 Dx2−3

Short Answer

Step by step solution

Step 1. Substitution.

Step 2. Factor.

Step 3. Substitution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

Decision Maths

Probability and Statistics

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Applied Mathematics

Study anywhere. Anytime. Across all devices.

Which of the following is not a factor of $x^{4} - 6 x^{2} - 27$ ?
role="math" localid="1648185076360" $A$ $x^{2} + 3$ $C$ $x + 3$
$B$ $x - 3$ $D$ $x^{2} - 3$