Chapter 8: Q5. (page 520)

Which of the following polynomials is prime?
A $5 x^{2} + 34 x + 24$
B $4 x^{2} + 22 x + 10$
C $4 x^{2} + 38 x + 70$
D $5 x^{2} + 3 x + 4$

Short Answer

Expert verified

$5 x^{2} + 3 x + 4$

Step by step solution

Step 1. Factor 5x2+34x+24.

Factorized the polynomial, $5 x^{2} + 34 x + 24$ .

$5 x^{2} + 34 x + 24 = 5 x^{2} + 30 x + 4 x + 24 = 5 x (x + 6) + 4 (x + 6) = (5 x + 4) (x + 6)$

Since the polynomial is factorized, it is not a prime.

Step 2. Factor 4x2+22x+10.

Factorized the polynomial, $4 x^{2} + 22 x + 10$ .

$4 x^{2} + 22 x + 10 = 4 x^{2} + 20 x + 2 x + 10 = 4 x (x + 5) + 2 (x + 5) = (4 x + 2) (x + 5)$

Since the polynomial is factorized, it is not a prime.

Step 3. Factor 4x2+38x+70.

Factorized the polynomial, $4 x^{2} + 38 x + 70$ .

$4 x^{2} + 38 x + 70 = 4 x^{2} + 28 x + 10 x + 70 = 4 x (x + 7) + 10 (x + 7) = (4 x + 10) (x + 7)$

Since the polynomial is factorized, it is not a prime.

Step 4. Factor 5x2+3x+4.

List the factors of 20 and look for the pair with sum of 3.

Factors of 20	Sum of factors
1	20
2	10
4	5

There are no factors with sum of 3. Hence, the given polynomial cannot be factored using integers. Therefore, $5 x^{2} + 3 x + 4$ is prime. As the obtained answer completely matches with option D, option D is the required answer.

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Which of the following polynomials is prime?
A $5 x^{2} + 34 x + 24$
B $4 x^{2} + 22 x + 10$
C $4 x^{2} + 38 x + 70$
D $5 x^{2} + 3 x + 4$

Short Answer

Step by step solution

Step 1. Factor 5x2+34x+24.

Step 2. Factor 4x2+22x+10.

Step 3. Factor 4x2+38x+70.

Step 4. Factor 5x2+3x+4.

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Which of the following polynomials is prime?A5x2+34x+24B4x2+22x+10C4x2+38x+70D5x2+3x+4

Short Answer

Step by step solution

Step 1. Factor 5x2+34x+24.

Step 2. Factor 4x2+22x+10.

Step 3. Factor 4x2+38x+70.

Step 4. Factor 5x2+3x+4.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Probability and Statistics

Decision Maths

Pure Maths

Logic and Functions

Calculus

Study anywhere. Anytime. Across all devices.

Which of the following polynomials is prime?
A $5 x^{2} + 34 x + 24$
B $4 x^{2} + 22 x + 10$
C $4 x^{2} + 38 x + 70$
D $5 x^{2} + 3 x + 4$