Question

1. Write the coefficient of x²
1. 4x²+7x+5
2. 2x³-3x²+5x-2

2. Write the degree.
1. 5x³+2x²-3x-1
2. 4x²+2x+3

3. Find the Value of:
5x-4x²+3 at
1. x=0
2. x=-1
3. x=-2
4. x=3

4. Find the zero of the following polynomials.
1. P(x)=x+5
2. P(x)=x-5

5. Factories:
1. 12x²-7x+1
2. 3x²-x-4
Solve the questions in step by step solution.​

Answer 1

Answer:

1.4

2.-3

3.3

4.2

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Answer 2

QuestioN - 1 :-

Write the coefficient of x² :-

• 4x² + 7x + 5

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• 2x³ - 3x² + 5x - 2

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AnsweR :-

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1) 4x² + 7x + 5

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• The coefficient of x² is 4.

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2) 2x³ - 3x² + 5x - 2

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• The coefficient of x² is (-3).

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QuestioN - 2 :-

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Write the Degree :-

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• 5x³ + 2x² -3x -1

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• 4x² + 2x +3

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AnsweR :-

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1) 5x³ + 2x² - 3x -1

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• The degree of this polynomial is 3.

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2) 4x² + 2x + 3

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• The degree of this polynomial is 2.

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QuestioN - 3 :-

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Find the value of 5x - 4x² + 3 at ,

• x = 0

• x = -1

• x = -2

• x = 3

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The value of 5x - 4x² + 3 at x = 0

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$\sf \: 5x - 4 {x}^{2} + 3 \\ \\ \implies \: \sf \: 5 \times 0 - 4 \times {0}^{2} + 3 \\ \\ \implies \sf \: 0 - 0 + 3 \\ \\ \implies \sf \: 3$

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The value of 5x - 4x² + 3 at x = -1

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$\sf \: 5x - 4 {x}^{2} + 3 \\ \\ \implies \sf \: 5 \times ( - 1) - 4 \times {( - 1)}^{2} + 3 \\ \\ \implies \sf \: - 5 - 4 \times 1 + 3 \\ \\ \implies \sf \: - 5 - 4 + 3 \\ \\ \implies \sf \: - 9 + 3 \\ \\ \implies \sf \: - 5$

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The value of 5x - 4x² + 3 at x = -2

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$\sf5x - 4 {x}^{2} + 3 \\ \\ \implies \sf \: 5 \times ( - 2) - 4 {( - 2)}^{2} + 3 \\ \\ \implies \sf \: - 10 - 4 \times 4 + 3 \\ \\ \implies \sf \: - 10 - 16 + 3 \\ \\ \implies \sf \: - 26 + 3 \\ \\ \implies \sf \: - 23$

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The value of 5x - 4x² + 3 at x = 3

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$\sf5x - 4 {x}^{2} + 3 \\ \\ \implies \sf \: 5 \times 3 - 4 \times {3}^{2} + 3 \\ \\ \implies \sf \: 15 - 4 \times 9 + 3 \\ \\ \implies \sf \: 15 - 36 + 3 \\ \\ \implies \sf \: 18 - 36 \\ \\ \implies \sf \: - 18$

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QuestioN - 4 :-

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Find the zeros of the following polynomials :-

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• p(x) = x + 5

• p(x) = x - 5

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AnsweR :-

⠀⠀

1) p(x) = x + 5

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To find the zeros of polynomial equate the polynomial to zero ,

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$\sf \: p(x) = 0 \\ \\ \implies \sf \: x + 5 = 0 \\ \\ \implies \sf \: x = - 5$

2) p(x) = x - 5

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$\sf \: p(x) = 0 \\ \\ \implies \sf \: x - 5 = 0 \\ \\ \implies \sf \: x = 5$

QuestioN - 5 :-

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Factories ths following →

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• 12x² - 7x + 1

• 3x² -x - 4

AnsweR :-

⠀⠀

1) 12x² - 7x + 1

⠀⠀

$\sf \implies \: 12 {x}^{2} - 7x + 1 \\ \\ \implies \sf \: 12 {x}^{2} - 4x - 3x + 1 \\ \\ \implies \sf \: 4x(3x - 1) - 1(3x - 1) \\ \\ \implies \sf \: (4x - 1)(3x - 1)$

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2) 3x² - x - 4

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$\implies \sf \: 3 {x}^{2} - x - 4 \\ \\ \implies \sf \: 3 {x}^{2} + 3x - 4x - 4 \\ \\ \implies \sf3x(x + 1) - 4(x + 1) \\ \\ \implies \sf(3x - 4)(x + 1)$

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Hope it will help you :)