Question

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Answer 1

Answer:

1. x² + 17x + 66

2. 18p²qr² + 24p³qr² + 18pq²r² - 30pqr⁴

3. - 18x² + 15x

4. 30a² + 11ab - 30b²

5. 18x³ - 57x² + 65x - 28

6. 2x³ - 13x² + 14x + 5

Step-by-step-explanation:

1. ( x + 6 ) ( x + 11 )

( x + 6 ) ( x + 11 )

→ x ( x + 11 ) + 6 ( x + 11 )

→ x² + 11x + 6x + 66

→ x² + 17x + 66

$\rule{200}{1}$

2. 6pqr² ( 3pq + 4p² + 3q - 5r² )

→ 18p²qr² + 24p³qr² + 18pq²r² - 30pqr⁴

$\rule{200}{1}$

3. ( - 3x ) ( 6x - 5 )

- 3x ( 6x - 5 )

→ - 18x² + 15x

$\rule{200}{1}$

4. ( 6a - 5b ) ( 5a + 6b )

→ 6a ( 5a + 6b ) - 5b ( 5a + 6b )

→ 30a² + 36ab - 25ab - 30b²

→ 30a² + 11ab - 30b²

$\rule{200}{1}$

5. ( 3x - 4 ) ( 6x² - 11x + 7 )

( 3x - 4 ) ( 6x² - 11x + 7 )

→ 3x ( 6x² - 11x + 7 ) - 4 ( 6x² - 11x + 7 )

→ 18x³ - 33x² + 21x - 24x² + 44x - 28

→ 18x³ - 33x² - 24x² + 21x + 44x - 28

→ 18x³ - 57x² + 65x - 28

$\rule{200}{1}$

6. ( x - 5 ) ( 2x² - 3x - 1 )

( x - 5 ) ( 2x² - 3x - 1 )

→ x ( 2x² - 3x - 1 ) - 5 ( 2x² - 3x - 1 )

→ 2x³ - 3x² - x - 10x² + 15x + 5

→ 2x³ - 3x² - 10x² - x + 15x + 5

→ 2x³ - 13x² + 14x + 5

Additional Information:

1. Polynomial:

Any mathematical expression which contains numbers and letters is called as a polynomial.

2. Constant terms:

Every number is a constant term.

The value of any constant term never changes.

3. Variables:

The letters used in making polynomials and mathematical expressions are called as variables.

As they vary in every example, expression, they are known as vari - ables [ One which is able to vary anytime ].

4. Kinds of polynomials:

There are two main kinds of polynomials:

1. Term polynomial

2. Degree polynomial

5. Term polynomial:

There are basically three types of term polynomial:

A. Monomial ( Only one term )

B. Binomial ( Two terms )

C. Trinomial ( Three terms )

6. Degree polynomial:

There are basically four types of degree polynomial:

A. Linear polynomial ( Degree is 1 )

B. Quadratic Polynomial ( Degree is 2 )

C. Cubic Polynomial ( Degree is 3 )

D. Biquadratic polynomial ( Degree is 4 )