Algebra 2 two questions please help?

Question

1. Use the polynomial to answer the question. 
x^2 - 8x + 15 
Which represents the polynomial in factored form? 

A. (x + 3)(x - 5) 

B. (x + 3)(x + 5) 

C. (x - 3)(x + 5) 

D.(x - 3)(x - 5) 

2. Use the polynomial to answer the question. 
12x^3 + 5 - 5x^2 - 6x^2 + 3x^3 + 2 - x 

Which expresses the polynomial in standard form? 

A. 15x^3 + 11x^2 - x + 7 

B. 15x^6 - 11x^4 - x +7 

C. 15x^3 - 11x^2 - x +7 

D. 15x^5 - 11x^2 - x +7

 

 

Answer 1

1) The polynomial x² - 8x + 15

Multiply first term x² and last term 15 = 15x²

The correct pair of the terms -5x and -3x multiply to 15x² and add to -8x.

Replace the middle term -8x with - 5x - 3x.

= x² - 5x - 3x + 15

Group the terms into two pairs.

= (x² - 5x) + (- 3x + 15)

Factor out x from the first group  and factor out 1 from the second group.

= x(x - 5) - 3(x - 5)

Factor out common term x - 5.

= (x - 5)(x - 3)

Factored form of x² - 8x + 15 = (x - 3)(x - 5)

Option d is correct.

Answer 2

2) The polynomial 12x³ + 5 - 5x² - 6x² + 3x³  + 2 - x

Write the terms highest exponents first.

P(x) = 12x³ + 3x³

Next write the terms with lower exponents in descending order.

P(x) = 12x³ + 3x³ - 5x² - 6x²  - x

A constant number always goes last.

P(x) = 12x³ + 3x³ - 5x² - 6x²  - x + 5 + 2

Combine like terms.

P(x) = 15x³ - 11x² - x + 7

Option C is correct