Alqebra oNE TrinomialS?

Question

1.x^2 + 14x + 49

2.a^2 +3a - 10

3.p^2 - 2p + 1

4.x^2 - 2xy – 48y^2

5.Factor a^2 + 4ab – 45b^2 on your paper. Which one of these is a factor of the trinomial?

Answer 1

1)

x^2 + 14x + 49

= x^2 + 7x + 7x + 49

= (x^2 + 7x) + (7x + 49)

= x(x + 7) + 7(x + 7)

= (x + 7)(x + 7)

= (x + 7)^2

2)

a^2 + 3a - 10

= a^2 + 5a - 2a - 10

= (a^2 + 5a) - (2a + 10)

= a(a + 5) - 2(a + 5)

= (a + 5)(a - 2)

3)

p^2 - 2p + 1

= p^2 - p - p + 1

= (p^2 - p) - (p - 1)

= p(p - 1) - 1(p - 1)

= (p - 1)(p - 1)

= (p - 1)^2

4)

x^2 - 2xy - 48y^2

= x^2 + 6xy - 8xy - 48y^2

= (x^2 + 6xy) - (8xy + 48y^2)

= x(x + 6y) - 8y(x + 6y)

= (x + 6y)(x - 8y)

5)

a^2 + 4ab - 45b^2

= a^2 + 9ab - 5ab - 45b^2

= (a^2 + 9ab) - (5ab + 45b^2)

= a(a + 9b) - 5b(a + 9b)

= (a + 9b)(a - 5b)

Answer 2

What are yopu supposed to do with problems 1-4?

Where are the factors of problem 5, to choose from?

Answer 3

1. (x+7)^2

2. (a+5)(a-2)

3. (p-1)^2

4. (x-8y)(x+ 6y)

5. (a+9b)(a-5b)