Question

16.8. 1) a² + 2a-15; 3) x² + 15x + 54; 5) m² + 15m + 56; 7) k²-17k+ 72 ​

Answer 1

Відповідь:

1) (a−3)(a+5); 3) (x+6)(x+9); 5) (m+7)(m+8); 7)(k−9)(k−8)​

Пояснення:

1) a² + 2a-15 = a^2+5a−3a−15 = a(a+5)−3a−15 = a(a+5)−3(a+5) = (a−3)(a+5)

2) x² + 15x + 54 = x² +9x+6x+54 = x(x+9)+6x+54 = x(x+9)+6(x+9) = (x+6)(x+9)

3) m² + 15m + 56 = m² +8m+7m+56 = m(m+8)+7m+56 = m(m+8)+7(m+8) = (m+7)(m+8)

4) k²-17k+ 72 =  k²-9k -8k + 72 = (k−9)(k−8)​

Answer 2

Let's factorize the given quadratic expressions.

1. a² + 2a - 15: To factorize this quadratic expression, we need to find two numbers whose sum is 2 and whose product is -15. The numbers that satisfy these conditions are 5 and -3. Therefore, we can factorize the expression as follows: (a + 5)(a - 3)

2. x² + 15x + 54: To factorize this quadratic expression, we need to find two numbers whose sum is 15 and whose product is 54. The numbers that satisfy these conditions are 6 and 9. Therefore, we can factorize the expression as follows: (x + 6)(x + 9)

3. m² + 15m + 56: To factorize this quadratic expression, we need to find two numbers whose sum is 15 and whose product is 56. However, there are no two numbers that satisfy these conditions since 56 does not have any factors that add up to 15. Therefore, this quadratic expression cannot be factorized further.

4. k² - 17k + 72: To factorize this quadratic expression, we need to find two numbers whose sum is -17 and whose product is 72. The numbers that satisfy these conditions are -8 and -9. Therefore, we can factorize the expression as follows: (k - 8)(k - 9)