Question

Разложите выражения на множители: 1) a^2+5а+6; 2) y^2-3y -4; 3) a^2+ 8а-9; 4) x^2-11х+24 ​

Answer 1

Ответ:

а) (a+3)(a+2)

б) (y+1)(y-4)

в) (x-3)(x-8)

Answer 2

Разложение выражений на множители:

1) a^2 + 5a + 6

To factorize this expression, we need to find two numbers whose product is equal to the product of the coefficient of the quadratic term (a^2) and the constant term (6), and whose sum is equal to the coefficient of the linear term (5a).

The coefficient of the quadratic term is 1, the coefficient of the linear term is 5, and the constant term is 6. We need to find two numbers whose product is (1 * 6) = 6 and whose sum is 5.

The numbers that satisfy these conditions are 2 and 3. Therefore, we can factorize the expression as follows:

a^2 + 5a + 6 = (a + 2)(a + 3)

2) y^2 - 3y - 4

To factorize this expression, we need to find two numbers whose product is equal to the product of the coefficient of the quadratic term (y^2) and the constant term (-4), and whose sum is equal to the coefficient of the linear term (-3y).

The coefficient of the quadratic term is 1, the coefficient of the linear term is -3, and the constant term is -4. We need to find two numbers whose product is (1 * -4) = -4 and whose sum is -3.

The numbers that satisfy these conditions are -4 and 1. Therefore, we can factorize the expression as follows:

y^2 - 3y - 4 = (y - 4)(y + 1)

3) a^2 + 8a - 9

To factorize this expression, we need to find two numbers whose product is equal to the product of the coefficient of the quadratic term (a^2) and the constant term (-9), and whose sum is equal to the coefficient of the linear term (8a).

The coefficient of the quadratic term is 1, the coefficient of the linear term is 8, and the constant term is -9. We need to find two numbers whose product is (1 * -9) = -9 and whose sum is 8.

The numbers that satisfy these conditions are 9 and -1. Therefore, we can factorize the expression as follows:

a^2 + 8a - 9 = (a + 9)(a - 1)

4) x^2 - 11x + 24

To factorize this expression, we need to find two numbers whose product is equal to the product of the coefficient of the quadratic term (x^2) and the constant term (24), and whose sum is equal to the coefficient of the linear term (-11x).

The coefficient of the quadratic term is 1, the coefficient of the linear term is -11, and the constant term is 24. We need to find two numbers whose product is (1 * 24) = 24 and whose sum is -11.

The numbers that satisfy these conditions are -3 and -8. Therefore, we can factorize the expression as follows:

x^2 - 11x + 24 = (x - 3)(x - 8)

These are the factorized forms of the given expressions.