**Factoring Quadratic Equation Examples :**

Here we are going to see some example problems on factoring quadratic equations.

Pattern of quadratic equation |
Signs of factors |

ax ax ax ax |
Both factors will have + Both factors will have - Greater number have - and smaller number have + Greater number have + and smaller number have - |

**Question 1 :**

Factorise the following:

(i) x^{2} + 10x + 24

**Solution :**

= x^{2} + 10x + 24

Since the coefficient of x^{2} is 1, we have to take the constant 24. The given equation is in the form ax^{2} + bx + c, so both factors are positive.

24 = 6 ⋅ 4 and 6 + 4 = 10

= x^{2} + 6x + 4x + 24

= x(x + 6) + 4(x + 6)

= (x + 6) (x + 4)

Hence the factors are (x + 6) and (x + 4).

(ii) z^{2} + 4z - 12

**Solution :**

= z^{2} + 4z - 12

Since the coefficient of x^{2} is 1, we have to take the constant -12. The given equation is in the form ax^{2} + bx - c, smaller factor will have negative.

-12 = 6 ⋅ (-2) and 6 + (-2) = 4

= x^{2} + 6x - 2x - 12

= x(x + 6) - 2(x + 6)

= (x - 2) (x + 6)

Hence the factors are (x - 2) and (x + 6)

Let us look into the next problem on "Factoring Quadratic Equation Examples".

(iii) p^{2} - 6p - 16

**Solution :**

= p^{2} - 6p - 16

Since the coefficient of x^{2} is 1, we have to take the constant -16. The given equation is in the form ax^{2} - bx - c, big number will have negative.

-16 = -8 ⋅ 2 and -8 + 2 = -6

= x^{2} - 8x + 2x - 16

= x(x - 8) + 2(x - 8)

= (x + 2) (x - 8)

Hence the factors are (x + 2) and (x - 8)

(iv) t^{2} + 72 - 17t

**Solution :**

= t^{2} - 17p + 72

Since the coefficient of t^{2} is 1, we have to take the constant 72. The given equation is in the form ax^{2} - bx + c, both factors will have negative sign.

-72 = -8 ⋅ (-9) and -8 + (-9) = -17

= x^{2} - 8x - 9x + 72

= x(x - 8) - 9(x - 8)

= (x - 9) (x - 8)

Hence the factors are (x - 9) and (x - 8)

(v) y^{2} - 16y - 80

**Solution :**

= y^{2} - 16y - 80

Since the coefficient of y^{2} is 1, we have to take the constant -80. The given equation is in the form ax^{2} - bx - c, large factors will have negative sign.

-80 = -20 ⋅ 4 and -20 + 4 = -16

= y^{2} - 20y + 4y - 80

= y(y - 20) + 4(y - 20)

= (y - 20) (y + 4)

Hence the factors are (y - 20) and (y + 4)

(vi) a^{2} + 10a - 600

**Solution :**

= a^{2} + 10a - 600

Since the coefficient of a^{2} is 1, we have to take the constant -600. The given equation is in the form ax^{2} + bx - c, small factors will have negative sign.

-600 = 30 ⋅ (-20) and 30 - 20 = 10

= a^{2} + 30a - 20a - 600

= a(a + 30) - 20(a + 30)

= (a - 20)(a + 30)

Hence the factors are (a - 20) and (a + 30).

After having gone through the stuff given above, we hope that the students would have understood, "Factoring Quadratic Equation Examples"

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