Question

factorise a²+a+28=0
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Answer 1

Step-by-step explanation:

Step-1 : Multiply the coefficient of the first term by the constant 1 • -28 = -28

Step-2 : Find two factors of -28 whose sum equals the coefficient of the middle term, which is -3 .

-28 + 1 = -27

-14 + 2 = -12

-7 + 4 = -3 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -7 and 4

a2 - 7a + 4a - 28

Step-4 : Add up the first 2 terms, pulling out like factors :

a • (a-7)

Add up the last 2 terms, pulling out common factors :

4 • (a-7)

Step-5 : Add up the four terms of step 4 :

(a+4) • (a-7)

Which is the desired factorization

Equation at the end of step

1

:

(a + 4) • (a - 7) = 0

STEP

2

:

Theory - Roots of a product

2.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

2.2 Solve : a+4 = 0

Subtract 4 from both sides of the equation :

a = -4

Solving a Single Variable Equation:

2.3 Solve : a-7 = 0

Add 7 to both sides of the equation :

a = 7

Supplement : Solving Quadratic Equation Directly

Solving a2-3a-28 = 0 directly

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Answer 2

Answer:

$a {}^{2} + a + 28 = 0 \\ a (a + 1) +1(1 + 28) \\ (a + 1)(a + 1)(1 + 28)$

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