Question

factorise:
${x}^{2} + 16x + 60 = 0$
​

Answer 1

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Q:-factorise:

${x}^{2} + 16x + 60 = 0$

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------>>>>Here is your answer<<<<--------

$⟹ {x}^{2} + 16x + 60 = 0$

$⟹ {x}^{2} + 10x + 6x + 60 = 0$

$⟹x(x + 10) + 6(x + 10)$

$⟹(x + 6)(x + 10)$

$⟹x = - 6 \: and \: x = - 10$

HOPE IT HELPS YOU..

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Thankyou:)

Answer 2

Step-by-step explanation:

Factoring x2-16x+60

The first term is, x2 its coefficient is 1 .

The middle term is, -16x its coefficient is -16 .

The last term, "the constant", is +60

Step-1 : Multiply the coefficient of the first term by the constant 1 • 60 = 60

Step-2 : Find two factors of 60 whose sum equals the coefficient of the middle term, which is -16 .

-60 + -1 = -61

-30 + -2 = -32

-20 + -3 = -23

-15 + -4 = -19

-12 + -5 = -17

-10 + -6 = -16 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -10 and -6

x2 - 10x - 6x - 60

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

x • (x-10)

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

6 • (x-10)

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

(x-6) • (x-10)

Which is the desired factorization

Equation at the end of step

1

:

(x - 6) • (x - 10) = 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.