Question

Help meeeeeeeeeee pleaseeeeeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!

Answer 1

• The perfect square trinomial is x² + 10x +
  `\boxed{\sf 25}`
• The factored perfect square trinomial is
  `\boxed{\sf (x + 5)(x + 5) \ or \ {(x + 5)}^2}`

Explanation:

Given:

Binomial: x² + 10x

To Find:

• Constant that should be added to the binomial so that it becomes a perfect square trinomial.
• Factor the trinomial.

Solution:

To find the constant we would compare the binomial with (a + b)² i.e. a² + 2ab + b² as it is the formula for perfect square.

By comparing we get:

a² = x²

2ab = 10x

b² = constant (To find out)

From this we can make out:

a = x

`\therefore`

`\rm \implies 2 * x * b = 10x \\ \\ \rm \implies b = (10x)/(2x) \\ \\ \rm \implies b = 5 \\ \\ \therefore \\ \\ \rm \implies {b}^(2) = 25`

So, constant that should be added to the binomial so that it becomes a perfect square trinomial is
`\boxed{\rm 25}`.

Perfect square trinomial is x² + 10x + 25

Factorisation of the trinomial:

`\rm \implies {x}^(2) + 10x + 25 \\ \\ \rm \implies {x}^(2) + 10x + {5}^(2) \\ \\ \rm \implies {x}^(2) + 5x + 5x + {5}^(2) \\ \\ \rm \implies x(x + 5) + 5(x + 5) \\ \\ \rm \implies (x + 5)(x + 5) \\ \\ \rm \implies {(x + 5)}^(2)`