Question

The algebra tiles represent the perfect square trinomial x2 10x c. what is the value of c? c =

Answer 1

The value of c for which the considered trinomial becomes perfect square trinomial is: 20 or -20

What are perfect squares trinomials?

They are those expressions which are found by squaring binomial expressions.

Since the given trinomials are with degree 2, thus, if they are perfect square, the binomial which was used to make them must be linear.

Let the binomial term was ax + b(a linear expression is always writable in this form where a and b are constants and m is a variable), then we will obtain:

$(ax + b)^2 = a^2x^2 + b^2 + 2abx$

Comparing this expression with the expression we're provided with:

$x^2 + 10x + c$

we see that:

$a^2 = 1 \implies a = \pm 1\\b^2 = 10\\b = \pm 10\\2ab = c\\\pm2(10)1 = c\\c = \pm 20$

Thus, the value of c for which the considered trinomial becomes perfect square trinomial is: 20 or -20

Learn more about perfect square trinomials here:

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