Factor the following expression completely: 2y^2+9y-35=square

Question

Answer 1

To factor the quadratic expression

completely, we need to find two binomials whose product gives us the original quadratic expression.First, we identify the coefficients:-

-

We need to find two numbers that multiply to \(a \cdot c = 2 \cdot (-35) = -70\) and add up to

.Let's denote these two numbers as

and

. So, we have:

By examining the pairs of factors of

, we find that

and

satisfy these conditions because:

Next, we rewrite the middle term

using

and

:

Now, we group the terms in pairs:

We factor out the greatest common factor (GCF) from each pair:

We notice that \((y + 7)\) is a common factor:

Thus, the completely factored form of the expression

is:

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