Questions: Factor -3x^2+3x+90= (x+ ) (x+ )

Transcript text: Factor $-3 x^{2}+3 x+90=$ $\square$ $(x+$ $\square$ $\int(x+$ $\square$ )

Solution

Solution Steps

To factor the given quadratic expression, we first identify the greatest common factor (GCF). Since the leading term is negative, the GCF will also be negative. We then factor out the GCF and simplify the remaining quadratic expression.

Solution Approach

Identify the GCF of the terms in the quadratic expression.
Factor out the GCF.
Simplify the remaining quadratic expression.

Step 1: Identify the Expression

We start with the quadratic expression: \[ -3x^2 + 3x + 90 \]

Step 2: Factor Out the GCF

The greatest common factor (GCF) of the terms in the expression is $-3$. We factor this out: \[ -3(x^2 - x - 30) \]

Step 3: Factor the Quadratic Expression

Next, we need to factor the quadratic expression $x^2 - x - 30$. We look for two numbers that multiply to $-30$ and add to $-1$. The numbers $-6$ and $5$ satisfy these conditions. Thus, we can factor the quadratic as: \[ x^2 - x - 30 = (x - 6)(x + 5) \]

Step 4: Combine the Factors

Putting it all together, we have: \[ -3(x - 6)(x + 5) \]