Question

1. quadratics:

factor ( x^2 - 2x - 15 )
find the zero’s ( x^2 + 5x - 14 )

Explanation:

Step1: Factor \(x^2 - 2x - 15\)

We need two numbers that multiply to \(-15\) and add to \(-2\). The numbers are \(-5\) and \(3\) (since \(-5\times3=-15\) and \(-5 + 3=-2\)). So we can factor the quadratic as:
\(x^2 - 2x - 15=(x - 5)(x + 3)\)

Step2: Find the zeros of \(x^2 + 5x - 14\)

First, factor the quadratic. We need two numbers that multiply to \(-14\) and add to \(5\). The numbers are \(7\) and \(-2\) (since \(7\times(-2)=-14\) and \(7+(-2)=5\)). So the factored form is:
\(x^2 + 5x - 14=(x + 7)(x - 2)\)
To find the zeros, set each factor equal to zero:

• For \(x + 7 = 0\), we get \(x=-7\).
• For \(x - 2 = 0\), we get \(x = 2\).

Answer:

• Factored form of \(x^2 - 2x - 15\) is \((x - 5)(x + 3)\).
• Zeros of \(x^2 + 5x - 14\) are \(x=-7\) and \(x = 2\).