Maths - Quadratics Tips and Tricks

Factoring out a negative leading coefficient

How can you solve something like $-x^2 + 7x - 15$?

Take out $-1$ as a factor.

What is the result of taking out $-1$ from $15 + 13x - 4x^2$?

\[-(4x^2 - 13x - 15)\]

How can you solve something like $x^4 + 5x^2 - 36 = 0$?

Substitute $a = x^2$.

Substitute $a = x^2$ into $x^4 + 5x^2 - 36 = 0$?

\[a^2 + 5a - 36 = 0\]

How could you solve something like $x - 9\sqrt{x} + 24 = 0$?

Substitute $a = x^{\frac{1}{2}}$.

Substitute $a = x^{\frac{1}{2}}$ into $x - 9\sqrt{x} + 24 = 0$?

\[a^2 - 9a + 24\]

What is the name for a quadratic in disguise?

A sneaky quad.

What are the two criteria for an equation being a sneaky quad?