Factorizing Quadratics: Simple Cases

The video tutorial covers factorising quadratics, starting with simple forms and progressing to more complex ones. It explains the purpose of factorisation, such as simplifying equations and finding real roots. The tutorial demonstrates factorising simple quadratics, solving them algebraically, and graphically identifying where they intersect the x-axis. It introduces the sum and product rule for factorising more complex quadratics, providing examples to illustrate the process. The video concludes with a preview of future content on more advanced quadratic factorisation.

What is the primary purpose of factorising a quadratic equation?

• To expand the equation

• To simplify the equation

• To change the variable

• To increase the degree of the equation

In the expression x^2 - 4x, what is the factorised form?

• (x - 2)(x - 2)

• x(x - 4)

• (x + 4)(x - 4)

• x(x + 4)

When factorising x^2 - 4x = 0, what are the roots of the equation?

• x = 2 and x = -2

• x = 0 and x = 4

• x = 0 and x = -4

• x = 4 and x = -4

What is the sum and product rule used for in factorising quadratics?

• Finding two numbers that add to make c and multiply to make b

• Finding two numbers that add to make b and multiply to make c

• Finding two numbers that divide to make b and subtract to make c

• Finding two numbers that subtract to make b and divide to make c

If a quadratic has a positive b and a negative c, what can be said about the numbers in the brackets?

• One number is positive and the other is negative

• Both numbers are negative

• Both numbers are zero

• Both numbers are positive

For the quadratic x^2 + 11x + 24, which pair of numbers will factorise it?

• 3 and 8

• 4 and 6

• 5 and 7

• 2 and 12

In the quadratic x^2 - x - 20, what are the correct numbers to factorise it?

• 3 and -6

• 6 and -3

• 5 and -4

• 4 and -5