Level 6 - NCEA Level 1

Fully factorise after completing the square

Lesson

Worked examples

Question 1

Factorise the quadratic using the method of completing the square to get it into the form $y=\left(x+a\right)\left(x+b\right)$y=(x+a)(x+b).

$y=x^2+4x+3$y=x2+4x+3

Question 2

Factorise the quadratic using the method of completing the square to get it into the form $y=\left(x-a\right)\left(x-b\right)$y=(x−a)(x−b).

$y=x^2-11x+28$y=x2−11x+28

Question 3

Factorise the quadratic using the method of completing the square to get it into the form $y=\left(x+a+\sqrt{b}\right)\left(x+a-\sqrt{b}\right)$y=(x+a+√b)(x+a−√b).

$y=x^2+8x+14$y=x2+8x+14

Outcomes

NA6-5

Form and solve linear equations and inequations, quadratic and simple exponential equations, and simultaneous equations with two unknowns

91027

Apply algebraic procedures in solving problems