1. Equations and Polynomials
Lesson
Similar to solving quadratics we have a few methods to choose between when solving cubic equations:
- Solve using algebraic manipulation - For cubics such as $2x^3+16=0$2x3+16=0.
- Factorise - Fully factorising the cubic and then we can then use the null factor law to solve. If $a\times b=0$a×b=0 then either $a=0$a=0 or $b=0$b=0.
- Technology - Once we have extracted the important information from a question and formed an equation, we could use technology to solve the equation graphically or algebraically.
When factorising a cubic recall we can factorise by:
- using the highest common factor
- factor special forms such as the sum and difference of cubes
- identifying a single factor, then using division to establish the remaining quadratic. From here you would employ any of the factorising methods for quadratics.
Practice questions
Question 1
Solve the equation $x^3=-8$x3=−8.
QUESTION 2
Solve the equation $x^3-49x=0$x3−49x=0.
State the solutions on the same line, separated by a comma.
QUESTION 3
The cubic $P\left(x\right)=x^3-2x^2-5x+6$P(x)=x3−2x2−5x+6 has a factor of $x-3$x−3.
Solve for the roots of the cubic. If there is more than one root, state the solutions on the same line separated by commas.