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AustraliaVIC
VCE 11 Methods 2023

3.02 Expansion of polynomials

Interactive practice questions

Fill in the blanks to make the expression true.

$\left(v-2\right)\left(v-3\right)$(v2)(v3)$=$=$v\left(v-3\right)$v(v3)$-$ $\editable{}\left(\editable{}\right)$()

Easy
< 1min

Expand and simplify the following:

$-\left(x+5\right)\left(x+2\right)$(x+5)(x+2)

Easy
1min

Expand and simplify the following:

$3\left(6x+\frac{1}{2}\right)\left(x-2\right)-5$3(6x+12)(x2)5

Easy
3min

Expand and simplify the following:

$2\left(2p+3q\right)\left(p-q\right)-\left(p+q\right)\left(3p+2q\right)$2(2p+3q)(pq)(p+q)(3p+2q)

Easy
4min
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Outcomes

U1.AoS2.3

recognition of equivalent expressions and simplification of algebraic expressions involving different forms of polynomial and power functions, the use of distributive and exponent laws applied to these functions, and manipulation from one form of expression to an equivalent form

U1.AoS2.6

the connection between the roots of a polynomial function, its factors and the horizontal axis intercepts of its graph, including the remainder, factor and rational root theorems

U1.AoS2.7

solution of polynomial equations of low degree, numerically, graphically and algebraically, including numerical approximation of roots of simple polynomial functions using the bisection method algorithm

U1.AoS2.18

apply distributive and exponent laws to manipulate and simplify expressions involving polynomial and power function, by hand in simple cases

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