Find the value of the linear polynomial if: (i) (ii) (iii)

Understand the Question Let the given polynomial be . To find the value of the polynomial at any given value of , substitute that value directly in place of and evaluate the arithmetic expression. Part (i) Step 1 · Substitute Let . Substituting : Answer > (i) Part (ii) Step 1 · Substitute Substituting : Answer > (ii) Part (iii) Step 1 · Substitute Substituting : Answer > (iii) Common Mistakes Negative Sign Errors: When evaluating for , . Avoid incorrectly calculating as or . Multiplying by Zero: Remember that , which gives , not .

Introduction to Linear Polynomials | Exercise 2.2

Question 1

Find the value of the linear polynomial $5x - 3$ if:

(i) $x = 0$

(ii) $x = -1$

(iii) $x = 2$

Solution

Understand the Question

Let the given polynomial be $p(x) = 5x - 3$ .
To find the value of the polynomial at any given value of $x$ , substitute that value directly in place of $x$ and evaluate the arithmetic expression.

(i) $x = 0$

Step 1 · Substitute $x = 0$

Let $p(x) = 5x - 3$ .

Diagram 1

Substituting $x = 0$ :

\begin{aligned} 5(0) - 3 &= 0 - 3 \\ &= -3 \end{aligned}

Answer

(i) $-3$

(ii) $x = -1$

Step 1 · Substitute $x = -1$

Diagram 2

Substituting $x = -1$ :

\begin{aligned} 5(-1) - 3 &= -5 - 3 \\ &= -8 \end{aligned}

Answer

(ii) $-8$

(iii) $x = 2$

Step 1 · Substitute $x = 2$

Diagram 3

Substituting $x = 2$ :

\begin{aligned} 5(2) - 3 &= 10 - 3 \\ &= 7 \end{aligned}

Answer

(iii) $7$

Common Mistakes

Negative Sign Errors: When evaluating for $x = -1$ , $5(-1) - 3 = -5 - 3 = -8$ . Avoid incorrectly calculating $-5 - 3$ as $-2$ or $+2$ .
Multiplying by Zero: Remember that $5(0) = 0$ , which gives $0 - 3 = -3$ , not $5 - 3 = 2$ .

Question 1

More questions in Exercise 2.2