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

Understand the Question Let the given polynomial be . To find the value of the polynomial at a given value of , substitute that value in place of the variable and evaluate using arithmetic order of operations. Part (i) Step 1 · Evaluate for Substitute into the polynomial: Answer > (i) Part (ii) Step 1 · Evaluate for Substitute into the polynomial: Answer > (ii) Part (iii) Step 1 · Evaluate for Substitute into the polynomial: Answer > (iii) Common Mistakes Squaring Negative Numbers: Remember that , not . A negative number raised to an even power is always positive. Sign Errors in Multiplication: In the middle term , multiplying two negative numbers gives a positive: , not .

Introduction to Linear Polynomials | Exercise 2.2

Question 2

Find the value of the quadratic polynomial $7s^2 - 4s + 6$ if:

(i) $s = 0$

(ii) $s = -3$

(iii) $s = 4$

Solution

Understand the Question

Let the given polynomial be $p(s) = 7s^2 - 4s + 6$ .
To find the value of the polynomial at a given value of $s$ , substitute that value in place of the variable $s$ and evaluate using arithmetic order of operations.

(i) $s = 0$

Step 1 · Evaluate for $s = 0$

Substitute $s = 0$ into the polynomial:

Diagram 1

\begin{aligned} 7s^2 - 4s + 6 &= 7(0)^2 - 4(0) + 6 \\ &= 7(0) - 0 + 6 \\ &= 0 - 0 + 6 \\ &= 6 \end{aligned}

Answer

(i) $6$

(ii) $s = -3$

Step 1 · Evaluate for $s = -3$

Substitute $s = -3$ into the polynomial:

\begin{aligned} 7s^2 - 4s + 6 &= 7(-3)^2 - 4(-3) + 6 \\ &= 7(9) - (-12) + 6 \\ &= 63 + 12 + 6 \\ &= 75 + 6 \\ &= 81 \end{aligned}

Answer

(ii) $81$

(iii) $s = 4$

Step 1 · Evaluate for $s = 4$

Substitute $s = 4$ into the polynomial:

\begin{aligned} 7s^2 - 4s + 6 &= 7(4)^2 - 4(4) + 6 \\ &= 7(16) - 16 + 6 \\ &= 112 - 16 + 6 \\ &= 96 + 6 \\ &= 102 \end{aligned}

Answer

(iii) $102$

Common Mistakes

Squaring Negative Numbers: Remember that $(-3)^2 = +9$ , not $-9$ . A negative number raised to an even power is always positive.
Sign Errors in Multiplication: In the middle term $-4(-3)$ , multiplying two negative numbers gives a positive: $-4 \times (-3) = +12$ , not $-12$ .

Question 2

More questions in Exercise 2.2