Question

5. Simplify the following expressions and evaluate them as directed:
(i) x²(3-2x+x²) for x = 1; x = -1 and x -1/2​

Answer 1

Answer:

(i) x²(3-2x+x²) for x = 1; x = -1 and x -1/2​

break this first,

3x^2-2x^3+x^4

now when x=1

3-2+1=2

when x=-1

3+2+1=6

when x=-1/2

3*1/4+2*1/8+1/16

=3/4+1/4+1/16

=1+1/16

=17/16

Answer 2

(a) Simplify

       x²(3 - 2x + x²)

    = 3x² - 2x³ + x⁴

(b) When x = 1,

       3x² - 2x³ + x⁴

    = 3(1)² - 2(1)³ + 1⁴

    = 3(1) - 2(1) + 1

    = 3 - 2 + 1

    = 2

(c) When x = -1,

       3x² - 2x³ + x⁴

    = 3(-1)² - 2(-1)³ + (-1)⁴

    = 3(-1) - 2(-1) - 1

    = -3 + 2 - 1

    = -2

(d) When x = $-\frac{1}{2}$

       3x² - 2x³ + x⁴

    = 3($-\frac{1}{2}$)² - 2($-\frac{1}{2}$)³ + ($-\frac{1}{2}$)⁴

    = 3($\frac{1}{4}$) - 2($-\frac{1}{8}$) + $\frac{1}{16}$

    = $\frac{3}{4}$ + $\frac{2}{8}$ + $\frac{1}{16}$

    = $\frac{12}{16}$ + $\frac{4}{16}$ + $\frac{1}{16}$

    = $\frac{17}{16}$

    = $1\frac{1}{16}$