Can someone help me with this question please?

Mathematics

2 answers:

Kitty [74]2 years ago

7 0

The correct answer for this is 12

Just think of it....use the guess and change method to get this answer.

Think of ways to convert 15 into a fraction.
there's 5's but it's not a 1/5 fraction. (i got 1/5 from 15 reduced to 20%)
Since the number for finding 1\5 (the correct fraction) was 3 i simply added 3+3+3+3 to get 1\5 (3) to 12 (4\5)

hope you understand! :)

vitfil [10]2 years ago

4 0

The price of the item now is $12.00

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Show that 2x +1 is a factor of 2x3 +5x2+4x+1 and factories completely

larisa [96]

$\text{According to the factor theorem, if f(b) = 0, then x-b is a factor of f(x).}\\\\\text{Given that,}\\\\f(x) = 2x^3 +5x^2 +4x +1 \\\\f\left(-\dfrac 12 \right) = 2\left( - \dfrac 12 \right)^3 +5 \left( - \dfrac 12 \right)^2 +4 \left( - \dfrac 12 \right) +1 \\\\\\~~~~~~~~~~~~=-2 \cdot \dfrac 18 + 5 \cdot \dfrac 14 -2 +1 \\\\\\~~~~~~~~~~~=\dfrac 54 -\dfrac14 -1\\\\\\~~~~~~~~~~~=\dfrac 44 -1 \\\\\\~~~~~~~~~~~=1-1\\\\\\~~~~~~~~~~~=0\\\\\text{So,}~ 2x +1 ~ \text{is a factor of f(x).}$

$\text{Now,}\\\\f(x) = 2x^3 +5x^2 +4x +1 \\\\~~~~~~=2x^3+x^2 +2x^2 +2x +2x+1\\\\~~~~~~=x^2(2x+1) +2x(2x+1) + (2x+1)\\\\~~~~~~=(2x+1)(x^2 +2x +1)\\\\~~~~~~=(2x+1)(x+1)^2$