(NEED ASAP) Polynomial Math Question

Question

9x^3 – 16x^2 = 0

X(9x^2 – 16x) = 0

X(3x-4)(3x-4) = 0

3x – 4 = 0   3x – 4 = 0

3x = 4

X = 4/3

1. Find the two errors shown in solving the equations above. Explain each error in detail.

2. Solve each equation correctly, entering each step.

Answer 1

9x³ – 16x² = 0

x(9x² – 16x) = 0

x(3x - 4)(3x - 4) = 0

3x – 4 = 0  3x – 4 = 0

3x = 4

x = 4/3

The first step was wrong because there are at least 2 x's on both terms. Both x's need to be factored out as opposed to one x. The second step was wrong because the definition of the difference of two squares (DOTS) was violated. By using DOTS, two factors should appeared with opposite signs: (3x - 4)(3x + 4).

Factor by greatest common factor (GCF) = X²

9x³ – 16x² = 0

x²(9x – 16) = 0

Set each factor to zero by zero product property (ZPP)

x² = 0 9x – 16 = 0

Left Equation: Square root on both sides to get x = 0.

Right Equation: Add 16 on both sides, then divide by 9 on both sides to get x = 16/9.

The solutions are x = 0 and x = 16/9.

Answer 2

Hi Haya,

The first error is that 9x^2 - 16x does not factor to (3x-4)(3x-4). You can check this in reverse by using the FOIL (first, outer, inner, last) method on (3x-4)(3x-4):

(3x-4)(3x-4) = (3x)(3x) + (3x)(-4) + (-4)(3x) + (-4)(-4) = 9x^2 -24x + 16

The second error is that you ignore the possibility that x = 0. That is, there is more than one possible value of x that satisfies this equation.

Starting with 9x^3 - 16x^2 = 0, we can factor out x^2 (rather than just one x) to get:

x^2(9x - 16) = 0

Now, our two possible solutions are:

(a) x^2 = 0

(b) 9x - 16 = 0

Solving (a) first, the only possible solution to x^2 = 0 is when x = 0.

Solving (b), we have 9x - 16 = 0 => 9x = 16 => x = 16/9.

Thus, the two possible solutions to this polynomial are:

x = 0

x = 16/9

If you're interested in some one-on-one time, hit me up!

Answer 3

First off could have factored out an x^2 to start

Second (9x^-16x) is NOT factored correctly

Here is the solution

x^2( 9x-16)=0

so X^2 =0 x=0. And 9x-16=0 x=16/9

The 2 solutions are x=0, x=16/9

Answer 4

In step 2, they should have factored out x² instead of x so it should say x²(9x - 16) = 0. Their step 3 is also incorrect factoring but that won't matter if you do step 2 as shown above.

x²(9x - 16) = 0 means x² = 0 (or x = 0) and 9x - 16 = 0 (or x = 16/9)