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3 years ago

What is 12x³ – 9x² – 4x + 3 in factored form?(4x-3) (3x²-1) is incorrect by the way.

Mathematics

1 answer:

Lena [83]3 years ago

8 0

Answer:

(4x -3)(√3x -1)(√3x +1)

Step-by-step explanation:

Your factoring is correct for integers. However the quadratic term can be factored further using irrational coefficients. It is the difference of the squares of (√3)x and 1, so can be factored as such.

12x³ -9x² -4x +3 = 3x²(4x -3) -(4x -3) = (3x² -1)(4x -3)

= ((√3)x -1)((√3)x +1)(4x -3) . . . . . . further factoring the difference of squares

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52.Consider the functionsf(x) = 2* x+6 and g(x) = 5*2x.

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Answer:

$x=\frac{6\ln \left(2\right)}{2\ln \left(5\right)-\ln \left(2\right)}\\x \approx 1.65$

Step-by-step explanation:

Given

$f(x) = 2^{\left(x+6\right)}$

$g(x) = 5^{2x}$

We want to find $f(x) = g(x)$

For this you need to:

if $f(x) = g(x)$ , then $\ln \left(f\left(x\right)\right)=\ln \left(g\left(x\right)\right)$

$\ln \left(2^{x+6}\right)=\ln \left(5^{2x}\right)$

Apply log rule: $\log _a\left(x^b\right)=b\cdot \log _a\left(x\right)$

$\left(x+6\right)\ln \left(2\right)=2x\ln \left(5\right)$

Solve for x

Expand $\left(x+6\right)\ln \left(2\right) = \ln \left(2\right)x+6\ln \left(2\right)$

$\ln \left(2\right)x+6\ln \left(2\right)=2x\ln \left(5\right)$

$\ln \left(2\right)x=2x\ln \left(5\right)-6\ln \left(2\right)\\\ln \left(2\right)x-2x\ln \left(5\right)=-6\ln \left(2\right)\\\left(\ln \left(2\right)-2\ln \left(5\right)\right)x=-6\ln \left(2\right)\\\\x=\frac{6\ln \left(2\right)}{2\ln \left(5\right)-\ln \left(2\right)}\approx 1.65$

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