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3 years ago

Simplify the following. (a) 3(-3 + 5x) - 1 (4 - 4x) (b) 3 squareroot 64 x^15 y^3 -2(-15 e^5 t/30 e^-2 t^-3)^0

Mathematics

1 answer:

Kaylis [27]3 years ago

6 0

Answer:

a. 19x-13 b. $2(32x^{15}y^{3}-1).$

Step-by-step explanation:

a. 3(-3+5x)-1(4-4x) = -9+15x-4+4x = 15x+4x-9-4 = 19x-13.

b. $64x^{15}y^{3}-2(-15e^{5}\frac{t}{30}e^{-2}t^{-3})^{0}$

= $64x^{15}y^{3}-2 = 2(32x^{15}y^{3}-1).$

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5x3 + 14x2 + 9x <br> help

Cerrena [4.2K]

<h3>Answer: x(x+1)(5x+9) </h3>

===================================================

Work Shown:

5x^3 + 14x^2 + 9x

x( 5x^2 + 14x + 9 )

To factor 5x^2 + 14x + 9, we could use the AC method and guess and check our way to getting the correct result.

A better way in my opinion is to solve 5x^2 + 14x + 9 = 0 through the quadratic formula

$x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(14)\pm\sqrt{(14)^2-4(5)(9)}}{2(5)}\\\\x = \frac{-14\pm\sqrt{16}}{10}\\\\x = \frac{-14\pm4}{10}\\\\x = \frac{-14+4}{10} \ \text{ or } \ x = \frac{-14-4}{10}\\\\x = \frac{-10}{10} \ \text{ or } \ x = \frac{-18}{10}\\\\x = -1 \ \text{ or } \ x = \frac{-9}{5}\\\\$

Then use those two solutions to find the factorization

x = -1 or x = -9/5

x+1 = 0 or 5x = -9

x+1 = 0 or 5x+9 = 0

(x+1)(5x+9) = 0

So we have shown that 5x^2 + 14x + 9 factors to (x+1)(5x+9)

-----------

Overall,

5x^3 + 14x^2 + 9x

factors to

x(x+1)(5x+9)

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Given,

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