4 years ago

Simplify the expression (4x − 3)(x + 5)

2 answers:

4 0

To do this, we use the distributive property
(4x - 3)(x + 5)
Distribute the 4x to x and 5
(4x) * (x) + (4x) * 5 -3(x + 5)
multiply the -3 by x and 5
4x² + 20x - 3x - 15
4x² + 17x- 15

worty [1.4K]4 years ago

3 0

(4x-3)(x+5) 4x^2+20x-3x-15
4x^2+17x-15

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What’s the remainder for this synthetic division problem?

Vesna [10]

3 | 1 5 -8 6

. | 3 24 48

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. | 1 8 16 54

That is to say,

$\dfrac{x^3+5x^2-8x+6}{x-3}=x^2+8x+16+\dfrac{54}{x-3}$

The remainder is 54.

Another way of doing it is to apply the polynomial remainder theorem, which says the remainder upon dividing a polynomial $p(x)$ by $x-c$ is exactly $p(c)$ . So recognizing that the listed coefficients refer to

$p(x)=x^3+5x^2-8x+6$

we find

$p(3)=3^3+5\cdot3^2-8\cdot3+6=54$

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3 years ago

What is the midpoint of (2,5) and (-4,10)

Aleonysh [2.5K]

Answer:

$=\left(-1,\:\frac{15}{2}\right)$

Step-by-step explanation:

$\mathrm{Midpoint\:of\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)\\\left(x_1,\:y_1\right)=\left(2,\:5\right),\:\left(x_2,\:y_2\right)=\left(-4,\:10\right)\\=\left(\frac{-4+2}{2},\:\frac{10+5}{2}\right)$