The binomial 5x – 4 is a factor of 10x2 – 23x + 12. What is the other factor?

1 answer:

6 0

$Method\ 1^o\\10x^2-23x+12=(5x-4)(ax+b)\\\\10x^2-23x+12=5ax^2+5bx-4ax-4b\\\\10x^2-23x+12=5ax^2+(5b-4a)x-4b\\\\therefore\\\\ \begin{array}{ccc}(1)\\(2)\\(3)\end{array}\left\{\begin{array}{ccc}5a=10\\5b-4a=-23\\-4b=12\end{array}\right\\\\(1)\ divide\ both\ sides\ by\ 5\to a=2\\(3)\ divide\ both\ sides\ by\ (-4)\to b=-3\\check\\subtitute\ the\ values\ of\ "a"\ and\ "b"\ to\ (2):\\5\cdot(-3)-4\cdot2=-15-8=-23\ /correct/\\\\Answer:\boxed{2x-3}$

$Method\ 2^o\\10x^2-23x+12=10x^2-8x-15x+12\\=2x\cdot5x-2x\cdot4-3\cdot5x-3\cdot(-4)\\=2x(5x-4)-3(5x-4)=(5x-4)\boxed{(2x-3)}$

You might be interested in

What is the inverse of the function f(x) = 2x + 1?

Lerok [7]

Answer:

1 + 2x = f(x) i believe

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

Which of the following is equal to 5 1/3

Andrews [41]

Answer:

Step-by-step explanation:

Using the rule of radicals/ exponents

$a^{\frac{m}{n} }$ ⇔ $\sqrt[n]{a^{m} }$

Given

$5^{\frac{1}{3} }$ = $\sqrt[3]{5}$ → C

7 0

2 years ago

The stream of water from a fountain follows a parabolic path. The stream reaches a maximum height of 7 feet, represented by a ve

xenn [34]

First of all, I'm going to assume that we have a concave down parabola, because the stream of water is subjected to gravity.

If we need the vertex to be at $x=4$ , the equation will contain a $(x-4)^2$ term.

If we start with $y=-(x-4)^2$ we have a parabola, concave down, with vertex at $x=4$ and a maximum of 0.

So, if we add 7, we will translate the function vertically up 7 units, so that the new maximum will be $(4, 7)$

We have

$y = -(x-4)+7$

Now we only have to fix the fact that this parabola doesn't land at $(8,0)$ , because our parabola is too "narrow". We can work on that by multiplying the squared parenthesis by a certain coefficient: we want