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2 years ago

Please help me, I'm struggling with this question

Mathematics

1 answer:

ozzi2 years ago

3 0

$\underline{\boxed{\tt{\red{\:Solution}}}}$

Given:-

f(x) = x²

Evaluation:-

e).

==> f(x) = x²

So,

==> f(3x) = (3x)² = 9x²

f).

==> f(x/2) = (x/2)² = x²/4

g).

==> 3f(x) = 3x²

h).

==> 2f(x-1)+5 = 2(x-1)²+5 = 2(x² + 1 - 2x ) + 5

= 5x² + 5 - 10x + 5

= 5x² - 10x + 10

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What are the factors of 2x + 3x - 54? Select two options

tiny-mole [99]

Answer:

The answer: The factors are (2x-9) and (x+6).

The Problem:

Factor $2x^2+3x-54$

Step-by-step explanation:

So I'm going to do trial factors using the choices to aid me.

Factored form for this problem if it exist will be in the form:

$(mx+n)(kx+p)$ .

In general this is what it would look like if we factored any quadratic in terms of $x$ (given the quadratic is not prime but technically you could factor even over the complex numbers).

Let's look at:

$(mx+n)(kx+p)$

We want to choose $k \text{ and } m$ such that when you multiply them you get 2. Well those would have to be 2 and 1.

$(2x+n)(x+p)$

we want to choose $n \text{ and } p$ such that when you multiply them you get -54. Based on the choices we want to get with -9 and 6, or 9 and -6. We don't know the order we want to choose it in either.

For example which of these would work:

$(2x-6)(x+9)$

$(2x+6)(x-9)$

$(2x-9)(x+6)$

$(2x+9)(x-6)$

We are going to consider only the outer and inner of FOIL since we already know the first times the first is $2x^2$ and the last times the last is $-54$ .