Question

Can I have help in the next few minutes?
there are 3 blanks i need the info for

Answer 1

a) (2x + 1)(3x - 4)

b) 546

Explanation:

a)

We need to try to factor the polynomial.

6(-4) = -24

6x² - 8x + 3x - 4 = 2x(3x - 4) + 1(3x - 4) =

= (2x + 1)(3x - 4)

b)

6(10)² - 5(10) - 4 = 600 - 50 - 4 = 546

Answer 2

(a) when x = 2: width = 2 units and length = 5 units

(b) 546 units²

Explanation:

Given expression:

`6x^2-5x-4`

Part (a)

To factor a quadratic in the form
`ax^2+bx+c`

Find 2 two numbers that multiply to
`ac` and sum to
`b`

Two numbers that multiply to -24 and sum to -5: -8 and 3

Rewrite
`b` as the sum of these 2 numbers:

`\implies 6x^2+3x-8x-4`

Factorize the first two terms and the last two terms separately:

`\implies 3x(2x+1)-4(2x+1)`

Factor out the common term
`(2x+1)`:

`\implies (3x-4)(2x+1)`

Therefore:

`\implies x=(4)/(3), \: x=-(1)/(2)`

As distance is positive,
`x > (4)/(3)`

Let
`x=2`

`\implies (3(2)-4)(2(2)+1)`

`\implies (2)(5)`

Therefore, possible dimensions of the rectangle are:

width = 2 units

length = 5 units

Part (b)

Substitute
`x=10` into the equation:

`\begin{aligned}\implies 6(10)^2-5(10)-4&=600-50-4\\&=546\end{aligned}`