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uysha [10]
2 years ago
9

Arrange the steps from start to finish to factor this expression using the grouping method x^2-5x-24 drag the tiles to the corre

ct boxes not all tiles will be used step by step
Mathematics
1 answer:
rosijanka [135]2 years ago
7 0

Answer:

(x - 8)(x + 3)

Step-by-step explanation:

x² - 5x - 24

Consider the factors of - 24 which sum to give the coefficient of the x- term (- 5)

The factors are - 8 and + 3 , since

- 8 × + 3 = - 24 and - 8 + 3 = - 5

Use these factors to split the x- term

x² - 8x + 3x - 24 ( factor the first/second and third/fourth terms )

= x(x - 8) + 3(x - 8) ← factor out (x - 8) from each term

= (x - 8)(x + 3) ← in factored form

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Answer:

Step-by-step explanation:

Based on the two graphs I see at the bottom of the photo, you're looking at a quadratic function. The answer you put in is a linear equation.

Quadratic functions follow the form ax^2+bx+c, where a, b, and c can be either positive or negative constants.

The table says that the equation, when graphed, should start at the top, slide to the bottom, and then slide back up to the top. So a must be positive.

c has to be -8 since it's the y-intercept.

So far, our equation is ax^2+bx-8. We'll need to plug in some points in order to work out what a and b are.

Let's use (-2,5) as the first set of points, and (4,14) as the second set.

5=a(-2)^2+b(-2)-8\\14=a(4)^2+b(4)-8\\

Now we have 2 equations with 2 unknowns. Solve for one variable:

5=4a-2b-8\\13+2b=4a\\\frac{13+2b}{4}=a

Now substitute that into the second equation:

14=(\frac{13+2b}{4})(4^2)+4b-8\\14+8=(13+2b)(4)+4b\\22-52=8b+4b\\-30=12b\\-\frac{30}{12}=-\frac{10}{4}=-\frac{5}{2}=b

Now substitute the result into the first equation.

\frac{13+2(-\frac{5}{2})}{4}=a\\\\\frac{13-5}{4}=a\\\\\frac{8}{4}=a\\\\ 2=a

Now substitute our values back into the original equation:

y(x)=2x^2-\frac{5}{2}x-8

Please let me know if this is correct.

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