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3 years ago

Factor x3 – 4x2 + 7x – 28 by grouping. What is the resulting expression?

Mathematics

2 answers:

kirill [66]3 years ago

8 0

Consider polynomial $x^3 - 4x^2 + 7x - 28.$ You can group first two terms and last two terms:

$x^3 - 4x^2 + 7x - 28=(x^3 - 4x^2) + (7x - 28).$

In first brackets the common factor is $x^2$ and in second brackets the common factor is 7, then

$x^3 - 4x^2 + 7x - 28=(x^3 - 4x^2) + (7x - 28)=x^2(x-4)+7(x-4)=(x-4)(x^2+7).$

Answer: the correct answer is D.

Luba_88 [7]3 years ago

4 0

X^3 -4x^2 +7x -28 = x^2(x-4) +7(x -4) = (x^2 +7)(x-4)

so the 4th choice will be right sure

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4 years ago

find the value of a and b for which the system of equations has infinitely many solutions : 2x + 3y = 7 ; (a-b)x + (a+b)y = 3a +

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Answer:

a= 5 and b=1

Step-by-step explanation:

To solve, we will follow the steps below:

2x + 3y = 7

(a-b)x + (a+b)y = 3a + b - 2

We should note that since it has infinitely many solutions then,

$\frac{a_{1} }{a_{2} } = \frac{b_{1} }{b_{2} } = \frac{c_{1} }{c_{2} }$

Hence

2/a-b = 3/a+b = 7/3a +b-2

2/a-b = 3/a+b

cross-multiply

3(a-b) = 2( a+b)

open the bracket

3a - 3b = 2a + 2b

collect like term

3a - 2a = 2b + 3b

a = 5b -------------------------------------------(1)

Similarly

3/a+b = 7/3a +b-2

cross-multiply

7(a+b) = 3(3a+b -2)

7a + 7b = 9a + 3b -6

take all the variables to the left-hand side of the equation

7a - 9a+ 7b-3b = -6

-2a + 4b = -6 ---------------------------------(2)

but a = 5b

substitute a= 5b in equation (2) and solve for b

-2(5) + 4b = -6

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add 10 to both-side of the equation

-10 + 10+ 4b = -6+10

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divide both-side of the equation by 4

b = 1

substitute b= 1 in equation (1)

a = 5b

a =5(1)

a=5

Therefore, a= 5 and b=1

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