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Factor the polynomial by grouping.​

Factor The Polynomial By Grouping class=

Sagot :

Ninnyahhidn

Answer:

Problem 1

- Solution:

1. Group the terms: (nm - np) + (2m - 2p)

2. Factor out the greatest common factor from each group: n(m - p) + 2(m - p)

3. Notice that the two binomials are the same. Factor out m - p: (m - p)(n + 2)

- Final Answer: (m - p)(n + 2)

Problem 2

- Solution:

1. Group the terms: (ad - bc) + (-bd + ac)

2. Factor out the greatest common factor from each group: d(a - b) + c(-b + a)

3. Notice that the two binomials are the same but in reverse order. Factor out a - b: (a - b)(d + c)

- Final Answer: (a - b)(d + c)

Problem 3

- Solution:

1. Group the terms: (z³ + z²) + (z + 1)

2. Factor out the greatest common factor from each group: z²(z + 1) + 1(z + 1)

3. Notice that the two binomials are the same. Factor out z + 1: (z + 1)(z² + 1)

- Final Answer: (z + 1)(z² + 1)

Problem 4

- Solution:

1. Group the terms: (3v + 15) + (uv + 3u)

2. Factor out the greatest common factor from each group: 3(v + 5) + u(v + 3)

3. Notice that the two binomials are not the same. Therefore, this polynomial cannot be factored by grouping.

- Final Answer: Cannot be factored by grouping.

Problem 5

- Solution:

1. Group the terms: (2xz + 6y) + (2xy + 6z)

2. Factor out the greatest common factor from each group: 2(xz + 3y) + 2(xy + 3z)

3. Notice that the two binomials are not the same. Therefore, this polynomial cannot be factored by grouping.

- Final Answer: Cannot be factored by grouping.

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