Question

Factor completely and then place the factors in the proper location on the grid.

8c 2 - 26c + 15


Find the greatest common factor of 270 and 360. (Give the answer in the numerical form in the top box and in exponential form by filling in the boxes for exponents.)
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2[]*3[]*5[] (these are where the exponents go[])

Find the greatest common factor of 8 a3b2 and 12 ab4 .

[] a[]b[]


Factor completely and then place the factors in the proper location on the grid.

81a 2 + 36a + 4


Factor the four-term polynomial.

mn - 15 + 3 m - 5 n

(m + 3)(n - 5)
(n - 3)(m - 5)
(n + 3)(m - 5)

Answer 1

1. 8c^2-26c+15= (4c-3) (2c-5). Break the expression into groups: =(8c^2-6c)+(-20c+15). Factor out 8c^2-6c: 2c(4c-3). Factor out -5 from -20c+ 15: -5(4c-3). Lastly factor out common term (4c-3) and thats how you'll get your answer (4c-3) (2c-5).

2. common factors for 270 and 360 is 90.To find this write the factors of each and find the largest one.270: 1, 270, 2, 135, 3, 90, 5, 54, 6, 45, 9, 30, 10, 27, 15, 18360: 1, 360, 2, 180, 3, 120, 4, 90, 5, 72, 6, 60, 8, 45, 9, 40, 10, 36, 12, 30, 15, 24, 18, 20
3. The factors for 8 a3b2 and 12 ab4 is 4. because 8: 1, 2, 4, 812: 1, 2, 3, 4, 6, 12.

4. 81a^2+36a+4= (9a+2)^2. Break down the expression into groups: (81a^2+18a)+(18a+4). Factor out 9a from 81a^2 +18a: 9a(9a+2). Factor out 2 from 18a+4: 2(9a+2). so the groups you got are now 9a(9a+2)+2(9a+2). Lastley factor out common term (9a+2) to get (9a+2) (9a+2). Finally you get the answer (9a+2)^2.

5. mn-15+3m-5n= (n+3)(m-5). factor out m from nm+3m: m(n+3). Factor out -5 from -5n-15: -5(n+3). And thats how you get the number (n+3)(m-5)

Hope this helped :) Have a great day

Answer 2

1.
`(2c-5)(4c-3)`

2.
`2* 3^2* 5`

3.
`4ab^2`

4.
`(9a+2)(9a+2)`

4.
`(m-5)(n+3)`

Explanation:

1.We are given that

`8c^2-26c+15`

We have to find the factor

Using factorization method

`8c^2-20c-6c+15`

`4c(2c-5)-3(2c-5)`

`(2c-5)(4c-3)`

2.We are given that 270 and 360

We have to find the HCF of 270 and 360

`270=2* 3^3* 5`

`360=2^3*3^2* 5`

Hence, HCF of 270 and 360 =
`2* 3^2* 5`

3.We are given that
`8a^3b^2` and
`12ab^4`

We have to find HCF

`8a^3b^2=2^3* a* a* a* b* b`

`12 ab^4=2^2* 3* a* b* b* b* b`

Common factors are 4,a,
`b^2`

Hence,HCF
`8a^3b^2` and
`12 ab^4 =4ab^2`

4.
`81a^2+36a+4`

We have to find the factors

`81a^2+18a+18a+4`

`9a(9a+2)+2(9a+2)`

`(9a+2)(9a+2)`

5.
`mn-15+3m-5n`

We have to find the factors

`mn+3m-5n-15`

`m(n+3)-5(n+3)`

`(m-5)(n+3)`