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Solve these questions with step-by-step explanations - if you can't do them all then that's ok

Solve these questions with step-by-step explanations - if you can't do them all then-example-1

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Answer:

a) (m +3) (m + 4)

b) (x + 7) (x + 5)

c) (k + 1) (k + 4)

Explanation:

a) m² + 7m + 12

Sum = 7 and product = 12

The factors are 4 and 3. When we add 4 and 3, we get 7 and when we multiply 3*4, we get 12.

Rewrite the middle term using factors.

m² + 7m + 12 = m² + 3m + 4m + 4*3

Take out the common variable 'm' from the first two terms and 4 from the third and fourth terms.

= m (m + 3) + 4 (m + 3)

= (m + 3) (m + 4)

m² + 7m + 12 = (m + 3) (m + 4)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~`

b) x² + 12x + 35

Sum = 12 and product = 35

The factors are 7 and 5. When we add 7 and 5, we get 12 and when we multiply 7*5, we get 35.

Rewrite the middle term using factors.

x² + 12x + 35 = x² + 7x + 5x + 7 * 5

Take out the common variable 'x' from the first two terms and 5 from the third and fourth terms.

= x (x + 7) + 5*(x + 7)

= (x + 7) (x + 5)

x² + 12x + 35 = (x + 7) (x + 5)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

c) k² + 5k + 4

Sum = 5 and product = 4

The factors are 4 and 1. When we add 4 and 1, we get 5 and when we multiply 1*4, we get 4.

Rewrite the middle term using factors.

k² + 5k + 4 = k² + 1k + 4k + 4*1

Take out the common variable 'k' from the first two terms and 4 from the third and fourth terms.

= k (k + 1) + 4(k + 1)

= (k + 1) (k +4)

k² + 5k + 4 = (k + 1) (k +4)

User Konrad Wright
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