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)
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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)
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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)