Which of these identities can be used to factorize the expression 4x2 - 19x + 16?
a. (x - a)2 = x2 - 2a + a2
b. (x + a)2 = x2 + 2a + a2
C. (x – a)(x - b) = x2 - (a + b)x + ab
d. (x - a)(x + a) = x2 - a2
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Which of these identities can be used to factorize the expression 4x2 - 19x + 16?
a. (x - a)2 = x2 - 2a + a2
b. (x + a)2 = x2 + 2a + a2
C. (x – a)(x - b) = x2 - (a + b)x + ab
d. (x - a)(x + a) = x2 - a2
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Answer:
Option C. (x – a)(x - b) = x2 - (a + b)x + ab
Step-by-step explanation:
Observe that this expressions are not of the type
(x + a)^2 or (x – a)^2 , i.e., they are not perfect squares.
For example, in x^2 + 5x + 6, the term 6 is not a perfect square. This expressions obviously also do not fit the type (x 2 – a 2 ) either. They, however, seem to be of the type C. (x – a)(x - b) = x^2- (a + b) x + a b.
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