The highest common factor of polynomial (x2 – 3x - 28) and (x2 – 1

1.	The highest common factor of polynomial (x2 – 3x - 28) and (x2 – 10x + 3a) is (x - 7) then find the value of a?1. 72. 123. 94. 16
Answer» Correct Answer - Option 1 : 7 Given: The given polynomials are (x² – 3x - 28) and (x² – 10x + 3a) and their HCF is (x - 7) Concept Used: Concept of HCF and factor theorem According to factor theorem If (x - a) is factor of P(x) then P(a) = 0 Calculation: Let the polynomials are P(x) = (x² – 3x - 28) and G(x) = x² – 10x + 3a) .If (x - 7) is the HCF of the given polynomial then (x - 7) is the factor of polynomials. Then according to the factor theorem ∴ G(7) = 0 Now, put x = 7 in G(x) ∴ 49 – 10 × 7 + 3a = 0 ⇒ a = 7 Hence, option (1) is correct

The highest common factor of polynomial (x2 – 3x - 28) and (x2 – 10x + 3a) is (x - 7) then find the value of a?1. 72. 123. 94. 16

Answer» Correct Answer - Option 1 : 7

Given:

The given polynomials are (x² – 3x - 28) and (x² – 10x + 3a) and their HCF is (x - 7)

Concept Used:

Concept of HCF and factor theorem

According to factor theorem If (x - a) is factor of P(x) then P(a) = 0

Calculation:

Let the polynomials are P(x) = (x² – 3x - 28) and G(x) = x² – 10x + 3a) .If (x - 7) is the HCF of the given polynomial then (x - 7) is the factor of polynomials. Then according to the factor theorem

∴ G(7) = 0

Now, put x = 7 in G(x)

∴ 49 – 10 × 7 + 3a = 0

⇒ a = 7

Hence, option (1) is correct

Discussion

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