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What are the two factors of quadratic polynomial x2-16x+64?
- a)(x-16) and (x-64)
- b)(x+8) and (x-8)
- c)(x+16) and (x-4)
- d)(x-8) and (x-8)
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
What are the two factors of quadratic polynomialx2-16x+64?a)(x-16) and...
Solution:
To find the factors of the quadratic polynomial x2-16x+64, we can use the factorization formula for perfect square trinomials.
Formula: (a-b)2 = a2-2ab+b2
Comparing x2-16x+64 with the formula, we can see that a = x and b = 8.
Therefore, (x-8)2 = x2-16x+64
Taking the square root of both sides, we get:
x-8 = ±√(x2-16x+64)
x-8 = ±(x-8)
Now, we can solve for x in each case:
Case 1: x-8 = x-8
Simplifying, we get 0 = 0, which is always true. Therefore, this case gives us only one factor.
Factor 1: x-8
Case 2: x-8 = -(x-8)
Simplifying, we get 2x = 16, which gives us x = 8. Therefore, this case gives us another factor.
Factor 2: x-8
Thus, the two factors of the quadratic polynomial x2-16x+64 are (x-8) and (x-8), which can be written as (x-8)2.
Therefore, the correct answer is option D, (x-8) and (x-8).
To find the factors of the quadratic polynomial x2-16x+64, we can use the factorization formula for perfect square trinomials.
Formula: (a-b)2 = a2-2ab+b2
Comparing x2-16x+64 with the formula, we can see that a = x and b = 8.
Therefore, (x-8)2 = x2-16x+64
Taking the square root of both sides, we get:
x-8 = ±√(x2-16x+64)
x-8 = ±(x-8)
Now, we can solve for x in each case:
Case 1: x-8 = x-8
Simplifying, we get 0 = 0, which is always true. Therefore, this case gives us only one factor.
Factor 1: x-8
Case 2: x-8 = -(x-8)
Simplifying, we get 2x = 16, which gives us x = 8. Therefore, this case gives us another factor.
Factor 2: x-8
Thus, the two factors of the quadratic polynomial x2-16x+64 are (x-8) and (x-8), which can be written as (x-8)2.
Therefore, the correct answer is option D, (x-8) and (x-8).
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Community Answer
What are the two factors of quadratic polynomialx2-16x+64?a)(x-16) and...
Let p(x)=xsq-16x+64 By factor theorem x-8 will befactor of if p(8)=0 now,p(8)=8sq-16×8+64=0 (keeping x=8) now find and again this like do
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What are the two factors of quadratic polynomialx2-16x+64?a)(x-16) and (x-64)b)(x+8) and (x-8)c)(x+16) and (x-4)d)(x-8) and (x-8)Correct answer is option 'D'. Can you explain this answer? for Class 9 2026 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about What are the two factors of quadratic polynomialx2-16x+64?a)(x-16) and (x-64)b)(x+8) and (x-8)c)(x+16) and (x-4)d)(x-8) and (x-8)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 9 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What are the two factors of quadratic polynomialx2-16x+64?a)(x-16) and (x-64)b)(x+8) and (x-8)c)(x+16) and (x-4)d)(x-8) and (x-8)Correct answer is option 'D'. Can you explain this answer?.
What are the two factors of quadratic polynomialx2-16x+64?a)(x-16) and (x-64)b)(x+8) and (x-8)c)(x+16) and (x-4)d)(x-8) and (x-8)Correct answer is option 'D'. Can you explain this answer? for Class 9 2026 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about What are the two factors of quadratic polynomialx2-16x+64?a)(x-16) and (x-64)b)(x+8) and (x-8)c)(x+16) and (x-4)d)(x-8) and (x-8)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 9 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What are the two factors of quadratic polynomialx2-16x+64?a)(x-16) and (x-64)b)(x+8) and (x-8)c)(x+16) and (x-4)d)(x-8) and (x-8)Correct answer is option 'D'. Can you explain this answer?.
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