alleryWhen x² + mx + 1 is divided by x − 2, the remainder is 7. Find m.
- −1
- 0
- 1
- 2
Show answer and solution
Correct answer: C. 1
The remainder condition gives 5+2m=7, so m=1.
ICSE Class 10 Algebra: Equations, Inequations & Matrices — practice questions — page 2
Explore 212 free Algebra: Equations, Inequations & Matrices questions in ICSE Class 10 Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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Showing questions 31–60 of 212.
When x² + mx + 1 is divided by x − 2, the remainder is 7. Find m.Read the answer and worked solution →After taking out x − 3, factor x³ − 3x² − 4x + 12 completely.Read the answer and worked solution →Which statement gives the remainder theorem for division by x − a?Read the answer and worked solution →Which condition shows that x − a is a factor of f(x)?Read the answer and worked solution →For f(x)=x³+px+8, division by x + 2 leaves remainder 6. Find p.Read the answer and worked solution →A cubic is x³ − 7x + 6. Which is its complete factorisation?Read the answer and worked solution →How many rows and columns does [[2, 1, 0], [4, 3, 5]] have?Read the answer and worked solution →A matrix with one row and four columns has what order?Read the answer and worked solution →Which description fits a 3 × 1 matrix?Read the answer and worked solution →Which is a null matrix?Read the answer and worked solution →What is the 2 × 2 identity matrix?Read the answer and worked solution →Can a 2 × 3 matrix be added to a 3 × 2 matrix?Read the answer and worked solution →A is 2 × 3 and B is 3 × 1. What is the order of AB?Read the answer and worked solution →If A is 2 × 3 and B is 2 × 1, which statement about AB and BA is correct?Read the answer and worked solution →Add [[1, 2], [3, 4]] and [[4, 1], [2, 0]].Read the answer and worked solution →Subtract [[2, 1], [0, 3]] from [[5, 4], [6, 8]].Read the answer and worked solution →Multiply [[1, −2], [3, 0]] by 2.Read the answer and worked solution →What is (1/2) × [[4, 6], [−2, 8]]?Read the answer and worked solution →Find [[1, 2], [0, 1]] × [[3, 1], [2, 4]].Read the answer and worked solution →Compute [[2, 0], [1, 3]] × [[1, 4], [2, 1]].Read the answer and worked solution →For what value of x are [[x, 2], [3, 4]] and [[1, 2], [3, 4]] equal?Read the answer and worked solution →Which inequality says that x is at most 15?Read the answer and worked solution →A height h must be at least 120 cm. Which condition fits?Read the answer and worked solution →Which condition means x exceeds -4?Read the answer and worked solution →From {-3, -1, 0, 2, 4}, select all solutions of 2x + 1 ≥ 1.Read the answer and worked solution →For whole numbers x, what is the solution set of x < 4?Read the answer and worked solution →What is the greatest integer less than -2.3?Read the answer and worked solution →Find the least integer satisfying x > -7/2.Read the answer and worked solution →Which listed value satisfies 3x + 1 < 8?Read the answer and worked solution →Three times x, decreased by 4, is at least 11. Write this.Read the answer and worked solution →
Worked practice questions
After taking out x − 3, factor x³ − 3x² − 4x + 12 completely.
- (x−3)(x−2)²
- (x−3)(x−4)(x+1)
- (x−3)(x+2)²
- (x−3)(x−2)(x+2)
Show answer and solution
Correct answer: D. (x−3)(x−2)(x+2)
The quotient is x²−4=(x−2)(x+2).
Which statement gives the remainder theorem for division by x − a?
- Remainder is f(a)
- Remainder is f(−a)
- Remainder is a + f(x)
- Remainder is zero always
Show answer and solution
Correct answer: A. Remainder is f(a)
The remainder on division by x−a equals the polynomial value f(a).
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