A LEVEL PURE MATHEMATICS -CAMBRIDGE
|ACTUAL EXAM QUESTIONS WITH WELL
DETAILED CORRECT ANSWERS|GRADED
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Terms in this set (199)
State the degree of each of the 3, 4, 0, 0
following polynomials. (write your
answer like "ans1, ans2, ans3")
a) x³ - 3x² + 2x - 7
b) 8 + 5x - 3x² + 7x + 6x⁴
c) 3
d) x⁰
One factor of 3x² -5x -2 is x - 2. Find 3x + 1
the other factor.
If 4x³ + 2x² + 3 ≡ (x - 2)(Ax² + Bx + C) A = 4, B = 10, C = 20, R = 43
+ R, find A, B, C and R
, Find the values of A, B, C, D and R. A = 3, B = 1, C = -1, D = 2, R = 0
6x⁴ + 5x³ - x² + 3x + 2 ≡ (2x + 1)(Ax³ +
Bx² + Cx + D) + R
Find the quotient and remainder x³ - x² + x, R = 2
when x⁴ + x +2 is divided by x + 1
using equating coefficients
Find the quotient and remainder x³ - x² + x, R = 2
when x⁴ + x +2 is divided by x + 1
using long division
What is the remainder theorem? When a polynomial p(x) is divided by x - t, let the
quotient be q(x) and the remainder be R. Then
p(x) = (x - t)q(x) + R
Find the remainder when x³ - 3x + 4 (x + 3 = 0)
is divided by (x + 3) using the (x = -3, sub x into the equation)
remainder theorem. -14
What is the extended remainder When a polynomial p(x) is divided by sx - t, the
theorem? (the useful one) remainder is the constant p(t/s)
When x³ + 2x² - px + 1 is divided by x (x³ + 2x² - px + 1 = 5)
- 1 the remainder is 5. Find the value (x - 1 = 0, x = 1)
of p p = -1
Find the quotient and the remainder (Need help)
when x⁴ - 2x³ -7x² + 7x + 5 is divided
by x² + 2x -1
What is the factor theorem? (Let p(x) be a polynomial), if x - t is a factor of
p(x), then p(t) = 0, if p(t) = 0 then x - t is a factor)
(Basically, substitute random things like 'x - 1' (x =
1) into a polynomial. If it equals zero, then it is a
factor.)
|ACTUAL EXAM QUESTIONS WITH WELL
DETAILED CORRECT ANSWERS|GRADED
A+|BRAND NEW 2026/2027 UPDATE
Save
Terms in this set (199)
State the degree of each of the 3, 4, 0, 0
following polynomials. (write your
answer like "ans1, ans2, ans3")
a) x³ - 3x² + 2x - 7
b) 8 + 5x - 3x² + 7x + 6x⁴
c) 3
d) x⁰
One factor of 3x² -5x -2 is x - 2. Find 3x + 1
the other factor.
If 4x³ + 2x² + 3 ≡ (x - 2)(Ax² + Bx + C) A = 4, B = 10, C = 20, R = 43
+ R, find A, B, C and R
, Find the values of A, B, C, D and R. A = 3, B = 1, C = -1, D = 2, R = 0
6x⁴ + 5x³ - x² + 3x + 2 ≡ (2x + 1)(Ax³ +
Bx² + Cx + D) + R
Find the quotient and remainder x³ - x² + x, R = 2
when x⁴ + x +2 is divided by x + 1
using equating coefficients
Find the quotient and remainder x³ - x² + x, R = 2
when x⁴ + x +2 is divided by x + 1
using long division
What is the remainder theorem? When a polynomial p(x) is divided by x - t, let the
quotient be q(x) and the remainder be R. Then
p(x) = (x - t)q(x) + R
Find the remainder when x³ - 3x + 4 (x + 3 = 0)
is divided by (x + 3) using the (x = -3, sub x into the equation)
remainder theorem. -14
What is the extended remainder When a polynomial p(x) is divided by sx - t, the
theorem? (the useful one) remainder is the constant p(t/s)
When x³ + 2x² - px + 1 is divided by x (x³ + 2x² - px + 1 = 5)
- 1 the remainder is 5. Find the value (x - 1 = 0, x = 1)
of p p = -1
Find the quotient and the remainder (Need help)
when x⁴ - 2x³ -7x² + 7x + 5 is divided
by x² + 2x -1
What is the factor theorem? (Let p(x) be a polynomial), if x - t is a factor of
p(x), then p(t) = 0, if p(t) = 0 then x - t is a factor)
(Basically, substitute random things like 'x - 1' (x =
1) into a polynomial. If it equals zero, then it is a
factor.)
