EXAM 2026-2027 ACTUAL COMPLETE REAL EXAM
QUESTIONS AND CORRECT ANSWERS (VERIFIED
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Construct the quadratic whose roots are 3 + Square root of 3,
3 − Square root
of 3. - ANSWER-The sum of the roots is 6. Their product
is 9 − 3 = 6.
Therefore, the quadratic is x2 −
6x + 6.
perfect square trinomial - ANSWER-a2 + 2ab + b2 = (a + b)2
completing the square - ANSWER-1) Transpose the constant
term to the right 2) Add a square number to both sides. Add the
square of half the coefficient of x.
3) The left-hand side is now the perfect square
Dividend/Divisor - ANSWER-= Quotient + Remainder/Divisor
Dividend - ANSWER-= Quotient· Divisor + Remainder.
The remainder theorem - ANSWER-The value of a
polynomial P(x) at x =a,
, P(a), is equal to the remainder upon dividing
P(x) by x − a
Use synthetic division to
divide
x3 − 8x2 + x + 2 by x − 7. - ANSWER-(x2 − x − 6)(x
− 7) − 40
The Factor Theorem - ANSWER-x − r is a factor of a polynomial
P(x) if and only
if r is a root of
P(x)
Fundamental Theorem of Algebra - ANSWER-A polynomial of
degree n has at
least one root, real or
complex.
The integer root theorem - ANSWER-If an integer is a root of a
polynomial whose coefficients are integers and whose leading
coefficient is ±1, then that integer is a factor of the constant
term.
Conjugate pairs - ANSWER-If the irrational number a +
Square root of b is a
root, then its conjugate a − Square root of b is
also a root.