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23 Cards in this Set

  • Front
  • Back

The leading term of a polynomial is

The leading term of a polynomial is the term with the highest power of x

The degree of a polynomial is

The degree of a polynomial is the highest power of x

A monic polynomial has

A monic polynomial has a leading coefficient of 1

A zero of a polymonial is

A zero of a polymonial is a value of x which makes the polynomial zero

The constant term of a polynomial is

The constant term of a polynomial is the term with no variable (variable has power 0)

If P(x) = 0 the values of x which are solutions to this equation are called

If P(x) = 0 the values of x which are solutions to this equation are called the roots of the polynomial equation.

For quadratic polynomial equations the __________ can indicate the number of roots

For quadratic polynomial equations the discriminant can indicate the number of roots

A polynomial P ( x ) can be written as


P(x) = A(x). Q(x)+ R(x)


A(x) is


Q(X) is


R(X) is

A polynomial P ( x ) can be written as


P(x) = A(x). Q(x)+ R(x)


A(x) is the divisor


Q(X) is the quotient


R(X) is the remainder

The degree of the remainder is

The degree of the remainder is less than the degree of the divisor

Remainder theorem states

Remainder theorem states that if P(x) is divided by (x - a) then the remainder is P(a)

Factor theorem states

Factor theorem states that if (x - a) is a factor of P(x) then P(a) = 0

If x - a is a factor of polynomial P(x), then a is a factor of

If x - a is a factor of polynomial P(x), then a is a factor of the constant term

To factorise a polynomial

To factorise a polynomial use the factors of the constant term and the factor theorem to find one (or more) factors and then use division to reduce polynomial to one that can be factorised

Solve 2cos³θ - cos²θ -cosθ = 0

Substitute x = cosθ, solve for x then find θ

When graphing a polynomial, the zeros give

When graphing a polynomial, the zeros give the x-intercepts

When graphing a polynomial, the constant gives

When graphing a polynomial, the constant gives the y-intercept

When graphing a polynomial, once the x-intercepts are plotted

When graphing a polynomial, once the x-intercepts are plotted use the sign of the leading coefficient to determine whether graph starts above or below x-axis

When graphing a polynomial, a double root

When graphing a polynomial, a double root causes the curve to touch the x-axis at that point

When graphing a polynomial, a triple root causes the curve to

When graphing a polynomial, a triple root causes the curve to have a point of inflexion on the x-axis at that point

If x = a is a double root of P(x) =0 then

If x = a is a double root of P(x) =0 then


P(a) = 0 and P'(a) = 0

For ax² + bx + c = 0

For ax² + bx + c = 0


∑α = -b/a


∑αβ = c/a

For ax³ + bx² + cx + d = 0

For ax³ + bx² + cx + d = 0


∑α = -b/a


∑αβ = c/a


∑αβγ = -d/a

For ax⁴ + bx³ + cx²+ dx + e = 0

For ax⁴ + bx³ + cx²+ dx + e = 0


∑α = -b/a product of roots one at a time


∑αβ = c/a product of roots two at a time


∑αβγ = -d/a product of roots three at a time


∑αβγδ = e/a product of roots four at a time