Factor Theorem (Grade 12 NSC Matric Mathematics): Quizzes

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Factor Theorem
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What must the remainder be for b(x)b(x) to be a factor of a(x)a(x)?

R(x)=0R(x) = 0

To test if (x−5)(x - 5) is a factor of p(x)p(x), what value should you substitute?

x=5x = 5

To test if (x+3)(x + 3) is a factor of f(x)f(x), what value should you substitute?

x=−3x = -3

If p(2)=7p(2) = 7, what can you conclude about (x−2)(x - 2)?

(x−2)(x - 2) is not a factor of p(x)p(x)

Is (y−1)(y - 1) a factor of f(y)=2y4+3y2−5y+7f(y) = 2y^4 + 3y^2 - 5y + 7?

No, because f(1)=7f(1) = 7

What is the first step when factorising a cubic polynomial?

Find one factor by trial and error

If (x−k)(x - k) is a factor of p(x)p(x), what must be true?

p(k)=0p(k) = 0

For (y+4)(y + 4) to be a factor of g(y)g(y), what must equal zero?

g(−4)g(-4)

Which expression is a factor of f(x)=x3+x2−9x−9f(x) = x^3 + x^2 - 9x - 9?

(x+1)(x + 1)

If p(a)=0p(a) = 0, which statement follows from the factor theorem?

(x−a)(x - a) is a factor of p(x)p(x)

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