1 of 8 0-day streak

Divide polynomials and state quotient and remainder

Question 1 of 8

No calculator

Let D(x) be the dividend and V(x) be the divisor. Divide D(x) by V(x)

D(x)=12x^{2} + 25x + 15

V(x)=4x + 3

Use exact coefficients. If a power is missing, write its zero coefficient. The remainder must be zero or have lower degree than V(x)

(a)1 mark

Which equation states the valid division identity? Then state the quotient and remainder

12x^{2} + 25x + 15=(4x + 3)(0)+(12x^{2} + 25x + 15)\Longrightarrow\text{stop}

12x^{2} + 25x + 15=(4x + 3)(3x + 4+(3))

12x^{2} + 25x + 15=(4x + 3)(3x + 4)+(3)

12x^{2} + 25x + 15=(4x + 3)(3x + 4)-(3)

(b)3 marks

Enter the coefficients of Q(x) and R(x), labelled by power. Include zero coefficients where a power is missing

coefficient of \(x^1\) in \(Q(x)\) \(Q(x)\): constant coefficient \(R(x)\): constant coefficient