Question

1 multiple choice 4 points which expression is equivalent to the expression (2x + 4)(x - 6)? 2x^2 - 24 2x^2 + 4x - 24 2x^2 - 8x - 24 x^2 - 4x - 12 2 multiple choice 4 points the expression (x - 4)^2 is equivalent to x^2 + 16 x^2 + 8x + 16 x^2 - 8x + 16 x^2 - 16 3 multiple choice 4 points the binomials (x - 2) and (2x + 3) are the factors of which polynomial? 2x^2 + x - 6 2x^2 - 6 2x^2 + 7x - 6 2x^2 - x - 6

Explanation:

Step1: Expand the first expression

Use FOIL method on $(2x + 4)(x - 6)$. First terms: $2x\times x=2x^{2}$, Outer terms: $2x\times(- 6)=-12x$, Inner terms: $4\times x = 4x$, Last terms: $4\times(-6)=-24$. Combine like - terms: $2x^{2}-12x + 4x-24=2x^{2}-8x-24$.

Step2: Expand the second expression

Use the formula $(a - b)^2=a^{2}-2ab + b^{2}$ for $(x - 4)^2$. Here $a = x$ and $b = 4$, so $(x - 4)^2=x^{2}-2\times x\times4+4^{2}=x^{2}-8x + 16$.

Step3: Expand the third expression

Use FOIL method on $(x - 2)(2x + 3)$. First terms: $x\times2x=2x^{2}$, Outer terms: $x\times3 = 3x$, Inner terms: $-2\times2x=-4x$, Last terms: $-2\times3=-6$. Combine like - terms: $2x^{2}+3x-4x-6=2x^{2}-x-6$.

Answer:

1. C. $2x^{2}-8x - 24$
2. C. $x^{2}-8x + 16$
3. D. $2x^{2}-x - 6$