Question

what is the answer to algebra with pizzazz page 100; what should you say if you see a tall, wrought-iron tower in paris, france?
there are 24 blanks

Answer 1

Part 1:

Given

$3n^2-17n+24 \\ \\ \Rightarrow3n^2-9n-8n+24 \\ \\ \Rightarrow3n(n-3)-8(n-3) \\ \\ \Rightarrow(3n-8)(n-3)$



Part 2:

Given

$4x^3y-49xy^3 \\ \\ \Rightarrow xy(4x^2-49y^2) \\ \\ \Rightarrow xy(2x-7y)(2x+7y)$



Part 3:

Given

$5x^2+20xy-60y^2 \\ \\ \Rightarrow5x^2-10xy+30xy-60y^2 \\ \\ \Rightarrow5x(x-2y)+30y(x-2y) \\ \\ \Rightarrow(5x+30y)(x-2y) \\ \\ \Rightarrow5(x+6y)(x-2y)$



Part 4:

Given

$3x^3-x^2y+12x-4y \\ \\ \Rightarrow3x^3+12x-x^2y-4y \\ \\ \Rightarrow3x(x^2+4)-y(x^2+4) \\ \\ \Rightarrow(3x-y)(x^2+4)$



Part 5:

Given

$2x^4y-3x^3y-20x^2y \\ \\ \Rightarrow x^2y(2x^2-3x-20) \\ \\ \Rightarrow x^2y(2x^2-8x+5x-20) \\ \\ \Rightarrow x^2y[2x(x-4)+5(x-4)] \\ \\ \Rightarrow x^2y(2x+5)(x-4)$



Part 6:

Given

$9x^3y+33x^2y^2+30xy^3 \\ \\ \Rightarrow3xy(3x^2+11xy+10y^2) \\ \\ \Rightarrow3xy(3x^2+6xy+5xy+10y^2) \\ \\ \Rightarrow3xy[3x(x+2y)+5y(x+2y)] \\ \\ \Rightarrow3xy(3x+5y)(x+2y)$



Part 7:

Given

$16a^3b^4+40a^2b^5+8ab^3 \\ \\ \Rightarrow8ab^3(2a^2b+5ab^2+1)$



Part 8:

Given

$t^4-37t^2+36 \\ \\ \Rightarrow(t-1)(t-36)$



Part 9:

Given

$2a^7b^3-288ab \\ \\ \Rightarrow2ab(a^6b^2-144) \\ \\ \Rightarrow2ab(a^3b-12)(a^3b+12)$



Part 10

Given

$35a^2b-5a-7ab^2+b \\ \\ \Rightarrow35a^2b-7ab^2-5a+b \\ \\ \Rightarrow7ab(5a-b)-(5a-b) \\ \\ \Rightarrow(7ab-1)(5a-b)$



Part 11:

$6a^4b^2-11a^3b^3+4a^2b^4 \\ \\ \Rightarrow a^2b^2(6a^2-11ab+4b^2) \\ \\ \Rightarrow a^2b^2(6a^2-3ab-8ab+4b^2) \\ \\ \Rightarrow a^2b^2[3a(2a-b)-4b(2a-b)] \\ \\ \Rightarrow a^2b^2(3a-4b)(2a-b)$



Part 12:

Given

$t^2(t+3)+6t(t+3)+9(t+3) \\ \\ \Rightarrow(t^2+6t+9)(t+3) \\ \\ \Rightarrow(t+3)(t+3)(t+3) \\ \\ \Rightarrow(t+3)^3$