Answer:
Part 1) x=49
Part 2) x=9
Part 3) x=258/7
Part 4) [tex]x^{2} -11x+18=(x-9)(x-2)[/tex]
Part 5) [tex]-5x^{2} +9x+2=-5(x-2)(x+2/10)[/tex]
Part 6) [tex]x^{2} +13x-3=(x-0.227)(x+13.23)[/tex]
Part 7) yes, [tex]x^{2} -16=(x+4)(x-4)[/tex]
Part 8) Is not a perfect square trinomial [tex]x^{2} -10x-25=(x-12.07)(x+2.07)[/tex]
Part 9) yes, [tex]x^{2} -36=(x+6)(x-6)[/tex]
Part 10) s not completely factored [tex]4x(x^{2} +2x+3)[/tex]
Part 11) [tex]3x^{2}(x+1)(x-6)[/tex]
Part 12) [tex]9x^{2} -120x-400=9(x-16.09)(x+2.76)[/tex]
Part 13) [tex]x^{2} -16x-48=(x+2.58)(x-18.58)[/tex]
Part 14) [tex]x^{2} -5x-24=(x+3)(x-8)[/tex]
Part 15) [tex]2x^{2} -7x+6=(x-2)(x-1.5)[/tex]
Part 16) [tex]10x^{3} -35x^{2}-20x=10x(x+0.5)(x-4)[/tex]
Part 17) [tex]8x^{2} -18x+12x-27=8(x-2.25)(x+1.5)[/tex]
Part 18) yes is a perfect square trinomial [tex]25(x+2.8)^{2}[/tex]
Part 19) [tex]x(4x^{2} -16)=4x(x+4)(x-4)[/tex]
Part 20) [tex]30x^{3}+28x^{2}+6x=30x(x+1/3)(x+3/5)[/tex]
Step-by-step explanation:
Part 1) [tex]\sqrt{x} =7[/tex]
squared both sides
[tex]x=7^{2}=49[/tex]
Part 2) [tex]\sqrt{x} +9=12[/tex]
[tex]\sqrt{x}=12-9[/tex]
[tex]\sqrt{x}=3[/tex]
squared both sides
[tex]x=3^{2}=9[/tex]
Part 3) [tex]\sqrt{7x-2}=16[/tex]
squared both sides
[tex]7x-2=16^{2}\\7x=256+2\\x=258/7[/tex]
Part 4) [tex]x^{2} -11x+18[/tex]
equate to zero
[tex]x^{2} -11x+18=0[/tex]
[tex]x^{2} -11x=-18[/tex]
[tex]x^{2} -11x+5.5^{2}=-18+5.5^{2}[/tex]
[tex](x-5.5)^{2}=12.25[/tex]
take the root square both sides
[tex](x-5.5)=(+/-)3.5[/tex]
[tex](x)=5.5(+/-)3.5[/tex]
[tex](x)=5.5(+)3.5=9[/tex]
[tex](x)=5.5(-)3.5=2[/tex]
therefore
[tex]x^{2} -11x+18=(x-9)(x-2)[/tex]
Part 5) [tex]-5x^{2} +9x+2[/tex]
equate to zero
[tex]-5x^{2} +9x+2=0[/tex]
[tex]-5x^{2} +9x=-2[/tex]
[tex]-5(x^{2} -(9/5)x)=-2[/tex]
[tex]-5(x^{2}-(9/5)x+81/100)=-2-81/20[/tex]
[tex]-5(x^{2}-(9/5)x+81/100)=-121/20[/tex]
[tex](x-(9/10))^{2}=121/100[/tex]
[tex](x-(9/10))=(+/-)11/10[/tex]
[tex]x=(9/10)(+/-)11/10[/tex]
[tex]x=(9/10)(+)11/10=2[/tex]
[tex]x=(9/10)(-)11/10=-2/10[/tex]
therefore
[tex]-5x^{2} +9x+2=-5(x-2)(x+2/10)[/tex]
Part 6) [tex]x^{2} +13x-3[/tex]
[tex]x^{2} +13x=3[/tex]
[tex](x^{2} +13x+6.5^{2})=3+6.5^{2}[/tex]
[tex](x^{2} +13x+6.5^{2})=45.25[/tex]
[tex](x+6.5)^{2}=45.25[/tex]
[tex](x+6.5)=(+/-)\sqrt{45.25} [/tex]
[tex]x=-6.5(+/-)\sqrt{45.25} [/tex]
[tex]x=-6.5(+)\sqrt{45.25}=0.227[/tex]
[tex]x=-6.5(-)\sqrt{45.25}=-13.23[/tex]
therefore
[tex]x^{2} +13x-3=(x-0.227)(x+13.23)[/tex]
Part 7) [tex]x^{2} -16[/tex]
yes is a difference of squares
because
[tex]x^{2} -16=(x+4)(x-4)[/tex]
Par 8) [tex]x^{2} -10x-25[/tex]
is not a perfect square trinomial
[tex]x^{2} -10x=25[/tex]
[tex]x^{2} -10x+25=25+25[/tex]
[tex](x-5)^{2}=50[/tex]
[tex](x-5)=(+/-)\sqrt{50}[/tex]
[tex]x=5(+/-)\sqrt{50}[/tex]
[tex]x=5(+)\sqrt{50}=12.07[/tex]
[tex]x=5(-)\sqrt{50}=-2.07[/tex]
therefore
[tex]x^{2} -10x-25=(x-12.07)(x+2.07)[/tex]
Part 9) [tex]x^{2} -36[/tex]
yes is a difference of squares
because
[tex]x^{2} -36=(x+6)(x-6)[/tex]
Part 10) [tex]x(4x^{2} +8x+12)[/tex]
Is not completely factored
factor 4
[tex]4x(x^{2} +2x+3)[/tex]
Part 11) [tex]3x^{4} -15x^{3}-18x^{2}[/tex]
Factor [tex]3x^{2}[/tex]
[tex]3x^{2}(x^{2} -5x-6)=3x^{2}(x+1)(x-6)[/tex]
Part 12) [tex]9x^{2} -120x-400[/tex]
is not a perfect square trinomial
[tex]9x^{2} -120x=400[/tex]
[tex]9(x^{2} -(120/9)x)=400[/tex]
[tex]9(x^{2} -(40/3)x+1600/36)=400[/tex]
[tex]9(x^{2} -(40/3)x+400/9)=400+400[/tex]
[tex](x-20/3)^{2}=800/9[/tex]
[tex]x=20/3(+/-)\sqrt{800/9}[/tex]
[tex]x=20/3(+)\sqrt{800/9}=16.09[/tex]
[tex]x=20/3(-)\sqrt{800/9}=-2.76[/tex]
therefore
[tex]9x^{2} -120x-400=9(x-16.09)(x+2.76)[/tex]
Part 13) [tex]x^{2} -16x-48[/tex]
[tex]x^{2} -16x+64=48+64[/tex]
[tex](x-8)^{2}=112[/tex]
[tex](x-8)=(+/-)\sqrt{112}[/tex]
[tex]x=8(+/-)\sqrt{112}[/tex]
[tex]x=8(+)\sqrt{112}=18.58[/tex]
[tex]x=8(-)\sqrt{112}=-2.58[/tex]
therefore
[tex]x^{2} -16x-48=(x+2.58)(x-18.58)[/tex]
Part 14) [tex]x^{2} -5x-24[/tex]
[tex]x^{2} -5x+6.25=24+6.25[/tex]
[tex](x-2.5)^{2}=30.25[/tex]
[tex](x-2.5)=(+/-)5.5[/tex]
[tex]x=2.5(+/-)5.5[/tex]
[tex]x=2.5(+)5.5=8[/tex]
[tex]x=2.5(-)5.5=-3[/tex]
therefore
[tex]x^{2} -5x-24=(x+3)(x-8)[/tex]
Part 15) [tex]2x^{2} -7x+6[/tex]
[tex]2(x^{2} -3.5x+49/16)=-6+49/8[/tex]
[tex]2(x-7/4)^{2}=1/8[/tex]
[tex](x-7/4)^{2}=1/16[/tex]
[tex](x-7/4)=(+/-)1/4[/tex]
[tex]x=7/4(+/-)1/4[/tex]
[tex]x=7/4(+)1/4=2[/tex]
[tex]x=7/4(-)1/4=1.5[/tex]
therefore
[tex]2x^{2} -7x+6=(x-2)(x-1.5)[/tex]
The answer of questions 16-17-18-19-20 in the attached document
