/5. Suppose -n*g + 1369/10 + 1/10*g**2 = 0. What is g?
37
Let u(a) = -a**3 + a**2 - a. Let v(j) = j**3 + 2. Let d(t) = -9*t**3 - 44*t**2 - 13*t - 14. Let y(i) = -5*d(i) - 35*v(i). Let x(f) = 5*u(f) - y(f). Factor x(h).
-5*h*(h + 14)*(3*h + 1)
Factor -5248/9*z - 4/9*z**2 - 1721344/9.
-4*(z + 656)**2/9
Let p(a) be the third derivative of -a**7/945 + a**6/270 + 2*a**5/135 - 2*a**4/27 + 449*a**2 + 2*a. Find i such that p(i) = 0.
-2, 0, 2
Let w(q) be the first derivative of -2*q**5/5 - 97*q**4/7 - 248*q**3/3 + 264*q**2/7 + 406. Determine k, given that w(k) = 0.
-22, -6, 0, 2/7
Suppose -329 = 112*x - 1113. Let n(g) be the third derivative of 0*g - 1/42*g**x + 20/3*g**3 + 0 - 1/8*g**6 + 5/2*g**4 + 1/6*g**5 + 11*g**2. Solve n(h) = 0.
-2, -1, 2
Let y = -1273973/15 + 424661/5. Factor -y*r**5 + 0 - 50/3*r - 40*r**2 - 92/3*r**3 - 8*r**4.
-2*r*(r + 1)**2*(r + 5)**2/3
Let w be ((-18)/(-54))/(1/(2 + 4)). Let c be w/8 + 25/200. Solve -21/8 + 9/4*y + c*y**2 = 0 for y.
-7, 1
Solve 49*v + 99/2*v**2 + 0 + 1/2*v**3 = 0 for v.
-98, -1, 0
Let c(b) be the second derivative of 7*b - 1/4*b**2 + 0 + 1/72*b**4 - 1/18*b**3. Factor c(z).
(z - 3)*(z + 1)/6
Let x = -357/10 - -197/5. Let b = x - 21/10. Factor 0 + 0*w + b*w**4 - 4/5*w**3 - 4/5*w**2.
4*w**2*(w - 1)*(2*w + 1)/5
Let g(y) be the second derivative of -y**6/60 - 2*y**5/5 - 53*y**4/24 + 35*y**3/6 - 102*y - 1. Determine v, given that g(v) = 0.
-10, -7, 0, 1
Let h be (-280)/(-16) + (-80)/5. Factor -8*r + 5/2*r**2 + h.
(r - 3)*(5*r - 1)/2
Let b be 38*13/429 + (-12)/(-66). Let t(o) = -o**3 + 5*o**2 + 6*o. Let y be t(6). Find g such that 1/3*g + y + g**3 + 5/3*g**2 - b*g**5 - 5/3*g**4 = 0.
-1, -1/4, 0, 1
Let m = -13673/3 - -4558. Let b(l) be the second derivative of -5/6*l**3 - m*l**4 + 0 - 1/20*l**5 - l**2 + 3*l. Factor b(o).
-(o + 1)**2*(o + 2)
Determine p so that -p**4 + 8543488*p - 758*p**3 + 3529*p**2 - 24545738*p - 115421*p**2 - 79376*p**2 + 16194277 = 0.
-253, 1
Let n be (8 + 3 - -5) + -4. Let i be (8/16)/(2/n). What is x in -2/11*x**2 + 2/11 - 2/11*x + 2/11*x**i = 0?
-1, 1
Suppose -7*l = -9*l, 4*m = -3*l + 16. Suppose -6*o - 3 = -3*o, -13 = -m*c - 3*o. What is f in -106/3*f**2 + 28*f + 14/3*f**c - 16/3 + 8*f**3 = 0?
-4, 2/7, 1
Let d be (2 + -38 - 8)*(6/(-3) - (-35)/21). Factor -d*a - 8*a**2 - 8 - 4/3*a**3.
-4*(a + 1)*(a + 2)*(a + 3)/3
Factor 57790 + 207*d + d**3 + 17*d - 57534 - 31*d**2.
(d - 16)**2*(d + 1)
Suppose 6 - 18 = -8*v - 3*p, -3*v + 8 = 2*p. Let r(n) be the first derivative of 1/7*n**2 - 24 + 4/21*n**3 + v*n. Factor r(i).
2*i*(2*i + 1)/7
Let c(r) = -r**3 + 126*r**2 + 399*r - 566. Let v(g) = -g**3 - 2*g**2 - g + 46. Let k(m) = 2*c(m) + 2*v(m). Let k(t) = 0. What is t?
-4, 1, 65
Let s = 202 - 199. Factor 22*w - 12*w**2 + 14 + 8 - 2*w**3 + 4*w**s - 34.
2*(w - 3)*(w - 2)*(w - 1)
Let s = 3102293/9 + -344699. Let s*w**3 + 8/9*w**2 + 64/9 - 56/9*w = 0. What is w?
-8, 2
Let r = -180 - -182. What is g in -55*g**4 - 19*g**5 - g**5 - 32 - 100*g**2 + 204*g**r + 48*g - 28*g**3 - 17*g**4 = 0?
-2, -1, 2/5, 1
Let i(r) be the third derivative of r**7/350 + r**6/40 - 6*r**5/25 + r**4/10 + 16*r**3/5 + 318*r**2 - 1. Determine a, given that i(a) = 0.
-8, -1, 2
Let b(a) be the second derivative of 2*a**6/15 - 3*a**5/5 - 41*a**4/3 + 2*a**3 + 80*a**2 + 3338*a. What is z in b(z) = 0?
-5, -1, 1, 8
Let y = -1426 - -1434. Let l be (y/12)/((-23)/(-69)). Factor 9/7*n**3 + 15/7*n**l - 3/7*n**5 - 3/7*n**4 + 0 + 6/7*n.
-3*n*(n - 2)*(n + 1)**3/7
Let g(h) = h**3 + 8*h**2 - 33*h + 2. Let f be g(-11). Let q be (1/2)/(f + (-30)/18). Suppose -3/2*w**4 + 3*w**3 - q*w**5 - 3/2*w + 3*w**2 - 3/2 = 0. What is w?
-1, 1
Let w(u) be the second derivative of u**5/40 - 139*u**4/8 - 279*u**3/4 - 419*u**2/4 - 3271*u. Factor w(j).
(j - 419)*(j + 1)**2/2
Suppose 0 = 6*o - 23 - 1. Find w, given that 40*w**2 + 2*w**3 - 31*w**3 + 10*w**o - 5*w**4 - w**3 = 0.
0, 2, 4
Suppose q - 2*j = 8, -4 = -4*q - 5113*j + 5114*j. Determine h so that -1/7*h**5 + 12/7*h + 13/7*h**3 - 25/7*h**2 + 1/7*h**4 + q = 0.
-4, 0, 1, 3
Suppose 28*r + 829 = -830 + 1659. Let 0*q**3 + 0*q + 1/2*q**4 - 1/6*q**2 + r - 1/3*q**5 = 0. What is q?
-1/2, 0, 1
Factor 1/11*a**3 + 99225/11*a + 0 - 630/11*a**2.
a*(a - 315)**2/11
Let p(z) be the first derivative of -7*z**4/16 + 491*z**3/12 - 8645*z**2/8 + 1225*z/4 - 5361. Let p(v) = 0. Calculate v.
1/7, 35
Suppose 0*c = -6*c + 24. Factor c*l**2 + 13*l - l + 0*l.
4*l*(l + 3)
Let u(n) = -3*n**2 - 109*n - n**2 + 53*n - 4*n**2 + 53*n + 6. Let o(p) = -9*p**2 - 3*p + 8. Let i(z) = -3*o(z) + 4*u(z). Find v, given that i(v) = 0.
-3/5, 0
Let g be ((-246)/(-42) - 5)/(408/66 - 6). Factor -g*o**2 + 3/7*o**3 - 39/7 - 75/7*o.
3*(o - 13)*(o + 1)**2/7
Let k = 1001 + -996. Suppose -23 = -f - 3*n - n, n - k = 0. Factor 8/5*u**2 + u**f + 4/5*u + 0 + 1/5*u**4.
u*(u + 1)*(u + 2)**2/5
Let h be (-21)/(-6) + -3 - 0. Let o(w) be the third derivative of 0*w + 1/5*w**5 + 0 - 23*w**2 + h*w**3 - 5/8*w**4. Let o(v) = 0. Calculate v.
1/4, 1
Let a = 676 - 674. Factor 9*q**3 - 91*q**3 + 2*q**4 + 1955*q**a - 497*q**2 + 24*q**3 - 50*q**3.
2*q**2*(q - 27)**2
Let n(l) = -2*l**4 + 223*l**3 - 114*l**3 - 108*l**3. Let u(f) = -f**4 + f**3. Let v(p) = 2*n(p) - 3*u(p). Factor v(h).
-h**3*(h + 1)
Suppose -724 + 301 - 1347 = -590*r. Factor -12/5*h**2 + 0 + 9/5*h + 3/5*h**r.
3*h*(h - 3)*(h - 1)/5
Let l(k) = k**2 + 9*k + 14. Let p be l(-6). Let t be (21/6 + p)*-6. Factor -3*y**4 + 3*y**2 + t*y**3 + 0*y - 2*y - y.
-3*y*(y - 1)**2*(y + 1)
Let s = -13 - -29. Let t(u) = 5 + 3*u + u**2 + 1 + 1. Let k(c) = -4*c**2 - 8*c - 20. Let m(l) = s*t(l) + 5*k(l). Find i, given that m(i) = 0.
-1, 3
Let o(j) be the second derivative of j**7/21 - 4*j**6/5 + 27*j**5/10 + 23*j - 2. Factor o(d).
2*d**3*(d - 9)*(d - 3)
Solve -79/5*n**3 - 46/5*n**2 + 4/5 - 36/5*n**4 + 1/5*n = 0 for n.
-1, -4/9, 1/4
Factor 1415001*h**3 - 38*h**2 - 116*h + 11*h - 1415002*h**3.
-h*(h + 3)*(h + 35)
What is j in -1109818049 + 852*j**3 - 272214*j**2 - j**4 - 948528112 + 99947*j + 38554441*j = 0?
213
Suppose 481 = 149*z + 430 - 247. Suppose -2/5*p**3 + 78/5*p**z + 4394/5 - 1014/5*p = 0. What is p?
13
Let n(c) be the third derivative of 1/24*c**4 - 2*c**2 + 0 + 27*c - 1/12*c**3 - 1/120*c**5. Factor n(s).
-(s - 1)**2/2
Factor 2/5*n**3 + 548/5*n**2 + 73984/5 + 7616*n.
2*(n + 2)*(n + 136)**2/5
Let m(d) = 6*d - 42. Let k be m(5). Let f(n) = n**4 - 7*n**3 + 12*n - 4. Let j(y) = -y**3 + 2*y - 1. Let x(z) = k*j(z) + 3*f(z). Suppose x(u) = 0. What is u?
-1, 0, 2
Suppose -12*j + 6 = -10*j. Factor -224 - 639*t**4 + 644*t**4 + 724 - 825*t + 395*t**2 - 75*t**j.
5*(t - 5)**2*(t - 4)*(t - 1)
Let l be -4*1/(-2) - 3/(-3). Let 10*d**2 - 18*d**5 + 20*d**4 + 28*d**5 - 25*d**l - 15*d**5 = 0. Calculate d.
0, 1, 2
Factor -239/3*t - 82/3*t**2 - 158/3 - 1/3*t**3.
-(t + 1)*(t + 2)*(t + 79)/3
Let a = 1507908 - 1507904. Find z, given that -1/5*z**2 + 2/5*z - 2/5*z**3 + 1/5*z**a + 0 = 0.
-1, 0, 1, 2
Let q = -9252 + 9252. Let a(c) be the first derivative of 4*c**5 + q*c**2 + 0*c + 22 + 5*c**4 + 5/3*c**3. Solve a(l) = 0 for l.
-1/2, 0
Factor -1992*b + 1009*b + 1230 + 579*b - 2*b**2.
-2*(b - 3)*(b + 205)
Let x be (-7)/(616/16) + 12/6930*303. Let d(j) be the first derivative of 0*j - 1/7*j**3 - 9/28*j**4 + 18 + x*j**5 + 0*j**2. Let d(f) = 0. What is f?
-1/4, 0, 1
Let x = -4/5643 + 1885/5643. Let c(w) be the first derivative of x*w**2 - 1/3*w - 29 - 1/9*w**3. Factor c(g).
-(g - 1)**2/3
Suppose -38 = -5*s + 2*c, s + 6 = 4*s + 3*c. Let f(d) = -7*d**3 + d**2 + 9*d - 3. Let v(y) = 8*y**3 - 2*y**2 - 8*y + 2. Let x(w) = s*f(w) + 5*v(w). Factor x(q).
-2*(q - 1)**2*(q + 4)
Let i(y) = -5*y**5 + 2*y**4 + 3*y**3 - 3*y**2 + y - 1. Let q(v) = 2*v**3 + v**2 - v + 1. Let u(t) = -i(t) - q(t). Determine s, given that u(s) = 0.
-1, 0, 2/5, 1
Let r(y) be the third derivative of 11/120*y**6 - 1/210*y**7 - 46*y - 2*y**2 - 11/15*y**5 + 19/6*y**4 - 8*y**3 + 0. Solve r(q) = 0.
2, 3, 4
Let g(l) be the second derivative of -8*l**6/25 + 3702*l**5/25 - 381921*l**4/20 + 95018*l**3/5 - 35574*l**2/5 + 5*l + 30. Determine j so that g(j) = 0.
1/4, 154
Let z(l) be the first derivative of 85 - 199 + 163 - 2700*l - l**3 - 90*l**2. Solve z(m) = 0.
-30
Let x(y) = y**2 + 24*y + 145. Let p be x(-14). Let r(n) be the third derivative of 0*n + 0 + 1/2*n**4 + 1/20*n**p - 27*n**2 + 0*n**3. What is s in r(s) = 0?
-4, 