5
Find h such that 32/19*h**3 + 2/19*h**4 - 64/19 - 100/19*h - 6/19*h**2 = 0.
-16, -1, 2
Let -188/3*s + 187/3 + 1/3*s**2 = 0. Calculate s.
1, 187
Let j(s) be the third derivative of -289/480*s**6 - 17/60*s**5 + 0 + 0*s**3 + 0*s + 66*s**2 - 1/24*s**4. What is h in j(h) = 0?
-2/17, 0
Let b = -7002/35 - -1434/7. Factor -2/5*f**2 - 22/5 + b*f.
-2*(f - 11)*(f - 1)/5
Suppose 3*w - 3 + 0 = 0. Suppose z - w = 3. Solve -8*u**2 - 3*u**2 + z*u**2 + 4*u**2 + 24*u = 0.
0, 8
Let u(t) be the third derivative of t**5/120 + 13*t**4/24 + 12*t**3 - t**2 + 1340*t. Factor u(v).
(v + 8)*(v + 18)/2
Factor -109*h + 1/5*h**2 - 1/5*h**4 + 109*h**3 + 0.
-h*(h - 545)*(h - 1)*(h + 1)/5
Suppose -408 - 22*a**2 + 60*a**2 - 25*a**2 + 412*a - 17*a**2 = 0. Calculate a.
1, 102
Solve -6/5*y**2 + 784/5*y - 104 = 0.
2/3, 130
Let k(z) be the first derivative of 10*z**3/3 - 9157*z**2 + 7324*z - 1311. Factor k(f).
2*(f - 1831)*(5*f - 2)
Let m(b) = 2*b**2 + 10*b - 10. Let p be m(1). Factor -45*w + 628*w**2 + 11 - 578*w**p - 60*w**4 - 1 + 20*w**3 + 25*w**5.
5*(w - 1)**3*(w + 1)*(5*w - 2)
Let x be (-14)/(-60)*30/140. Let a(l) be the second derivative of -x*l**4 - 9/10*l**2 - 2/5*l**3 - 4*l + 0. Factor a(h).
-3*(h + 1)*(h + 3)/5
Let i(q) = -16*q**3 - 1341*q**2 - 3646*q - 1793. Let p(o) = -3*o**3 - 277*o**2 - 729*o - 359. Let c(w) = -2*i(w) + 11*p(w). Find x such that c(x) = 0.
-363, -1
Let 30 - 5*y - 5/3*y**2 = 0. Calculate y.
-6, 3
Let h(x) = 6*x**2 + 11*x - 7. Let g be h(-7). Suppose g = 18*t + 30. Solve -8/5*m**5 + 52/5*m - 44/5*m**3 - 2 + t*m**4 - 8*m**2 = 0 for m.
-1, 1/4, 1, 5
Let z(v) be the first derivative of -4*v**3/3 + 5580*v**2 - 7784100*v + 2844. Determine q so that z(q) = 0.
1395
Let g = -490 - -492. Factor -141*p**3 + 139*p**3 - 4 + 4*p**2 - 2*p**g + 2*p**4 - 3*p**2 + 10*p - 5*p**2.
2*(p - 1)**3*(p + 2)
Let i be (3 - -6)*11*(-3 + 2). Let z be 4*(-1)/10*(i - 1). Solve -4*b**3 + z*b**4 - b**3 - 36*b**4 - 7*b**3 + 8*b**2 = 0.
0, 1, 2
Let y = -4494 + 4523. Let p(k) be the second derivative of 1/4*k**4 + 0*k**2 + 0 - 3/10*k**5 + y*k + 1/2*k**3. Factor p(d).
-3*d*(d - 1)*(2*d + 1)
Suppose u - 187 = -5*m + 186, 3*m = 4*u - 1492. Factor 12*q**4 + 12 + u*q**3 - 23*q**2 + 127*q**2 - 437*q**3 - 64*q.
4*(q - 3)*(q - 1)**2*(3*q - 1)
Let j(b) be the first derivative of -2*b**5/45 + 11*b**4/9 - 70*b**3/9 + 5792. Determine i so that j(i) = 0.
0, 7, 15
Let d(t) be the third derivative of -t**6/30 - 128*t**5/15 + 391*t**4/6 - 524*t**3/3 + 2*t**2 - 14*t - 1. Factor d(k).
-4*(k - 2)*(k - 1)*(k + 131)
Let o(x) be the second derivative of 193*x - 3/100*x**5 + 0 - 1/10*x**4 + 0*x**2 - 1/10*x**3. What is t in o(t) = 0?
-1, 0
Let b = -12 + 27. Suppose -b = 7*k - 36. Suppose 5*a**2 + 12*a - 5*a**4 - 9*a - k*a = 0. What is a?
-1, 0, 1
Suppose 2*w + w = -4*a + 176, -2*a = 3*w - 88. Find q such that -4 - 24*q**2 - 97*q**2 - 25*q**2 + 6*q**3 + a*q + 79 + 21 = 0.
-2/3, 1, 24
Let t(l) be the first derivative of l**7/168 + l**6/24 + 40*l**3/3 + 47. Let q(a) be the third derivative of t(a). What is x in q(x) = 0?
-3, 0
Suppose 968/3 - 2*q**2 + 1448/3*q = 0. Calculate q.
-2/3, 242
Let a(u) be the second derivative of u**7/420 + 11*u**6/45 - 133*u**3/6 - 181*u. Let g(z) be the second derivative of a(z). Suppose g(h) = 0. Calculate h.
-44, 0
Let d(a) = -2*a**2 + 16*a - 31. Let q be d(5). Let o(v) = 4*v + 1. Let s(z) = -3*z**2 + 22*z + 28. Let t(y) = q*s(y) + 4*o(y). Factor t(h).
3*(h - 4)*(h + 2)
Suppose -d - 10*t + 7*t + 2 = 0, -5*t = 5*d - 10. Let o = -611/6 - -102. Factor k**d + 2/3 - 3/2*k - o*k**3.
-(k - 4)*(k - 1)**2/6
Suppose 5*j + 21 = 31. Factor -4*o**3 + 23*o**2 - 80*o**j + 4*o**4 + 24*o**2 + 29*o**2 + 4*o.
4*o*(o - 1)**2*(o + 1)
Let g be 62/217*35/4. Let t(s) be the first derivative of 3/2*s - 3*s**2 - 3/4*s**4 + g*s**3 - 19. Factor t(b).
-3*(b - 1)**2*(2*b - 1)/2
Suppose 3*k + 17 = -2*s, s + 13 + 6 = -5*k. Let g be (-8)/s*-1 - -560. Let -2*x**4 - 72*x**3 - 8*x**2 - g*x**5 - 208*x**4 + 358*x**5 = 0. Calculate x.
-2/5, -1/4, 0
Let c be 2730/(25 + -12)*4/(-3). Let f be ((-4)/(-21))/((-240)/c). Factor 0 - 4/9*n**4 - 2/9*n**3 + 0*n + f*n**2.
-2*n**2*(n + 1)*(2*n - 1)/9
Let l = -245029 - -2205385/9. Find m such that -16/9 + l*m**2 - 86/9*m**3 + 2*m**4 - 40/9*m = 0.
-2/9, 1, 2
Suppose 0 = 4*t + 2*o - 30, 4*o - 10 = 2*o. Let -110*g**t + 122*g**5 - 92*g**5 - 18*g**4 + 35*g**3 + 5*g**2 + 58*g**4 = 0. What is g?
-1/4, 0, 1
Let n(b) = -9*b - 205. Let y be n(-23). Let -10*s**2 + 6*s**2 - 21 - 22*s + 5*s**2 + y*s**2 - 4*s**2 = 0. What is s?
-21, -1
Let w(u) = -2*u**3 + 13*u**2 - 7*u + 9. Let p be w(6). Suppose 7*c**4 + 4*c - 3*c**2 - 4*c**4 + 2*c - 6*c**p = 0. What is c?
-1, 0, 1, 2
Let s(j) be the first derivative of -549*j**5/5 + 339*j**4/2 + 268*j**3 + 36*j**2 - 2336. Let s(p) = 0. What is p?
-2/3, -6/61, 0, 2
Determine v so that 368/7*v**3 + 3222/7 - 2/7*v**4 - 1796/7*v**2 + 1056/7*v = 0.
-1, 3, 179
Factor -66*u**2 + 66 + 7/4*u**3 - 7/4*u.
(u - 1)*(u + 1)*(7*u - 264)/4
Let m be (527459/(-2130))/391 + (1 + 1)*(-25)/(-60). Find x such that -1/5*x + m*x**2 + 0 = 0.
0, 1
Let n = -57 + 63. Suppose -9*h = -n*h - 6. Factor 75*v**4 + 690*v**3 + 71*v**h + 17*v**2 - v**2 + 75 - 420*v + 33.
3*(v + 1)*(v + 9)*(5*v - 2)**2
Let o(z) be the first derivative of 4*z**5/5 - 1128*z**4 + 4504*z**3 - 6752*z**2 + 4500*z + 8021. Suppose o(u) = 0. What is u?
1, 1125
Suppose -k + 0*k = 5. Let n be k/(-315)*(6 - 0)*6. Find l such that 1/7*l**2 - 4/7*l + n = 0.
2
Suppose -4*l - 771 = 3*w + 719, 5*l - w = -1853. Let m be 159/l - (24/(-7) + 1). Let 5*g - 2*g**2 + 9*g**2 - 10*g**m - 2*g**2 = 0. Calculate g.
0, 1
Let f(r) be the first derivative of r**6/120 + r**5/20 - 3*r**4/8 + 46*r**3/3 - 35. Let q(w) be the third derivative of f(w). Suppose q(d) = 0. Calculate d.
-3, 1
Suppose 17*t + 1 = -305. Let j be 4/t + 750/2160. What is v in -1/8*v**4 + 0 + 1/8*v**2 + 1/8*v - j*v**3 = 0?
-1, 0, 1
Find l such that -548/7*l - 552/7 + 4/7*l**2 = 0.
-1, 138
Let a(u) be the first derivative of 2/45*u**3 + 3 + 0*u**2 - 2/15*u. Factor a(f).
2*(f - 1)*(f + 1)/15
Let u(s) be the second derivative of 1/6*s**4 + 169*s**2 + 43 - s + 26/3*s**3. Factor u(o).
2*(o + 13)**2
Suppose -117 = -146*g - 93*g + 361. Solve -2/5*w**5 + 4/5 - 4/5*w**g + 0*w**4 + 8/5*w**3 - 6/5*w = 0.
-2, -1, 1
Let x(a) be the second derivative of a**6/30 - 1417*a**5/20 + 41890*a**4 - 83544*a**3 + 16*a + 384. Factor x(u).
u*(u - 708)**2*(u - 1)
Let j(s) be the first derivative of s**6/10 + 36*s**5/5 + 177*s**4/20 - 940. Factor j(m).
3*m**3*(m + 1)*(m + 59)/5
Let q = -8/861 + 37613/1722. Let x = q + -37/2. Solve -5/3*c**2 - 5*c - x = 0 for c.
-2, -1
Let z(o) be the first derivative of -3*o**4/16 + 35*o**3/4 - 84*o**2 - 195*o - 378. Suppose z(s) = 0. What is s?
-1, 10, 26
Let u = 38 - 89. Let k = u - -79. Factor k*i**3 + 120*i**2 + 197*i - 21*i**5 - 178*i**3 + 6 + 90*i**4 - 242*i.
-3*(i - 1)**4*(7*i - 2)
Let t(g) be the second derivative of -g**7/105 + g**6/5 + 37*g**5/50 - 43*g**4/30 - 44*g**3/5 - 68*g**2/5 + 6195*g. Solve t(v) = 0.
-2, -1, 2, 17
Let d(p) = 7*p**3 + 30*p**2 + 331*p + 288. Let a(r) = 27*r**3 + 124*r**2 + 1325*r + 1152. Let s(l) = 5*a(l) - 19*d(l). Determine x so that s(x) = 0.
-12, -1
Let s be 315/45 + 74/(-2). Let d be (-75)/s*9/(-20)*-1. Suppose -9/8*y**2 - 3/8*y**3 + 0 + 3/4*y + d*y**4 - 3/8*y**5 = 0. Calculate y.
-1, 0, 1, 2
Solve 26/3*i**2 - 75*i + 216 - 1/3*i**3 = 0.
8, 9
Let u(o) = 2*o**2 - o. Let c be u(-2). Suppose 0 = -3*d - 15*d + 3*d + 30. Factor -c + 2 + 32*q + 7*q**d + 31*q**2 + 10*q**3.
2*(q + 2)**2*(5*q - 1)
Let b be (-4 + (-150)/(-35) + (-109)/14)/((-12033)/4584). Let m be ((-16)/(-42))/(2/3). Factor 24/7*t - m*t**2 - b.
-4*(t - 5)*(t - 1)/7
Let r(p) = 11*p + 79. Let v be r(-7). Determine n, given that -v*n**3 - n**3 - 447 - 2625 - 2667*n - 213*n + 189*n**2 = 0.
-1, 32
Let b(w) be the third derivative of 2*w**5/5 - 25*w**4/6 + 8*w**3/3 - 3*w**2 + 51*w. Find a such that b(a) = 0.
1/6, 4
Let c(o) = 3*o**2 + 2*o + 8*o**3 + 4 - 7*o**3 - 12*o - 2*o**3. Let f(w) = -7 + w**2 + 7 - 3*w + 4*w. Let x(b) = -2*c(b) - 4*f(b). Let x(n) = 0. Calculate n.
1, 2
Let c(o) be the third derivative of o**7/525 - 16*o**6/25 - 129*o**5/50 - 97*o**4/30 + 16228*o**2. Let c(d) = 0. What is d?
-1, 0, 194
Suppose 2*q**5 - 1 - 47/6*q**4 + 77/6*q**2 + 5/6*q + 7/6*q**3 = 0. What is q