1)
Let z = 41 + -34. Suppose z*n = -0*n + 105. Solve 54 + 3*j**5 - 6*j**2 + 53 - 12*j**4 - 107 + n*j**3 = 0 for j.
0, 1, 2
Find k such that 37*k**2 + 4387 - 95*k**2 - 4*k**3 - 106*k**2 + 6193 - 1196*k = 0.
-23, 5
Suppose -4*k = -w - 1255, -942 = -3*k - 0*k + w. Solve k - q - q**3 + 5*q**2 - 3*q - 313 = 0 for q.
0, 1, 4
Let i(j) be the third derivative of -j**5/12 + 2185*j**4/6 - 1909690*j**3/3 - 13*j**2 - 48. Let i(a) = 0. What is a?
874
Let m(o) be the second derivative of o**7/84 + o**6/60 - 11*o**5/40 - 29*o**4/24 - 13*o**3/6 - 2*o**2 - 1258*o. Factor m(g).
(g - 4)*(g + 1)**3*(g + 2)/2
Let n be 8/16*(-5856)/54. Let p = -54 - n. Solve -1/9*h**2 - 1/9 + p*h = 0 for h.
1
Let o be ((-16)/(-60)*18)/(4/10). Suppose -45*j = -47*j + o. Find p, given that 218*p**2 + j*p + 50*p - 214*p**2 = 0.
-14, 0
Let o be (16/20)/((3 - -1)/20). Suppose -o = 4*c, 5*m - 2*c + 0*c - 17 = 0. Factor -4*h**3 + 2*h**3 - 4*h**2 + 3*h**m + h**3.
2*h**2*(h - 2)
Let k(t) = -t**3 + 11*t**2 - 28*t + 2. Let u be k(7). Factor 25*r - 5*r**3 - 3 - 5 - 3 - 4 - 5*r**u.
-5*(r - 1)**2*(r + 3)
Let m be (100/(-105))/((-1530)/1785). Let -2/3*i**4 - 2/9*i**2 + 0 - m*i**3 + 2/9*i = 0. Calculate i.
-1, 0, 1/3
Let s(l) be the first derivative of 4*l**3 + 0*l**2 - 4/5*l**5 + 0*l - 2*l**4 + 40. Factor s(t).
-4*t**2*(t - 1)*(t + 3)
Suppose 2*c - 3*a = -5, -6*a + a + 17 = c. Factor 6*r**4 - 8*r**c - 209*r + 209*r - 2*r**3.
2*r**2*(r + 1)*(3*r - 4)
Let r(g) be the second derivative of g**4/8 + 43*g**3/4 + 3722*g + 2. Determine v so that r(v) = 0.
-43, 0
Let z = -566705 + 1703959/3. Factor 1/3*u**2 + 124/3*u + z.
(u + 62)**2/3
Let m(a) be the first derivative of -2/45*a**5 - 10/9*a**3 - 8/9*a - 6 + 7/18*a**4 + 13/9*a**2. Let m(w) = 0. What is w?
1, 4
Let z = 758048/5 - 151592. Factor 968/5 + 2/5*u**2 - z*u.
2*(u - 22)**2/5
Let l(r) be the first derivative of 2*r**5/5 - 15*r**4/2 - 32*r**3/3 - 2888. Factor l(w).
2*w**2*(w - 16)*(w + 1)
Let v(b) = b**3 - 85*b**2 + 46*b**2 + 45*b**2 + 75 + 3*b. Let t be v(-7). Let 2/23*i**3 + 0 + 0*i + 2/23*i**4 - 2/23*i**t - 2/23*i**2 = 0. Calculate i.
-1, 0, 1
Suppose 5/3*k**4 + 50/3*k + 20*k**2 + 10*k**3 + 5 = 0. What is k?
-3, -1
Let b be 0/(-3) + 6/(0 + 3). Solve 728*i**2 + 243*i + 81 - 75*i**3 + 756*i**b - 1349*i**2 = 0.
-3/5, 3
What is w in 8952*w - 2270 + 536*w**2 - 539*w**2 + 11225 = 0?
-1, 2985
Find z such that -12/7*z + 38/7*z**2 + 38/7*z**3 + 8/7*z**4 + 0 = 0.
-3, -2, 0, 1/4
Let t(c) be the second derivative of c**4/15 - 34*c**3/15 + 24*c**2 + 69*c - 15. Factor t(a).
4*(a - 12)*(a - 5)/5
Let g be (-4)/38 + (-13458)/(-57). Factor -g*w + 2*w**2 + 0*w**2 - 92 + 146*w.
2*(w - 46)*(w + 1)
Factor -120*s**4 + 3*s**5 + 2*s**5 + 20*s**2 - 150*s**2 + 20*s**3 - 275*s**3.
5*s**2*(s - 26)*(s + 1)**2
Let 0 + 0*s + 0*s**2 - 245/2*s**3 - 5/2*s**4 = 0. Calculate s.
-49, 0
Let w = 53992 + -917624/17. Factor 46/17*p**2 + 2/17*p**3 + w*p - 288/17.
2*(p - 1)*(p + 12)**2/17
Factor 36 - 20 - 55 - 49 - 2*q**2 + 90*q.
-2*(q - 44)*(q - 1)
Suppose -4*m + 5*r = -0*m - 22, -4*m + 2 = 5*r. Suppose 2*o + 3*b + 1 = m*o, 5*o = -4*b + 43. Factor -8*i**2 + 20*i - 24 + o*i**2 - 3*i**2.
-4*(i - 3)*(i - 2)
Let x(w) be the second derivative of -3*w**5/40 + 35*w**4/8 - 31*w**3 + w + 3444. Determine v, given that x(v) = 0.
0, 4, 31
Let c(t) be the third derivative of t**9/1512 - t**8/420 + t**6/90 - t**5/60 + 11*t**3/3 - 21*t**2 + 2. Let f(z) be the first derivative of c(z). Factor f(k).
2*k*(k - 1)**3*(k + 1)
Let j(l) = 3*l**2 + 3*l + 2. Let o = -53 + 55. Suppose -3*n - 4*i = 3, -4*n + 4*i = -o*n + 2. Let p(b) = -b**2. Let t(q) = n*j(q) - 2*p(q). Solve t(w) = 0.
-2, -1
Let v = 7539 - 7532. Let z(r) be the second derivative of -3/10*r**5 + 0*r**2 - 16*r + 4/3*r**3 + 2/3*r**4 - 2/15*r**6 + 1/21*r**v + 0. Factor z(y).
2*y*(y - 2)**2*(y + 1)**2
Let k(d) be the first derivative of -d**6/105 + d**5/105 + d**4/126 - 46*d + 38. Let m(j) be the first derivative of k(j). Factor m(s).
-2*s**2*(s - 1)*(3*s + 1)/21
Let k(m) be the first derivative of -1/9*m**3 - 4/3*m**2 + 3*m + 75. Let k(p) = 0. Calculate p.
-9, 1
Let x(n) = -n**2 - 7*n - 10. Let s be x(-4). Factor -64 + 4*m**3 - 22*m**3 + s*m**4 + 863*m**2 - 819*m**2.
2*(m - 4)**2*(m - 2)*(m + 1)
Suppose 0 = -v - 120 + 125. Let n(z) = -4*z**5 - 11*z**4 - 3*z**3 + 5*z**2 + 5*z. Let o(s) = s**4 - s. Let a(c) = v*n(c) + 10*o(c). Factor a(k).
-5*k*(k + 1)**3*(4*k - 3)
Let x(n) = -21*n**2 - 14*n + 387. Let k(u) = 235*u**2 + 145*u - 4260. Let y(h) = 4*k(h) + 45*x(h). Solve y(g) = 0 for g.
-15, 5
Let r(q) be the third derivative of -q**7/168 + q**6/18 - q**5/6 + 197*q**3/6 + 31*q**2. Let b(u) be the first derivative of r(u). Let b(y) = 0. Calculate y.
0, 2
Let n be (120/(-2520))/(16/(-28)). Let p(x) be the third derivative of 0*x + 0 - 3*x**2 + 15/8*x**4 - n*x**5 - 20/3*x**3. Factor p(r).
-5*(r - 8)*(r - 1)
Suppose 2955*o**2 + 257*o**3 - 255*o**3 + 90*o - 108 - 2979*o**2 = 0. What is o?
3, 6
Let t(i) be the third derivative of 2*i**2 + 0*i + 49 - 3/4*i**4 - 1/20*i**5 + 0*i**3. Determine v, given that t(v) = 0.
-6, 0
Let r(x) be the third derivative of -x**7/70 + 99*x**6/20 + 399*x**5/20 + 25*x**4 - 1226*x**2. Suppose r(n) = 0. Calculate n.
-1, 0, 200
Let y be (3 - 4/((-32)/(-42)))*-4. Let x(f) = 17*f**2 + 56*f + 89. Let p(k) = -8*k**2 - 28*k - 45. Let o(u) = y*p(u) + 4*x(u). Determine v so that o(v) = 0.
-7/2
Let y(q) be the first derivative of q**6/12 - 59*q**5/5 + 113*q**4/8 + 236*q**3/3 - 117*q**2 + 4551. Suppose y(n) = 0. What is n?
-2, 0, 1, 2, 117
Suppose 24*v = 25*v - 17. Let -v*h**2 - 5*h**4 - 6 + 23*h**2 + 17*h**2 + 7*h - 2*h + 7*h**3 = 0. What is h?
-1, 2/5, 3
Let u(t) = t**4 - t**2 + t. Let p = 195 - 198. Let q(o) = -2*o**4 + 3*o**3 + 6*o**2 - 2*o. Let h(f) = p*u(f) - q(f). Let h(g) = 0. Calculate g.
-1, 0
Let t(o) be the first derivative of o**5/10 + 2*o**4 + 7*o**3 + 10*o**2 + 31*o + 30. Let u(q) be the first derivative of t(q). Find r such that u(r) = 0.
-10, -1
Suppose 5*m - 52 = -4*t, -17 = -m + 2*t - 5*t. Suppose m*j**2 + 49 + 25*j + 10*j + j**3 + 7*j**2 + 28*j = 0. Calculate j.
-7, -1
Suppose 1 = 4*v - 7. Let f be (87/(-12))/(v/(-8)). Suppose 4*s**4 - 8 + f - 12*s**2 + 4*s**3 - 13 - 4*s = 0. Calculate s.
-2, -1, 1
Let t(u) = -5*u**4 + 94*u**3 + 306*u**2 - 9*u + 3. Let z(a) = -9*a**4 + 188*a**3 + 610*a**2 - 15*a + 5. Let d(y) = 5*t(y) - 3*z(y). Factor d(l).
2*l**2*(l - 50)*(l + 3)
Let o(c) = 205*c**2 + 3630*c - 41825. Let l(j) = 131*j**2 + 2310*j - 26616. Let s(h) = -25*l(h) + 16*o(h). Suppose s(r) = 0. What is r?
-76, 10
Let l(g) be the third derivative of -2 - 3/4*g**4 - 1/20*g**5 + 121*g**2 + 0*g - 5/2*g**3. Factor l(b).
-3*(b + 1)*(b + 5)
Solve -m**4 + 35*m**2 + 60*m**3 + 5*m**5 - 419*m + 1259*m - 345*m**3 + 540 - 14*m**4 = 0.
-6, -1, 2, 9
Let f(n) be the third derivative of -n**5/120 + 181*n**4/24 - 32761*n**3/12 - 507*n**2. Factor f(m).
-(m - 181)**2/2
Let z(d) be the third derivative of -d**5/60 - d**4/3 + 11*d**3/2 + 12*d**2 - 4. Determine r, given that z(r) = 0.
-11, 3
Let k(n) be the first derivative of -n**5/40 + 7*n**4/8 + 51*n**3/4 + 113*n**2 - 144. Let w(x) be the second derivative of k(x). Factor w(g).
-3*(g - 17)*(g + 3)/2
Let g(h) be the third derivative of h**8/112 - 797*h**7/35 + 845881*h**6/40 - 7443611*h**5 - 37536058*h**4 - 75284384*h**3 + 5*h**2 - 509*h. Factor g(b).
3*(b - 532)**3*(b + 1)**2
Let k(f) be the first derivative of 0*f**2 - 1/3*f**3 + 3 - 1/6*f**4 - 26*f. Let d(h) be the first derivative of k(h). Suppose d(o) = 0. What is o?
-1, 0
Suppose 4*w + 56 = 84. Find z such that 7 - 325*z**2 - 36*z - w + 34*z = 0.
-2/325, 0
Suppose 0 = -596*f + 298*f + 322*f - 72. Suppose 2*w**2 - 78/11*w - 2/11*w**f + 90/11 = 0. Calculate w.
3, 5
Suppose -498*h + 1402 + 590 = 0. Let i = 5569/8 - 695. What is d in -3/4*d**3 - d + i*d**h + 0 - 5/2*d**2 = 0?
-2/3, 0, 2
Let h(o) be the first derivative of -o**4/36 + 56*o**3/9 - 1568*o**2/3 - 157*o - 19. Let a(u) be the first derivative of h(u). Factor a(p).
-(p - 56)**2/3
Factor -14*g**4 - 504*g**2 + 12*g**4 + 3478*g**3 - 3382*g**3.
-2*g**2*(g - 42)*(g - 6)
Let s(r) be the second derivative of r**6/90 + 125*r**5/6 + 129791*r**4/12 - 391250*r**3/9 + 195938*r**2/3 + 149*r - 9. What is q in s(q) = 0?
-626, 1
Suppose -129*v = -126*v - 45. Let s(x) = x**3 - x**2 - x + 2. Let w(r) = 4*r**