3)
Suppose -14*y**2 - 4*y - 12*y**2 + 30*y**2 = 0. Calculate y.
0, 1
Let t(y) be the third derivative of 0 + 0*y**3 + 2/45*y**5 + 1/180*y**6 - 11*y**2 - 1/315*y**7 - 1/9*y**4 + 0*y. Let t(a) = 0. What is a?
-2, 0, 1, 2
Factor 480 - 320*r - 5*r**4 + 61*r**3 - 44*r**3 + 18*r**3 - 10*r**2.
-5*(r - 4)**2*(r - 2)*(r + 3)
Let t(s) be the first derivative of s**6/45 - s**5/15 + s**4/18 + 9*s - 2. Let y(h) be the first derivative of t(h). Factor y(m).
2*m**2*(m - 1)**2/3
Let f(c) be the first derivative of -c**6/2520 + c**5/168 - c**4/28 - 16*c**3/3 + c**2/2 - 50. Let y(t) be the third derivative of f(t). Factor y(p).
-(p - 3)*(p - 2)/7
Let p = -5854 - -17564/3. Suppose -8/9*d**4 - 10/9*d**3 + 38/9*d**2 - p - 14/9*d = 0. What is d?
-3, -1/4, 1
Suppose -9/2*z**3 - 3/2*z**5 - 15/2*z**2 + 15/2*z**4 + 6*z + 0 = 0. What is z?
-1, 0, 1, 4
Suppose 5*k + 8 = 9*k. Find z, given that -112*z + 112*z + 9*z**3 + k*z**2 - 11*z**4 = 0.
-2/11, 0, 1
Let n be 6/(-21) + 66/84. Let p(h) be the first derivative of 3/8*h**2 - 6 - 1/12*h**3 - n*h. Factor p(s).
-(s - 2)*(s - 1)/4
Let v(g) = 8*g**3 - 8*g**2 + 5*g - 3. Let y be v(1). Factor 3*j - 9/2*j**y + 0 + 3/2*j**4 + 0*j**3.
3*j*(j - 1)**2*(j + 2)/2
Factor -2*n - 3*n + 80*n**3 - 5*n**2 - 75*n**3 + 5*n**4.
5*n*(n - 1)*(n + 1)**2
Let f(t) = -4*t**2 + 25*t - 118. Suppose 6*j + i - 16 = 10*j, -2*i + 23 = -5*j. Let n(r) = -7*r**2 + 49*r - 237. Let g(p) = j*n(p) + 5*f(p). Factor g(m).
(m - 11)**2
Let t = 52 - 49. Factor -10*q - 22*q**2 + 4*q**2 + t*q**2.
-5*q*(3*q + 2)
Find i such that 0 - 23/7*i**2 + 22/7*i + 1/7*i**3 = 0.
0, 1, 22
Suppose -2*k = y - 5, 0*y = k + 14*y + 38. Factor 0*d + 0 + 2/11*d**k + 0*d**3 + 0*d**2.
2*d**4/11
Let c be 10/(-3)*(-168)/35. Factor c*o**2 + 184 - 32*o - 84 - 48*o.
4*(2*o - 5)**2
Let y(q) be the third derivative of -2*q**7/525 + q**6/75 + 19*q**5/75 + 14*q**4/15 + 8*q**3/5 - q**2 + 8. Determine d so that y(d) = 0.
-2, -1, 6
Let x(g) = 45*g**2 - 170*g - 775. Let m(y) = 5*y**2 - 19*y - 86. Let v(s) = -35*m(s) + 4*x(s). Factor v(n).
5*(n - 6)*(n + 3)
Let o(f) be the first derivative of -3/25*f**5 - 3/20*f**4 + 3/10*f**2 + 1/5*f**3 + 42 + 0*f. Find v such that o(v) = 0.
-1, 0, 1
Suppose -12/11*p**2 + 2/11*p**4 + 1/11*p**3 + 0 + 9/11*p = 0. Calculate p.
-3, 0, 1, 3/2
Suppose 0 = -6*k - 783*k - 176*k + 3860. Factor 2/5*z + 0 - 8/5*z**2 - 8/5*z**k + 12/5*z**3 + 2/5*z**5.
2*z*(z - 1)**4/5
Suppose 3*j - 4*j = 30. Let z be (-80)/j - (-2)/6. Suppose 3*r**4 - 3*r**3 + 4*r**5 - 2*r**5 - z*r**2 - 3*r**5 + 4*r**5 = 0. What is r?
-1, 0, 1
Suppose -28*x = -24*x - 16. Suppose -p + x*l = -4*p - 6, -5*l = -5*p + 25. Let -2/5*y**3 - 2/5 - 6/5*y - 6/5*y**p = 0. What is y?
-1
Let n = -12 + 12. Suppose n = -4*p + 2*p. What is c in p*c**3 - 2*c**2 - 2*c + 2*c**3 - c - c = 0?
-1, 0, 2
Suppose -6*k - 22 = -17*k. Factor 27/4*b**3 + 0 - 21/4*b**k - 3/2*b.
3*b*(b - 1)*(9*b + 2)/4
Let v be (-6)/8 + (-1)/4 - (-8910)/6237. Suppose v*o**2 + 18/7 - 15/7*o = 0. What is o?
2, 3
Suppose -57 = 62*x - 81*x. Let y(v) be the second derivative of -10*v - 1/15*v**6 + 1/5*v**5 + 0 - 2/3*v**x + v**2 + 0*v**4. Factor y(h).
-2*(h - 1)**3*(h + 1)
Let w(t) be the third derivative of t**8/1512 - 8*t**7/945 + 23*t**6/540 - 14*t**5/135 + t**4/9 - 114*t**2 - 2*t. Determine c, given that w(c) = 0.
0, 1, 2, 3
Let g(r) be the third derivative of -r**8/504 - r**7/35 - r**6/6 - 22*r**5/45 - 2*r**4/3 + 77*r**2 - 2. Factor g(w).
-2*w*(w + 2)**3*(w + 3)/3
Let w(h) be the third derivative of h**6/360 - 2*h**5/45 - 25*h**4/24 - 7*h**3 + 4*h**2 + 3*h. Determine k, given that w(k) = 0.
-3, 14
Let s be (-29)/84 - (-12)/36. Let k = s - -19/28. Factor 0 + 4/3*y**3 + k*y - 16/9*y**2 + 0*y**4 - 2/9*y**5.
-2*y*(y - 1)**3*(y + 3)/9
Let o be 1*6/33 + 60/33. What is p in -39 + 19 + 23 + o*p - p**2 = 0?
-1, 3
Factor -27/4*u**3 + 3/4*u**4 - 27/2 - 9/4*u**2 + 87/4*u.
3*(u - 9)*(u - 1)**2*(u + 2)/4
Let h(x) be the second derivative of -x**6/165 + 4*x**5/55 + 21*x**4/11 + 144*x**3/11 + 459*x**2/11 + 287*x. Suppose h(n) = 0. What is n?
-3, 17
Let u(q) be the second derivative of q**7/21 - q**6/5 - 3*q**5/5 + 5*q**4/3 + 7*q**3 + 9*q**2 - 14*q + 1. Solve u(v) = 0.
-1, 3
Let b(p) = 9*p**5 + 2*p**4 - 13*p**3 - 6*p**2 + 12. Let l(a) = -a**3 - a**2 + 3. Let c(w) = b(w) - 4*l(w). Find s, given that c(s) = 0.
-1, -2/9, 0, 1
Let o(r) be the second derivative of -1/6*r**3 + 0 + 1/60*r**5 - 7*r + 0*r**4 + 9/2*r**2. Let x(k) be the first derivative of o(k). Factor x(b).
(b - 1)*(b + 1)
Let x be -1 - ((-27)/(-72))/(4/(-12)). Let k(h) be the first derivative of -1/24*h**3 - 1/8*h**2 - x*h + 5. Solve k(y) = 0 for y.
-1
Let i(v) = -4*v**3 + 28*v**2 - 56*v + 26. Let q(t) = t**3 + t**2 + t. Let c(a) = i(a) + 2*q(a). Determine k so that c(k) = 0.
1, 13
Let m(h) be the second derivative of 5*h + 0*h**2 - 1/147*h**7 + 1/70*h**5 + 0 + 1/105*h**6 - 1/42*h**4 + 0*h**3. Determine k, given that m(k) = 0.
-1, 0, 1
Let o(m) be the second derivative of m**6/24 - m**5/24 + 3*m**3 - 5*m. Let j(z) be the second derivative of o(z). Factor j(f).
5*f*(3*f - 1)
Let h(d) = d**3 + d**2 + d - 1. Let s(u) = -3*u**3 - 7*u**2 - 14*u + 2. Let b be -4 - (-3 - (5 - 3)). Let t(c) = b*s(c) + 6*h(c). Factor t(z).
(z - 2)*(z + 1)*(3*z + 2)
Let p(t) be the first derivative of 5*t**3/3 - 285*t**2 + 16245*t - 272. Let p(j) = 0. What is j?
57
Let g be 2*(-3)/(-6) - 46/13 - -3. Factor -4/13 - g*n - 2/13*n**2.
-2*(n + 1)*(n + 2)/13
Let p(u) be the first derivative of -2*u**5/45 + 2*u**4/9 + 22*u**3/9 - 4*u**2/9 - 64*u/9 + 256. Solve p(w) = 0 for w.
-4, -1, 1, 8
Let i be -14 + 132*1/9. Factor -2/3*d**4 - 4/9*d**3 - 2/9*d**5 + 2/9 + 4/9*d**2 + i*d.
-2*(d - 1)*(d + 1)**4/9
Let a = 9 + 1. Let y be 18/a + (-2)/(-10). Solve 0*r**2 - y*r - r - 6*r**2 + 7*r**2 = 0 for r.
0, 3
Suppose 0 = 4*a + 12, 0*a + 3*a - 366 = -5*d. Suppose -3*x + 565 - d = f, 4*x + 3*f - 660 = 0. Factor 72*g - 4 - x*g**2 - 5 + 1.
-2*(9*g - 2)**2
Let x = -7900/11 + 719. Let t = x + -30/77. Factor 72/7*h + 48/7 + t*h**3 + 27/7*h**2.
3*(h + 1)*(h + 4)**2/7
Let u = 61 - 18. Let a = 47 - u. What is c in -9/2*c**a + 0*c - c**3 + 0 + 0*c**2 - 2*c**5 = 0?
-2, -1/4, 0
Suppose 2*w - 92 = -2*d, 4*d = 4*w - 59 - 149. Let b = -49 + w. Factor 2/11 + 2/11*n**4 + b*n - 4/11*n**2 + 0*n**3.
2*(n - 1)**2*(n + 1)**2/11
Let i(h) be the third derivative of -h**7/525 - h**6/300 + h**5/30 - h**4/20 - 21*h**2 + 3*h. Suppose i(v) = 0. What is v?
-3, 0, 1
Factor -40/11*h**2 - 36/11 - 74/11*h - 2/11*h**3.
-2*(h + 1)**2*(h + 18)/11
Suppose 2*p - 55 = -37. Let f be -3 + (-2 - 1) + (p - 3). Factor 1/2*y - 1/2*y**5 - y**4 + y**2 + 0 + f*y**3.
-y*(y - 1)*(y + 1)**3/2
Let h(k) be the first derivative of k**3/6 - 3*k**2/4 - 58. Find q such that h(q) = 0.
0, 3
Let h(g) = 3*g - 19. Let x be h(8). Let q(i) = -2*i**2 + 10*i - 14. Let r(p) = -p**2 + 9*p - 13. Let u(k) = x*q(k) - 6*r(k). Determine a, given that u(a) = 0.
-2, 1
Let w(j) be the first derivative of 55 + 3*j**2 + 3/4*j**4 + 0*j + 3*j**3. Factor w(l).
3*l*(l + 1)*(l + 2)
Let s(r) = r**3 - 9*r**2 - 6. Let q be s(9). Let v be q/(-10) + (-9)/45. Suppose 0 - 2/5*w**3 + 2/5*w**2 + 2/5*w - v*w**4 = 0. What is w?
-1, 0, 1
Let b = 50 + -47. Let g be 4 - (7 + 1)*b/12. Factor 1/2*w**3 - 2 + 4*w - 5/2*w**g.
(w - 2)**2*(w - 1)/2
Let b(u) be the first derivative of -5*u**3 - 15 - 5/4*u**4 - 5*u - 15/2*u**2. What is x in b(x) = 0?
-1
Let w(h) be the first derivative of -32/5*h**3 + 1/2*h**6 - 66/25*h**5 + 57/10*h**4 + 39/10*h**2 - 6/5*h - 5. Determine l, given that w(l) = 0.
2/5, 1
Let p(q) be the third derivative of 0*q + 25*q**2 - 1/15*q**3 + 1 - 1/150*q**5 + 1/30*q**4. Suppose p(s) = 0. What is s?
1
Suppose -35*k - 8 = -37*k. Let f(x) be the third derivative of -3*x**2 - 1/30*x**5 - 1/6*x**k + 0 + 0*x + x**3. Factor f(c).
-2*(c - 1)*(c + 3)
Let q be 138/63 + (-10)/(-70). Solve -1/3*i**2 + 0 + q*i**5 + 5*i**3 - 2/3*i - 19/3*i**4 = 0.
-2/7, 0, 1
Let d(p) be the first derivative of -5/4*p**4 - 5/3*p**3 + 5*p + 5/2*p**2 - 18. Factor d(m).
-5*(m - 1)*(m + 1)**2
Let m(k) be the third derivative of k**5/20 + 15*k**4/8 + 27*k**3 + 2*k**2 + 80*k. Let m(y) = 0. Calculate y.
-9, -6
Let i = 19/2370 - -2/79. Let y(j) be the third derivative of 0 + 0*j - 3*j**2 + 1/3*j**3 + 1/6*j**4 + i*j**5. Find b, given that y(b) = 0.
-1
Let s(h) be the third derivative of -h*