**2 + 8*y**k + 0.
y*(y + 1)**2*(4*y + 1)**2/2
Let l be ((-24)/(-42))/(80/168). Determine o, given that -9/5*o**2 + 9/5*o**4 + 0 - l*o + 6/5*o**3 = 0.
-1, -2/3, 0, 1
Let y(f) be the first derivative of -f**6/264 - f**5/55 - f**4/66 + 13*f**2/2 - 7. Let q(j) be the second derivative of y(j). Factor q(k).
-k*(k + 2)*(5*k + 2)/11
Find c, given that -67*c**3 + 55*c + 32*c**3 + 90 - 40*c**2 + 30*c**3 = 0.
-9, -1, 2
Let o(n) = -n**5 - n**3 + 2*n**2 - n - 1. Let w(g) = 8*g**5 + 2*g**4 + 5*g**3 - 18*g**2 + 8*g + 9. Let v(q) = 14*o(q) + 2*w(q). Suppose v(s) = 0. What is s?
-2, -1, 1
Let o(t) = 4*t + 8. Let s be o(-1). Suppose 110 = s*u + 110. Factor -1/3*d**4 + 0*d**3 + u + 2/3*d + d**2.
-d*(d - 2)*(d + 1)**2/3
Let w(f) be the third derivative of -f**5/15 - 19*f**4/6 - 12*f**3 + f**2 - 6. Factor w(s).
-4*(s + 1)*(s + 18)
Let j(m) be the second derivative of m**7/56 + 7*m**6/30 + 13*m**5/20 + 3*m**4/8 - 23*m**3/24 - 7*m**2/4 - 15*m + 3. Determine t so that j(t) = 0.
-7, -1, 2/3
Let u = 66/865 + 30077/2595. Determine y so that -u*y + 170/3*y**3 + 200/3*y**4 + 10/3 - 25*y**2 = 0.
-1, -1/2, 1/4, 2/5
Let b = -125 - -125. Let m(o) be the third derivative of -7*o**2 + 1/2*o**3 + 1/8*o**4 + 0 + 1/80*o**5 + b*o. Determine k, given that m(k) = 0.
-2
Let g(n) be the second derivative of -5*n**7/42 - n**6/6 + n**5/4 + 5*n**4/12 - 116*n. Let g(q) = 0. Calculate q.
-1, 0, 1
Let t(d) be the third derivative of d**5/120 + d**4/48 - 162*d**2. Factor t(q).
q*(q + 1)/2
Let j = 20/189 - -158/2079. Find z such that 0 - j*z**2 + 2/11*z = 0.
0, 1
Let x = 307 + -433. Let d = x + 128. Determine m so that 2*m**d - 2/3 - 20/9*m + 8/9*m**3 = 0.
-3, -1/4, 1
Let t(m) = 9*m**2 - 262*m + 18249. Let l(q) = q**2 + q + 3. Let c(y) = -40*l(y) + 5*t(y). Factor c(f).
5*(f - 135)**2
Let n(h) be the third derivative of h**6/300 - 7*h**5/150 - 3*h**4/10 + 488*h**2. Suppose n(q) = 0. Calculate q.
-2, 0, 9
Let d(s) = s**2 - 5*s - 3. Let q be d(6). Suppose 360 - v**2 + v**q - v + v**4 - 360 = 0. What is v?
-1, 0, 1
Let s(w) be the second derivative of w**6/260 - 5*w**5/78 + 14*w**4/39 - 16*w**3/39 + 14*w**2 - 38*w. Let o(q) be the first derivative of s(q). Factor o(n).
2*(n - 4)**2*(3*n - 1)/13
Suppose -24 = i + 5*a, -5*i - 5*a + 2*a - 10 = 0. Factor 718*r**2 + 6 - 715*r**2 - i + r**3 - 9*r.
(r - 1)**2*(r + 5)
Suppose -6*i + 0 = -6. Suppose 0 = -u + 3 - i. What is z in 7*z**2 - 6*z**u + 0*z**2 + z**2 = 0?
0
Find j such that 5*j + 7/4*j**4 + 65/4*j**2 + 10*j**3 - 3 = 0.
-3, -2, -1, 2/7
Suppose -3*v - 4*i - 38 = -60, 0 = 5*v + 5*i - 30. Factor -10/3*b - 25/3*b**v - 1/3.
-(5*b + 1)**2/3
Suppose 16 = 5*k + l, l - 1 = 2*k - 6. Let o be (-6)/4 + -1 + k. Factor 1 - o*p**2 + 1/2*p.
-(p - 2)*(p + 1)/2
Suppose 14*k - 4 = 12*k + 3*u, -3*u = -5*k + 1. Let w(z) = -2*z**2 + 6*z + 8. Let b(x) = 0 - 4 - x**2 + 5. Let a(o) = k*w(o) + 5*b(o). What is v in a(v) = 0?
-1
Suppose 2*l + o = 30 - 25, 3 = 3*o. Let -2/13*v**3 + 2/13*v**4 + 4/13 + 2/13*v - 6/13*v**l = 0. Calculate v.
-1, 1, 2
Suppose -570*d - 1658*d**2 + 760*d**2 + 768 + 805*d**2 - 102*d - 3*d**3 = 0. What is d?
-16, 1
Let n(h) be the second derivative of h**5/60 - h**4/4 - 5*h**3/9 + 320*h. What is i in n(i) = 0?
-1, 0, 10
Let f = 2/107 + 27/4280. Let r(d) be the third derivative of 0*d + 0 + 0*d**3 + 0*d**4 + f*d**6 - d**2 + 1/20*d**5. Determine s, given that r(s) = 0.
-1, 0
Suppose 5*w + 3*y - 66 = 0, 4*w + 7*y - 6*y = 57. Factor -21*c + 4 - 2*c**3 - 2*c**3 + w*c + 6*c**3.
2*(c - 1)**2*(c + 2)
Suppose 13*f + 38 = 15*f. Let c(l) = 2*l**2 - 41*l + 59. Let q be c(f). Determine s, given that 8/3*s**3 + 0*s + 2/3*s**4 + 0 + 8/3*s**q = 0.
-2, 0
Let x(f) be the first derivative of 2*f**3/39 - 102*f**2/13 + 5202*f/13 - 244. Factor x(d).
2*(d - 51)**2/13
Let g be 2/(-8) - (-7)/28. Let h = g + 1. Factor -z**2 + 0 + 0*z + 2*z - 2 + h.
-(z - 1)**2
Let d(z) = -z**2 + 2*z + 2. Let k(x) = 4*x**2 - 9*x - 6. Let n(b) = 15*d(b) + 5*k(b). What is r in n(r) = 0?
0, 3
Let h(b) = -b**3 + 12*b**2 - 10*b - 7. Let r be h(11). Let m = -369 - -372. Factor 0*i**2 + 0*i + 0 - 1/7*i**r + 0*i**m.
-i**4/7
Let l(r) be the third derivative of r**5/30 + 29*r**4/12 - 10*r**3 - 40*r**2. Determine v, given that l(v) = 0.
-30, 1
Let c be (-7)/4*1/(-7). Let t = -4540 + 4542. Factor 1/4 + j**3 - j - c*j**t.
(j - 1)*(j + 1)*(4*j - 1)/4
Suppose 0 = -j + 6*j + 5*b - 80, -5*b = -20. Let g be (-8)/j*(-3 + 0). Determine x, given that -x**2 + 2*x**g + 2*x**2 + 6*x = 0.
-2, 0
Let z(d) = 8*d**5 - 71*d**4 - 22*d**3 + 4*d**2 + 4*d. Let w(t) = 17*t**5 - 142*t**4 - 45*t**3 + 9*t**2 + 9*t. Let c(b) = -4*w(b) + 9*z(b). Factor c(u).
u**3*(u - 18)*(4*u + 1)
Let g(b) be the second derivative of 5*b**4/12 + 5*b**3/6 - 4*b**2 + 13*b. Let a(t) = 26*t**2 + 26*t - 41. Let w(j) = -2*a(j) + 11*g(j). Factor w(v).
3*(v - 1)*(v + 2)
Let v(h) be the third derivative of h**5/480 + 11*h**4/64 - 2*h**2 - 18*h. Suppose v(d) = 0. What is d?
-33, 0
Let k(j) be the first derivative of -j**8/84 - 2*j**7/105 + 3*j**2/2 - 14. Let p(f) be the second derivative of k(f). Solve p(i) = 0 for i.
-1, 0
Let m(n) be the first derivative of -16 + 2/15*n**3 - 4/5*n + 1/5*n**2. Factor m(j).
2*(j - 1)*(j + 2)/5
Let j(v) be the first derivative of 2*v**3/9 + 35*v**2/3 - 24*v - 13. Factor j(b).
2*(b - 1)*(b + 36)/3
Let u(v) be the first derivative of 4*v**5/5 - v**4 - 22. Solve u(y) = 0.
0, 1
Solve 6*s + 19/2*s**2 + 13/4*s**3 - 1/4*s**5 + 0 - 1/2*s**4 = 0.
-3, -2, -1, 0, 4
Factor -48 + 192*j + 153*j**2 + 14*j**3 - 45*j**2 - 16.
2*(j + 4)**2*(7*j - 2)
Let y(o) be the first derivative of 2*o**5 + 49*o**4/12 + 2*o**3/3 - 5*o**2/2 - 2*o/3 + 11. Find a such that y(a) = 0.
-1, -2/15, 1/2
Let g(n) be the first derivative of -n**7/210 + n**6/45 + 6*n**3 - 2*n + 44. Let m(v) be the third derivative of g(v). Determine f, given that m(f) = 0.
0, 2
Let s(q) = -q**5 - 17*q**4 - 7*q**3 - 7*q**2 + 16*q + 8. Let c(n) = -2*n**4 - n**3 - n**2 + 2*n + 1. Let p(j) = -40*c(j) + 5*s(j). Factor p(g).
-5*g**2*(g - 1)*(g + 1)**2
Let i(p) be the first derivative of -2*p**3/39 + 172*p**2/13 - 14792*p/13 + 92. Factor i(k).
-2*(k - 86)**2/13
Let d = 90 - -77. What is m in d + 13*m + 10*m**2 - 159 + 3*m + 2*m**3 = 0?
-2, -1
Let z(o) = o**2 + 20*o + 21. Let v be z(-19). Suppose m + 10*h - 20 = 5*h, 0 = 5*m - 3*h + 12. Factor 0*l + m + 2/5*l**v.
2*l**2/5
Let r = 75231/7 - 10747. Factor r*s**2 - 16/7 - 2*s.
2*(s - 8)*(s + 1)/7
Solve -21/2*t**2 + 12 - 27/2*t**3 - 3/2*t**4 + 27/2*t = 0 for t.
-8, -1, 1
Let j(c) = -4*c**3 - 24*c**2 - 28*c + 36. Let u(m) = 4*m**3 + 23*m**2 + 24*m - 36. Let a(f) = 3*j(f) + 4*u(f). Let a(g) = 0. What is g?
-3, 1
Determine q so that 9/2*q + 0 + 3/4*q**2 - 3*q**3 + 3/4*q**4 = 0.
-1, 0, 2, 3
Let m be (-3)/(-3*(6 + -5))*10. Let d be (2*(-16)/(-40))/(6/m). Factor -4/3*y**2 + 0 + 0*y - d*y**3.
-4*y**2*(y + 1)/3
Let l(c) be the third derivative of 1/32*c**6 + 1/2*c**3 + 0 - 1/280*c**7 - 5/32*c**4 + 5*c**2 - 3/80*c**5 + 0*c. Determine z, given that l(z) = 0.
-1, 1, 4
Let w(u) be the third derivative of u**5/450 + u**4/90 + 16*u**2 - 1. Solve w(n) = 0 for n.
-2, 0
Let o(g) be the first derivative of 2*g**6/39 + 2*g**5/65 - 21*g**4/26 + 4*g**3/3 - 8*g**2/13 - 131. Find w such that o(w) = 0.
-4, 0, 1/2, 1, 2
Find z, given that 2/5*z**2 + 52/5 + 54/5*z = 0.
-26, -1
Suppose 4*t = 10*t + 36. Let v be ((-7)/14)/(t/9). Factor 9/4*a + v*a**2 + 3/2.
3*(a + 1)*(a + 2)/4
Determine y, given that 0*y + 2*y**4 - 14/9*y**5 + 0 - 8/9*y**2 + 8/3*y**3 = 0.
-1, 0, 2/7, 2
Let c(h) = -5*h**2 - 28*h - 34. Let f(a) = 11*a**2 + 58*a + 67. Let j(l) = 5*c(l) + 2*f(l). Factor j(w).
-3*(w + 2)*(w + 6)
Suppose -9*a - 99 = -6*a. Let w = 38 + a. Factor 6*j**5 + 10*j**3 - 4*j**2 + j**5 - 8*j**4 - 5*j**w.
2*j**2*(j - 2)*(j - 1)**2
Let l(k) = 3*k**3 + 3*k**2 + 30*k. Let h(b) = 7*b**3 + 7*b**2 + 59*b. Let c(u) = -6*h(u) + 13*l(u). Let c(t) = 0. Calculate t.
-4, 0, 3
Let i(j) = j**4 + 26*j**3 + 64*j**2 + 40*j - 4. Let f = -98 + 99. Let w(d) = -d**4 - d**3 + d**2 - 1. Let n(v) = f*i(v) - 4*w(v). Factor n(h).
5*h*(h + 2)**3
Let b = 262 - 260. Let v(s) be the first derivative of 0*s - 3/5*s**4 + 1 - 1/15*s**6 + 8/25*s**5 - 1/5*s**b + 8/15*s**3. Find x such that v(x) = 0.
0, 1
Suppose 79*j - 20 = 75*j. Suppose 3*z = -j*z + 4*z. Suppose 2/3*n**2 + 2/3*n**3 + 0*n + z = 0. What is n?
-1, 0
Let j(r