he third derivative of w**8/252 + 44*w**7/315 + 13*w**6/30 - 22*w**5/45 - 20*w**4/9 + w**2 - 241*w. Suppose f(g) = 0. What is g?
-20, -2, -1, 0, 1
Let d be -2*((-1)/2 - 1). Let f = d - 3. Factor 10/7*n**3 + 2/7*n + f + 8/7*n**2 + 4/7*n**4.
2*n*(n + 1)**2*(2*n + 1)/7
Let v(d) be the first derivative of -d**4/102 - d**3/51 + 2*d**2/17 + 15*d + 17. Let j(p) be the first derivative of v(p). Factor j(h).
-2*(h - 1)*(h + 2)/17
Factor -6/7*c**2 - 324/7 + 330/7*c.
-6*(c - 54)*(c - 1)/7
Let s(h) be the first derivative of -2*h**4/3 - 8*h**3/3 - 3*h**2 + 132. Suppose s(x) = 0. What is x?
-3/2, 0
Suppose 93*m**2 + 57*m**2 - m + 7*m + 318*m**3 + 21*m**2 = 0. Calculate m.
-1/2, -2/53, 0
Let k(w) be the second derivative of -1/30*w**4 - 3/25*w**5 - 1/75*w**6 - 16/5*w**2 + 0 + 14*w + 8/5*w**3. Solve k(j) = 0.
-4, 1
Let s(z) be the third derivative of z**5/270 + 5*z**4/36 - 76*z**3/27 + 704*z**2. Factor s(x).
2*(x - 4)*(x + 19)/9
Let o(a) be the third derivative of a**7/175 + a**6/25 + a**5/10 + a**4/10 - 66*a**2 + a. Suppose o(x) = 0. What is x?
-2, -1, 0
Suppose 3 = 4*j - 33. Let u = j + -13. Let s(a) = a**2 + 2*a + 1. Let o(w) = -4*w**2 - 6*w - 4. Let q(f) = u*o(f) - 14*s(f). Solve q(r) = 0 for r.
1
Suppose 4*l - 20*l = 16. Let o be l/3*(-1638)/147. Factor -8/7*n**2 - o*n - 6/7.
-2*(n + 3)*(4*n + 1)/7
Let u(i) = 155*i**3 + 45*i**2 - 65*i + 45. Let g(s) = -7*s**3 - 2*s**2 + 3*s - 2. Let q = 0 + -45. Let v(o) = q*g(o) - 2*u(o). Factor v(w).
5*w*(w - 1)*(w + 1)
Let i(t) be the second derivative of -4*t**5/15 + 13*t**4/6 - 2*t**3 + 8*t**2 + t. Let w(z) be the first derivative of i(z). Suppose w(n) = 0. What is n?
1/4, 3
Let v(g) be the third derivative of 7*g**6/30 - 18*g**5/5 + 89*g**4/6 + 20*g**3 - 813*g**2. Suppose v(d) = 0. Calculate d.
-2/7, 3, 5
Let 0*x - 4/7*x**4 + 4/7*x**2 - 10/7*x**5 + 0 + 10/7*x**3 = 0. What is x?
-1, -2/5, 0, 1
Let o(t) be the second derivative of -t + 0*t**3 + 0 + 3/40*t**5 + 1/4*t**4 + 0*t**2. Determine n so that o(n) = 0.
-2, 0
Let -10/3*w + 1/3*w**2 + 3 = 0. What is w?
1, 9
Let l(f) be the second derivative of -8/5*f**2 + 0*f**3 + 1/25*f**5 + 1/5*f**4 + 0 + 39*f. Factor l(a).
4*(a - 1)*(a + 2)**2/5
Let z(y) = y**2 - 638*y + 10557. Let t be z(17). What is c in t + 1/3*c**4 + 0*c + 4/3*c**3 + 0*c**2 = 0?
-4, 0
Let b(v) = -8*v**2 + 523*v - 510. Let q(i) = 12*i**2 - 785*i + 766. Let n(j) = 7*b(j) + 5*q(j). Let n(w) = 0. What is w?
1, 65
Let s(n) be the second derivative of -n**4/20 - 102*n**3/5 - 15606*n**2/5 + 135*n. Determine h so that s(h) = 0.
-102
Let z(y) = 27*y**2 + 27*y + 9*y**3 + 7 + 4 + 5*y**4 - 4*y**2. Let o(l) = 6*l**4 + 8*l**3 + 22*l**2 + 28*l + 12. Let q(s) = -3*o(s) + 4*z(s). Factor q(g).
2*(g + 1)**2*(g + 2)**2
Let d(c) be the first derivative of 512/7*c + 12 - 320/21*c**3 + 1/21*c**6 - 6/7*c**5 + 40/7*c**4 + 0*c**2. Suppose d(p) = 0. Calculate p.
-1, 4
Suppose -1 = -4*y + 7. Suppose y*v = -3*m - 13 + 2, -17 = -v + 3*m. Determine d so that 2/5*d**v + 0 - 2/5*d = 0.
0, 1
Let g = 1717 - 1707. Let h(x) be the first derivative of 1/9*x**3 + x - g - 2/3*x**2. Let h(r) = 0. Calculate r.
1, 3
Factor -11/6*f + 1/6*f**3 - 2 + 1/3*f**2.
(f - 3)*(f + 1)*(f + 4)/6
Let m be (-12)/(5 - 4)*-1 + 2. Suppose -12*t - 3*q - 3 = -m*t, t + 5*q + 5 = 0. Factor -1/2*b**4 - b + t*b**2 + 1/2 + b**3.
-(b - 1)**3*(b + 1)/2
Let x = 4071 - 20346/5. Factor 0 - 3/5*c**4 + 0*c**3 + x*c**2 - 6/5*c.
-3*c*(c - 1)**2*(c + 2)/5
Suppose 6 = h - 0*h. Let i be (-1)/(-2)*0/6. Find w such that 0 + 3*w**2 + h*w + i = 0.
-2, 0
Let w(v) = v**2 - v. Let i(d) = -d**3 - 12*d**2 + 6*d - 17. Let h(p) = -i(p) - 6*w(p). Let f(k) be the first derivative of h(k). Factor f(b).
3*b*(b + 4)
Let q(a) be the first derivative of -2*a**4/17 - 26*a**3/51 + 157*a**2/17 + 80*a/17 - 837. Find h, given that q(h) = 0.
-8, -1/4, 5
Let b = -208 + 1669/8. Let o(h) be the second derivative of b*h**4 + 0 - h**3 - 1/10*h**5 - 6*h - h**2. Factor o(m).
-(m - 2)**2*(4*m + 1)/2
Let u = -86 - -83. Let o be u/(216/16) + 14/9. Factor -4/3 - o*a - 1/3*a**2.
-(a + 2)**2/3
Let x(t) be the third derivative of -t**9/120960 + t**8/17280 - t**7/6048 + t**6/4320 + t**5/30 - 9*t**2. Let u(d) be the third derivative of x(d). Factor u(c).
-(c - 1)**2*(3*c - 1)/6
Let w(m) be the first derivative of -1/22*m**2 + 5/33*m**3 - 1/11*m**4 + 1 + 0*m. Determine q so that w(q) = 0.
0, 1/4, 1
Let u(p) be the first derivative of 1 - 6*p + 2/21*p**3 - 1/42*p**4 + 3/7*p**2. Let m(a) be the first derivative of u(a). Factor m(q).
-2*(q - 3)*(q + 1)/7
Let h = 39 - 36. Factor 4*c + 3*c**4 + 16*c**h + 4*c - 20*c**2 + 0*c**2 - 7*c**4.
-4*c*(c - 2)*(c - 1)**2
Let c(k) = -k**2 + 10*k + 149. Let o be c(18). Let g = -5 + 9. Factor 3/5*j**o + 6/5*j**g - 21/5*j - 24/5*j**2 - 6/5*j**3 - 6/5.
3*(j - 2)*(j + 1)**4/5
Factor 2*n**3 - 17*n**4 - 9*n**2 + 4 + 2*n**3 - 2*n**3 + 20*n**4.
(n - 1)**2*(n + 2)*(3*n + 2)
Suppose -3*g = -13 + 7. Suppose -g*d - 2*d = -12. Factor -3*i**3 - 4*i + 12*i + i**d.
-2*i*(i - 2)*(i + 2)
Let j(y) be the second derivative of 20*y - 1/3*y**3 + 0 + 1/10*y**5 - 1/15*y**6 + 1/6*y**4 + 0*y**2. Solve j(z) = 0 for z.
-1, 0, 1
Let n(r) = r**2 + r + 3. Let k(d) = 24*d**2 + 790*d - 72884. Let w(b) = 2*k(b) - 52*n(b). Suppose w(l) = 0. What is l?
191
Let u(c) be the third derivative of -c**8/560 - c**7/350 + c**6/200 + c**5/100 - 72*c**2. Factor u(g).
-3*g**2*(g - 1)*(g + 1)**2/5
Suppose -4*z = 2 - 10. Let l be (-20)/z*(-34)/85. Factor l*w**4 + 98*w**2 + 4*w**3 - 98*w**2.
4*w**3*(w + 1)
Let j = 14240 + -99668/7. What is q in 6/7 + j*q**2 - 38/7*q = 0?
1/6, 3
Let p = -109 + -93. Let w be p/(-40) - (-11)/(-44). Factor 0*g + w*g**3 + 0 - 3*g**4 + 3/5*g**5 - 12/5*g**2.
3*g**2*(g - 2)**2*(g - 1)/5
Suppose 128/13*u + 32/13 + 8/13*u**5 + 2/13*u**4 - 16/13*u**2 - 64/13*u**3 = 0. Calculate u.
-2, -1/4, 2
Let x be (-2)/(-6)*3916/33. Let b = x + -74/9. Find i such that 104/3*i**2 - 32*i + 2/3*i**5 - 128/3 + b*i**3 + 8*i**4 = 0.
-4, -1, 1
Factor 18*r + 0 + 5*r**4 + 13/2*r**3 + 1/2*r**5 - 30*r**2.
r*(r - 1)**2*(r + 6)**2/2
Let g be -4 + ((-32)/20)/(-2*10/75). Factor 0 + 6/5*b + 2/5*b**3 - 8/5*b**g.
2*b*(b - 3)*(b - 1)/5
Suppose -9*k + 217 = 46. Suppose 2*y = 3*v + 15, -4*y + 4 = 3*v + k. Determine s, given that 3/4*s**3 + 7/4*s**4 + y + 0*s + 1/2*s**5 + 0*s**2 = 0.
-3, -1/2, 0
Let m(n) be the second derivative of -21/20*n**5 + 0 + 0*n**3 + 0*n**2 - 1/14*n**7 + 3*n + 1/2*n**6 + 3/4*n**4. Determine d so that m(d) = 0.
0, 1, 3
Factor 44*j + 3*j**3 + 12 - 40*j + 29*j + 27*j**2 - 3*j**4.
-3*(j - 4)*(j + 1)**3
Let o(x) = x**3 - 116*x**2 - 4*x + 467. Let w be o(116). Let d be 6/3 - 6/4. Suppose -d*r**w + 0*r + 0 - 3/2*r**4 + 0*r**2 = 0. What is r?
-1/3, 0
Let w(l) be the second derivative of -1/20*l**5 + 1/12*l**4 - 1/30*l**6 + 0 + 0*l**2 + 1/42*l**7 - 4*l + 0*l**3. Factor w(k).
k**2*(k - 1)**2*(k + 1)
Factor 40/3*k**3 + 0*k - 20*k**2 + 40/3 - 5/2*k**4.
-5*(k - 2)**3*(3*k + 2)/6
Suppose 26*a = 4*a - 2*a. Let a + 0*k + 0*k**2 - 2/7*k**3 = 0. What is k?
0
Let r = -1/387 - 2278/387. Let f = r + 425/63. Factor 8/7*g + 2/7*g**2 + f.
2*(g + 1)*(g + 3)/7
Let h = -18 - -18. Let s = 27 + -107/4. Factor 0*l - s*l**2 + h.
-l**2/4
Let y(a) be the second derivative of -1/2*a**3 + 0 - 21*a + 9/4*a**2 + 1/24*a**4. Find n, given that y(n) = 0.
3
Let y(v) be the second derivative of v**4/28 + 5*v**3/7 - 33*v**2/14 + 70*v + 3. Let y(x) = 0. What is x?
-11, 1
Suppose o + 5*g + 2 = 4*g, -2 = 5*o + g. Let m(h) be the third derivative of 0*h + o + 1/100*h**5 + 1/10*h**3 + 5*h**2 - 1/20*h**4. Factor m(q).
3*(q - 1)**2/5
Let c(f) be the third derivative of 1/30*f**6 + 0 + 0*f + 1/3*f**5 + 4/3*f**4 + f**2 + 8/3*f**3. Factor c(j).
4*(j + 1)*(j + 2)**2
Let k = 40 + -14. Suppose -k*f = -27*f + 3. What is a in 0*a**3 + 2 - 4*a**2 - a**4 + 3*a**2 + 3*a - a**3 - 2*a**f = 0?
-2, -1, 1
Let o(h) be the second derivative of h**4/3 - 178*h**3/3 - 180*h**2 - h + 78. Factor o(k).
4*(k - 90)*(k + 1)
Let r(t) = -25*t**2 - 980*t - 16345. Let s(q) = 8*q**2 + 327*q + 5448. Let u(p) = -3*r(p) - 10*s(p). Let u(g) = 0. Calculate g.
-33
Suppose 8*p - 15 = 9. Suppose 0 = 4*q + d - 4 - 11, 2*q - d = p. Factor -2/9*n**q - 2/3*n - 10/9*n**2 + 2.
-2*(n - 1)*(n + 3)**2/9
Let p(g) be the second derivative of -2*g**6/15 - 8*g**5/5 - 6*g**4 + 54*g**2 + 138*g. Let p(q) = 0. Calculate q.
-3, 