7.
2*(v + 1)**3/7
Suppose 96/11 - 13718/11*k**4 + 77976/11*k**3 + 25536/11*k**2 + 2720/11*k = 0. Calculate k.
-2/19, 6
Suppose -708588 - 324*q**2 - 4/3*q**3 - 26244*q = 0. Calculate q.
-81
Factor -272/3*j**2 - 416/3*j - 64/3*j**3 - 224/3 + 2/3*j**4 + 2/3*j**5.
2*(j - 7)*(j + 2)**4/3
Let x = 239 - 239. Let v(m) be the first derivative of -1/5*m**4 + x*m**3 + 1/15*m**6 + 1 + 0*m + 0*m**5 + 1/5*m**2. Let v(a) = 0. Calculate a.
-1, 0, 1
Let l(r) be the first derivative of 3*r**4/28 - 249*r**3/7 + 62001*r**2/14 - 1715361*r/7 - 23. Factor l(b).
3*(b - 83)**3/7
Let g(j) be the first derivative of -49*j**5/20 - 399*j**4/4 - 3361*j**3/3 - 912*j**2 - 256*j + 69. Factor g(v).
-(v + 16)**2*(7*v + 2)**2/4
Let r(n) = -4*n**2 + 40*n - 100. Let f(b) = -4*b**2 + 40*b - 100. Suppose 11*d - 9*d = -10. Let x(u) = d*r(u) + 4*f(u). Let x(w) = 0. Calculate w.
5
Suppose -291*j = -559*j. Solve 0*d**2 + j + 3/4*d**3 + 0*d - 1/4*d**4 = 0.
0, 3
Let h = 45 - 10. Solve -h + 5 + 14 + 14 + n + n**2 = 0 for n.
-2, 1
Let i = -209/3 + 70. Determine n so that 1/3*n + 0 - 1/6*n**2 + 1/6*n**4 - i*n**3 = 0.
-1, 0, 1, 2
Let t(x) = -2*x**3 + x**2 - 4*x - 5. Let c be t(-1). Let q(k) be the second derivative of -5/6*k**3 - k**c + 1/4*k**4 + 0 + 4*k. Factor q(g).
(g - 2)*(3*g + 1)
Let d = -65 - -63. Let m be d/6 - (-32)/15. Factor 8/5*s - 3/5*s**2 - m*s**3 + 4/5.
-(s - 1)*(3*s + 2)**2/5
Let w(d) = -35*d**4 + 55*d**3 - 15*d**2 - 95*d - 50. Let y(g) = -g**4 + g**3 - g**2 - g. Let o(j) = -w(j) + 30*y(j). What is b in o(b) = 0?
-1, 2, 5
Let z = -1104/13 + 5676/65. Factor -16/5 - z*v**2 - 32/5*v.
-4*(v + 2)*(3*v + 2)/5
Let k(s) be the third derivative of -s**7/1470 + 3*s**5/140 + s**4/42 - 2*s**3/7 + 68*s**2. Suppose k(n) = 0. Calculate n.
-2, 1, 3
Factor 648*b - 27*b**2 + 3/8*b**3 - 5184.
3*(b - 24)**3/8
Let a(o) be the first derivative of 0*o**2 - 1/18*o**4 - 8*o + 2/9*o**3 - 1. Let j(z) be the first derivative of a(z). What is l in j(l) = 0?
0, 2
Let u(m) be the first derivative of -2*m**3/21 - 2*m**2/7 + 116. What is n in u(n) = 0?
-2, 0
Let d be (-8)/192*-4*128/8. Factor d + 16/3*v - 2/3*v**2 - 4/3*v**3.
-2*(v - 2)*(v + 2)*(2*v + 1)/3
Let n(q) be the third derivative of -q**5/30 - 11*q**4/2 - 363*q**3 - 159*q**2. Suppose n(y) = 0. What is y?
-33
Let u(v) be the second derivative of v**7/21 - 34*v**6/75 + 69*v**5/50 - 8*v**4/15 - 76*v**3/15 + 48*v**2/5 + 409*v. Let u(o) = 0. What is o?
-1, 4/5, 2, 3
Let a(d) = -10*d**4 - 45*d**3 - 20*d**2 - 15*d + 15. Let g(k) = k**4 + 2*k**3 + k - 1. Let h(v) = -a(v) - 15*g(v). Factor h(j).
-5*j**2*(j - 4)*(j + 1)
Let o be (0/((-8)/4))/(-6 - -3). Factor -2/3*c**3 + 0 + o*c**4 + 0*c + 2/9*c**5 + 4/9*c**2.
2*c**2*(c - 1)**2*(c + 2)/9
Let t = 7 - -17. Let j be ((-2)/6)/((-2)/t) + -2. Determine u, given that 3/4 + 0*u - 3/4*u**j = 0.
-1, 1
Let f(r) be the third derivative of 0*r + 1/75*r**5 + 1/15*r**4 - 1/300*r**6 + 15*r**2 + 0*r**3 - 1/1050*r**7 + 0. Factor f(v).
-v*(v - 2)*(v + 2)**2/5
Let k = -30035/3 - -10023. Factor 110/3*g + k*g**3 + 25/3 + 116/3*g**2 + g**4.
(g + 1)*(g + 5)**2*(3*g + 1)/3
Let t = 6 - 4. Let d be ((-3)/(-2))/(3/4). Factor t*m**4 - 6*m - 12*m**2 + 3*m + d*m**4 - 5*m.
4*m*(m - 2)*(m + 1)**2
Let i be (-260)/22 - 2/11. Let h be 2*(i/21)/(-4). Factor 0 + 2/7*j + h*j**2.
2*j*(j + 1)/7
Let f(z) be the first derivative of 1/8*z**4 + 3/2*z - 1/2*z**3 - 1/4*z**2 + 2. Factor f(i).
(i - 3)*(i - 1)*(i + 1)/2
Let t(l) be the second derivative of -l**6/75 - 19*l**5/10 - 93*l**4/10 - 277*l**3/15 - 92*l**2/5 - 4*l - 136. Factor t(k).
-2*(k + 1)**3*(k + 92)/5
Let v be (-14)/(-28)*(-4 - -2). Let d be (-28)/15 - (-2 + 1 + v). Determine r so that 0 - d*r**2 - 2/15*r**3 + 0*r = 0.
-1, 0
Let q(k) = 3*k**3 + k**2 - k + 1. Let w(i) = -10*i**3 - 4*i**2 + 3*i - 3. Let v = -28 - -35. Let l(f) = v*q(f) + 2*w(f). Factor l(r).
(r - 1)**2*(r + 1)
Let i be -1 + 30/(-6 + 3). Let y be (-2)/i - (-6)/(-33). Suppose 2 + m**2 - 2 + y*m**2 = 0. Calculate m.
0
Let c(b) be the third derivative of b**7/70 - 19*b**6/20 + 18*b**5 + 19*b**4/4 - 361*b**3/2 - 38*b**2 - 3. Factor c(m).
3*(m - 19)**2*(m - 1)*(m + 1)
Let u(r) be the second derivative of r**6/40 + r**5/4 + 7*r**4/8 + 3*r**3/2 + r**2 + 32*r. Let v(l) be the first derivative of u(l). Factor v(w).
3*(w + 1)**2*(w + 3)
Let g(d) be the first derivative of -1369*d**6/9 - 11248*d**5/15 - 4703*d**4/6 - 920*d**3/9 - 4*d**2 + 5. Find w, given that g(w) = 0.
-3, -1, -2/37, 0
Let l be (-20)/15*1*9/(-6). Let w be (2/4)/((-1)/(-1)). Solve -w*b**l - 1/4*b**3 - 1 + 7/4*b = 0.
-4, 1
Let a be 8523/72 + (-9)/24. Factor 10 + 44*h**3 - 1 + 64*h - a*h**2 - 10 - 7.
2*(h - 2)*(2*h - 1)*(11*h - 2)
Let t(d) be the first derivative of 1/2*d**4 - 15 + 0*d - d**2 + 0*d**3. Factor t(o).
2*o*(o - 1)*(o + 1)
Let u = -1940 + 1940. Find g, given that -1/7*g**2 + u + 4/7*g = 0.
0, 4
Determine b, given that 0*b**5 - b**5 + 20*b**4 + 21*b**4 - 40*b**4 = 0.
0, 1
Suppose 63*b + 10 = 65*b. Let u be b/(-5*4/(-20)). Factor -8/17*a**4 + 0 - 36/17*a**3 + 16/17*a**u - 22/17*a**2 - 4/17*a.
2*a*(a - 2)*(2*a + 1)**3/17
Factor 1/5*m**5 + 2/5*m**2 - 29/5 - 58/5*m**3 + 57/5*m + 27/5*m**4.
(m - 1)**3*(m + 1)*(m + 29)/5
Let l(q) be the third derivative of q - 2/27*q**4 + 36*q**2 + 0 - 16/27*q**3 - 1/270*q**5. Let l(y) = 0. Calculate y.
-4
Suppose -13 = -13*l + 39. Let x(f) be the first derivative of 1/15*f**5 + l + 0*f**2 - 1/18*f**3 + 0*f + 1/24*f**4. Determine j, given that x(j) = 0.
-1, 0, 1/2
Solve 1/2*d**2 + 65/2*d + 32 = 0 for d.
-64, -1
Let m(r) = 2*r. Let y be m(1). Let g(u) be the first derivative of -57/25*u**5 + 3 + 9/4*u**4 + 0*u - 3/5*u**y + 7/10*u**6 - 1/5*u**3. Factor g(i).
3*i*(i - 1)**3*(7*i + 2)/5
Let y(b) be the first derivative of 2/9*b**2 - 2/27*b**3 + 2/3*b + 13. Factor y(x).
-2*(x - 3)*(x + 1)/9
Let q(r) be the first derivative of r**3 - 141*r**2/2 + 138*r - 286. Factor q(t).
3*(t - 46)*(t - 1)
Let b = 515/216 - 19/8. Let k(w) be the third derivative of -b*w**4 + 0*w + 0 + 1/270*w**5 + 0*w**3 + 1/270*w**6 + 2*w**2. Let k(z) = 0. What is z?
-1, 0, 1/2
Let l = 17/2 + -49/6. Suppose -3 = 2*z - 3*z. Let 1/6*h**2 - l*h + 1/2*h**z + 0 = 0. What is h?
-1, 0, 2/3
Suppose -3*n - 70 = -5*j + 26, -j + 28 = -5*n. Find y such that -2*y**3 + 65*y**2 - j*y**3 - 10 - 60*y**4 - 15*y + 11*y**5 + 5*y**2 + 24*y**5 = 0.
-1, -2/7, 1
Suppose -1/4*v**3 - 23/4*v - 5/2*v**2 - 7/2 = 0. What is v?
-7, -2, -1
Let x(a) be the first derivative of -2*a**3/33 + 12*a**2/11 - 2*a - 22. What is g in x(g) = 0?
1, 11
Solve -5*b**2 + 80 + 9 - 26*b - 24*b + 31 = 0 for b.
-12, 2
Suppose 0 = -k + 3*l - 5, 3*k + 2*l - 1 = 6*k. Let b be (2 + k)*(-4)/(-3). Determine d so that -2/3*d**2 - 6 - b*d = 0.
-3
Let q(m) be the second derivative of -m**5/45 - 5*m**4/9 + 68*m**3/27 - 320*m. Factor q(x).
-4*x*(x - 2)*(x + 17)/9
Let r(w) = -3*w**2 + 286*w - 20449. Let i(v) = 2*v**2. Let c(h) = -i(h) - r(h). Factor c(j).
(j - 143)**2
Let n be (-2 + (-1)/(-2))*(-78)/260. Let z(i) be the second derivative of -i**2 + 5/6*i**3 + 0 + n*i**5 + 5*i + 4/3*i**4. Determine w, given that z(w) = 0.
-1, 2/9
Let l(o) be the first derivative of 1/3*o**2 - 2/15*o**5 - 1/6*o**4 + 9 + 0*o + 2/9*o**3. Factor l(g).
-2*g*(g - 1)*(g + 1)**2/3
Let s(y) be the first derivative of y**6/18 - 2*y**5/3 - y**4/4 + 140*y**3/9 + 98*y**2/3 + 18. Factor s(g).
g*(g - 7)**2*(g + 2)**2/3
Let f(r) be the third derivative of 5*r**7/21 + 3*r**6/4 - 331*r**5/30 + 109*r**4/4 - 30*r**3 + 44*r**2 - 3*r. Suppose f(m) = 0. What is m?
-5, 3/5, 2
Let w(p) be the third derivative of -p**7/42 - p**6/4 - 3*p**5/4 + 5*p**4/6 + 10*p**3 + 6*p**2 - 1. Let w(g) = 0. Calculate g.
-3, -2, 1
Let h(z) = z**3 - 96*z**2 - 507*z + 202. Let v be h(101). Factor 0 - 2/9*j**5 + 0*j - 8/9*j**4 - 2/3*j**3 + v*j**2.
-2*j**3*(j + 1)*(j + 3)/9
Solve -339580 - 562322 - 365040*p - 63180*p**2 - 3645*p**3 + 198862 = 0 for p.
-52/9
Let a(z) be the third derivative of -13*z**7/210 + 13*z**6/120 - 7*z**4/24 + 9*z**2. Let p(f) = -4*f**4 + 4*f**3 - 2*f. Let c(d) = 2*a(d) - 7*p(d). Factor c(k).
2*k**3*(k - 1)
Suppose 29*g + 2288 = 18*g. Let s = 208 + g. Find o such that 0*o**2 + 0 - 1/2*o**4 + 0*o + 1/2*o**5 + s*o**3 = 0.
0, 1
Let u(k) be the third derivative of 3*k**6/260 + k**5/195 - 3*k**4/52 - 2*k**3/39 - 63*k**2. Find m, given that u(m) = 0.
-1, -2/9, 1
Suppose -r + 5*n = 4