n = -7*q + 3*q + 8, -2*q + 4 = -3*n. Let a be (-4)/4*(n - 0)/2. Factor -27/4*w**3 - 9*w**2 + a - 3*w.
-3*w*(3*w + 2)**2/4
Let n(j) be the first derivative of -2*j**3/63 - 11*j**2/7 - 64*j/21 + 500. Let n(m) = 0. Calculate m.
-32, -1
Let -130*n**2 + 10*n**3 + 360*n - 48*n**2 - 726*n**2 = 0. Calculate n.
0, 2/5, 90
Let f(q) = -2*q + 36. Let i be f(0). Factor 7*y**2 - i - 18*y**2 + 10*y**2 - 12*y.
-(y + 6)**2
Suppose -6/5*x**3 - 4/5*x + 2/5*x**4 - 2*x**2 + 2/5*x**5 + 0 = 0. Calculate x.
-1, 0, 2
Let i = -293/180 + 16/9. Let p(a) be the first derivative of 1 - 9/8*a**2 + 1/4*a**3 - 3/2*a + 9/16*a**4 + i*a**5. Let p(k) = 0. What is k?
-2, -1, 1
Let p(g) = g + 11. Let y be p(-11). Let r**2 - 10*r**3 + y*r**2 + 3*r**4 + r**3 + 5*r**2 = 0. Calculate r.
0, 1, 2
Let i(t) = -t**3 - 141*t**2 - 548*t. Let v be i(-137). Factor 0*w + v - 1/5*w**2 + 1/5*w**3.
w**2*(w - 1)/5
Let k = -7 + -2. Let a = k + 15. Determine p so that -a*p**4 + p**2 - 14*p**3 - 5*p**2 + 3*p**2 - 2*p - 9*p**2 = 0.
-1, -1/3, 0
Factor -1/4*x**4 - 1/4*x**3 + 1/4*x**2 + 1/4*x + 0.
-x*(x - 1)*(x + 1)**2/4
Let r(g) be the first derivative of -g**6/45 + 2*g**5/3 - 3*g**4 + 52*g**3/9 - 17*g**2/3 + 14*g/5 - 332. Factor r(v).
-2*(v - 21)*(v - 1)**4/15
Suppose 3 + 4 = f - p, -p + 13 = 4*f. Suppose -21 = -3*j + 5*u - 0*u, -4*j + 20 = -4*u. Factor -f + 2*t**2 + 12*t + 2*t**2 - 9*t**j.
-(t - 2)*(5*t - 2)
Let p(z) be the second derivative of -z**6/75 - z**5/50 + 3*z**4/10 - 11*z**3/15 + 4*z**2/5 - 44*z. Determine r so that p(r) = 0.
-4, 1
Let b(z) be the first derivative of 32*z**3/3 - 108*z**2 + 729*z/2 - 121. Factor b(s).
(8*s - 27)**2/2
Let n = -9 + 13. Let l = n + -2. Let 23*o**l - 11*o**2 + 2 - 10*o**2 + 4*o = 0. Calculate o.
-1
Let r(z) be the first derivative of z**6/12 - 7*z**5/20 + 3*z**4/8 + z**3/3 - z**2 + 3*z/4 + 21. Determine q, given that r(q) = 0.
-1, 1, 3/2
Let i(d) be the second derivative of 21*d**5/4 + 39*d**4 - 65*d**3/2 - 14*d. Let z(c) = 15*c**3 + 67*c**2 - 28*c. Let l(t) = 2*i(t) - 15*z(t). Factor l(s).
-3*s*(s + 5)*(5*s - 2)
Let z(j) be the second derivative of j**4/6 + 5*j**3/3 - 6*j**2 + 93*j. Let z(k) = 0. What is k?
-6, 1
Let o(x) be the second derivative of -x**5/20 + x**4/2 + x**3/6 - 3*x**2 - 7*x - 1. Find j, given that o(j) = 0.
-1, 1, 6
Suppose 0 = -s - 4 + 7. Solve 4*t - 10*t**3 + s*t**4 - 9*t**2 + 16*t**3 - 4*t = 0.
-3, 0, 1
Factor -4/5*g + 14/15 - 2/15*g**2.
-2*(g - 1)*(g + 7)/15
Let a = 1196/5 - 239. Let m(b) be the second derivative of 0*b**4 - 1/25*b**5 - 1/75*b**6 - 2*b + 0 + 2/15*b**3 + a*b**2. Determine n so that m(n) = 0.
-1, 1
Let h(n) be the second derivative of 3*n**5/20 + 7*n**4/4 + 6*n**3 + 29*n - 8. Find l such that h(l) = 0.
-4, -3, 0
Let q(a) = -a**3 - 11*a**2 + 13*a + 24. Let s be q(-12). Factor -t - 7*t + 2*t**2 - 2*t**2 - 4*t**2 + s.
-4*(t - 1)*(t + 3)
Let 1/4*h**4 - 5/4*h**2 - h**3 + 0*h + 0 = 0. Calculate h.
-1, 0, 5
Let k = 51 + -20. Suppose 0 = r - 5*h - 22, -5*h + 5 - k = -3*r. Factor 2/9*p**r - 2/9*p - 2/9*p**4 + 2/9*p**3 + 0.
-2*p*(p - 1)**2*(p + 1)/9
Let 22*v**2 + 12*v**3 + 3*v**3 - 3*v**3 - 12*v + 0*v + 23*v**2 = 0. What is v?
-4, 0, 1/4
What is n in 0 + 15/4*n**3 + 3*n + 8*n**2 - 9/4*n**4 = 0?
-2/3, 0, 3
Let w(g) be the third derivative of g**7/2940 - g**6/180 + 11*g**5/420 - 5*g**4/84 + 31*g**3/6 + 5*g**2. Let l(m) be the first derivative of w(m). Factor l(y).
2*(y - 5)*(y - 1)**2/7
Let a(p) be the first derivative of 2*p**3/39 - 30*p**2/13 + 112*p/13 + 166. Let a(i) = 0. What is i?
2, 28
Suppose -6*b = -9*b + 27. Determine d, given that -b*d**4 - 3*d - 6 + 14*d**4 - 57*d**3 + 16*d**4 + 45*d**2 = 0.
-2/7, 1
Let y(u) be the second derivative of u**6/135 + u**5/18 - 7*u**4/54 - 5*u**3/27 + 2*u**2/3 + 821*u. Factor y(h).
2*(h - 1)**2*(h + 1)*(h + 6)/9
Solve -14 + 9*i - 36*i + 2*i - 6 - 5*i**2 = 0.
-4, -1
Let f(a) be the third derivative of -a**5/135 + a**4/6 - 4*a**3/3 - 59*a**2 + 2*a. Factor f(c).
-4*(c - 6)*(c - 3)/9
Let v = -42 + -82. Let c = -124 - v. Factor -2/7*q**2 + c + 6/7*q.
-2*q*(q - 3)/7
Let w(u) be the third derivative of u**8/131040 + u**7/8190 + u**6/1170 - u**5/20 - 16*u**2. Let j(g) be the third derivative of w(g). Factor j(h).
2*(h + 2)**2/13
Let k = -21423/130 + 824/5. Let l(q) be the second derivative of 0 - 4/13*q**2 + 11*q + 0*q**3 + 1/26*q**4 - k*q**5. Solve l(t) = 0.
-1, 2
Let s(w) be the first derivative of -2/15*w**5 - 2/3*w**4 - 4 - 2/3*w**2 - 10/9*w**3 + 0*w. Factor s(n).
-2*n*(n + 1)**2*(n + 2)/3
Suppose 2*k - 76 = 4*g, 2*g = -5*k + 2*k - 54. Let p be (-35)/g*-3 + 5. What is h in p - 9/7*h**3 - 3/7*h**4 + 12/7*h + 0*h**2 = 0?
-2, 0, 1
Let s = 649 - 915. Let h = s - -272. Factor -27/2*q**3 - 33/4*q**4 - 3/2*q**5 - 3*q**2 + 0 + h*q.
-3*q*(q + 2)**3*(2*q - 1)/4
Let t = -2 + 2. Let q(k) = 2*k**3 - 23*k**2 + 16*k + 144. Let m be q(10). Factor t*y + 0*y**3 + 4/11*y**2 - 2/11*y**m - 2/11.
-2*(y - 1)**2*(y + 1)**2/11
What is l in -8*l**4 - 7*l**4 + 162 + 13*l + 12*l**3 - 121*l + 13*l**4 = 0?
-3, 3
Suppose -12 = -5*g + 8. Suppose -2*u + 6 + g = 0. Determine x, given that 1/4*x - 1/2*x**2 + 1/4*x**u - 1/2*x**3 + 1/4*x**4 + 1/4 = 0.
-1, 1
Determine m, given that 17*m - 9550 + 9502 + 5*m - 2*m**2 = 0.
3, 8
Let x(d) be the second derivative of d**5/4 + 25*d**4/12 + 35*d**3/6 + 15*d**2/2 + 16*d + 3. Let x(n) = 0. What is n?
-3, -1
Let k(y) be the second derivative of 0 + 1/5*y**5 - 2*y**3 + 0*y**2 - 19*y - 2/3*y**4. Factor k(o).
4*o*(o - 3)*(o + 1)
Let v(s) = -8*s**2 + 10*s + 11. Let u(m) = -m**2 + 2*m + 2. Let t(o) = -7*u(o) + v(o). Find c, given that t(c) = 0.
-3, -1
Let u(h) be the third derivative of -h**7/840 - 13*h**6/160 - 217*h**5/120 - 87*h**4/8 - 27*h**3 - 865*h**2. What is g in u(g) = 0?
-18, -2, -1
Factor 3*i**4 - 52*i + 0*i**4 + 119*i**2 + 72*i**3 - 104*i**3 - 37*i**2 - i**4.
2*i*(i - 13)*(i - 2)*(i - 1)
Suppose 13*x = 6*x - 1036. Let n = -52 - x. Factor 18*c**3 - 93*c**5 - 8*c**4 - 12*c**2 - 4*c**4 + n*c**5 + 3*c.
3*c*(c - 1)**4
Let r = 139 - 136. Let o = -5/18 - -43/90. Determine b, given that 1/5 + 3/5*b + 3/5*b**2 + o*b**r = 0.
-1
Let p(y) be the second derivative of -1/54*y**4 + 3*y + 0 + 1/27*y**3 + 2/9*y**2. What is r in p(r) = 0?
-1, 2
Factor -1/7*m**4 + 0*m**3 + 6/7*m**2 - 8/7*m + 3/7.
-(m - 1)**3*(m + 3)/7
Let w(g) be the first derivative of 17 + 9/5*g**3 + 12/5*g + 18/5*g**2. Factor w(p).
3*(3*p + 2)**2/5
Suppose 176/3*j**2 - 75 + 484/3*j**3 - 145*j = 0. Calculate j.
-15/22, 1
Let l(m) be the first derivative of -2/27*m**3 + 26 + 2/9*m + 0*m**2. Factor l(y).
-2*(y - 1)*(y + 1)/9
Let v = 1279 - 1263. Let i(x) be the second derivative of 6*x**4 - v*x**3 + 1/10*x**6 + 24*x**2 + 8*x + 0 - 6/5*x**5. Determine q so that i(q) = 0.
2
Let i(s) be the first derivative of 2*s**3/21 - 74*s**2/7 + 2738*s/7 - 23. Factor i(n).
2*(n - 37)**2/7
Let s(h) be the first derivative of h**3/24 - h**2/16 - 9*h - 773. Factor s(l).
(l - 9)*(l + 8)/8
Let l(k) be the second derivative of 0 - k + 3/14*k**3 - 5/28*k**4 + 3/140*k**5 + 27/14*k**2. Factor l(c).
3*(c - 3)**2*(c + 1)/7
Factor 51*d**2 - 42*d**3 + 32*d + 47*d**3 + 15*d**2 + 31*d**3 + 2*d**4.
2*d*(d + 1)**2*(d + 16)
Let z(w) be the third derivative of -w**5/210 - 19*w**4/84 + 2*w**3 + w**2 - 40. Factor z(t).
-2*(t - 2)*(t + 21)/7
Let l(u) = -u**2 - 10*u - 6. Let s be l(-12). Let d be (-1)/2 + (-20)/s. Solve -1/3*m**3 + d*m**4 + 0 + 1/6*m**2 + 0*m = 0 for m.
0, 1
Let r(c) be the first derivative of -c**4/4 + 8*c**3/3 - 8*c**2 + 10. Solve r(h) = 0 for h.
0, 4
Let u(c) be the second derivative of c**7/168 + c**6/24 - c**5/6 - c**3/3 + 35*c. Let b(i) be the second derivative of u(i). Factor b(y).
5*y*(y - 1)*(y + 4)
Let t be 0/((-266)/114*(12/14)/(-1)). Factor t*g + 12/5*g**2 + 0 + 3/5*g**3.
3*g**2*(g + 4)/5
Let w be 9 + (-3)/1 + 0. Suppose 0*k - w = -2*k. Determine x, given that 6*x**k + 3*x + 12*x + x**4 + 13*x**2 - 3*x - 1 + 5 = 0.
-2, -1
Solve 2*r**3 + 185 + 6*r - 5*r**3 - 181 + r**3 = 0 for r.
-1, 2
Let j = 4243 + -4243. Determine f, given that 0*f - 6/11*f**3 - 8/11*f**4 + j*f**2 + 0 = 0.
-3/4, 0
Let o(l) = -2*l**3 + 1. Let j(x) = x**3 - 30*x**2 - 55*x - 33. Let a(h) = -j(h) - 3*o(h). Suppose a(b) = 0. Calculate b.
-3, -2, -1
Let u = 19 + -16. Let n(f) be the first derivative of -6 + 5/6*f**u - 1/4*f**4 - f - 1/4*f**2. Solve n(d) = 0 for d.
-1/2, 1, 2
Factor -16/15