, 1
Let s(l) = -19*l**3 + 293*l**2 - 436*l - 182. Let k(n) = -800*n**3 + 12305*n**2 - 18310*n - 7645. Let m(b) = 2*k(b) - 85*s(b). Find t, given that m(t) = 0.
-1/3, 2, 18
Let o be (-36)/21 + (-1)/(-7*(-4)/112*-2). What is k in o*k**2 - 6/7*k + 4/7 = 0?
1, 2
Let u = 403/9163 + -1/17. Let b = 27988/2695 - u. Find k, given that -16/5 - b*k + 14/5*k**2 = 0.
-2/7, 4
Let f(l) be the first derivative of -541*l**4/34 + 2168*l**3/51 - 545*l**2/17 + 4*l/17 - 3015. Solve f(c) = 0 for c.
2/541, 1
Let c(i) be the third derivative of i**8/72 - 2*i**7/315 - 91*i**6/180 + 13*i**5/45 + 7*i**4 - 8*i**3 - 5*i**2 - 49. Find b such that c(b) = 0.
-3, -2, 2/7, 2, 3
Let b(o) be the third derivative of -o**6/360 + 625*o**5/12 - 9765625*o**4/24 + 30517578125*o**3/18 - 1692*o**2. Factor b(t).
-(t - 3125)**3/3
Suppose 20*v - 5*i = 21*v - 19, 3*v - 5*i = -3. Factor -5*y**v - 3*y**3 - 14 + 26 + 4*y + 4*y**4 - 12.
-y*(y - 1)*(y + 2)**2
Let k(g) be the second derivative of g**5/4 + 40*g**4/3 - 550*g**3/3 + 760*g**2 - 4131*g. Factor k(y).
5*(y - 4)*(y - 2)*(y + 38)
Let u(t) = -t**2 - 20*t + 4. Let a be u(-20). Let c be (1/3*a)/(12/18). Solve 3*i**5 + 24*i**4 - i**3 - 10*i**2 - 14*i**4 + c*i**5 - 4*i**3 = 0 for i.
-2, -1, 0, 1
Let a(t) be the second derivative of -1/42*t**3 - 17 + 1/84*t**4 + 0*t**2 + t. Factor a(z).
z*(z - 1)/7
Let h(a) = -a**2. Suppose 4 - 16 = -4*p. Suppose -p*g + g = -10. Let z(j) = 3*j**2 - 8*j - 7. Let x(r) = g*z(r) + 20*h(r). Determine l so that x(l) = 0.
-7, -1
Let h = -10 + 1. Let z(u) = -u**2 - 12*u - 23. Let t(r) = 4*r**2 + 49*r + 91. Suppose 3*o = 4*v + 2*o + 6, -5*o = 10. Let b(i) = h*z(i) + v*t(i). Factor b(l).
(l + 5)**2
Let a(w) be the first derivative of -w**3/9 + 269*w**2/6 - 268*w/3 + 2774. What is h in a(h) = 0?
1, 268
Let r(k) = -k**3 - k**2 + 6*k + 8. Let a be r(-1). Factor -6*s - 5*s**2 - 5*s + a*s - 5*s - s.
-5*s*(s + 3)
Let d be (-204)/153 - (-1 + (-2)/8)*(42 - 38). Factor -d - 10/3*v + 4*v**2 + 10/3*v**3 - 1/3*v**4.
-(v - 11)*(v - 1)*(v + 1)**2/3
Let 3*k**5 - 2445*k**4 - 7876164*k**2 + 2*k**5 - 38451*k**3 - 15044496*k**2 + 439411*k**3 - 42515280 + 64560240*k + 477180*k**2 = 0. Calculate k.
1, 2, 162
Let o = -487 + 21919/45. Let f(s) be the third derivative of 0 + o*s**3 + 0*s - 49/900*s**6 + 8*s**2 + 7/150*s**5 + 2/15*s**4. Factor f(b).
-2*(b - 1)*(7*b + 2)**2/15
Let g(h) be the first derivative of 44*h**2 + 48*h - 2/5*h**5 + 44/3*h**3 + 1/2*h**4 - 41. Suppose g(z) = 0. Calculate z.
-2, -1, 6
Factor 48 + 2/7*w**2 - 172/7*w.
2*(w - 84)*(w - 2)/7
Suppose -14 + 5 = -4*a + 3. Let s(d) be the third derivative of -1/100*d**5 - 1/5*d**a - 3/40*d**4 - d**2 + 0*d + 0. Factor s(n).
-3*(n + 1)*(n + 2)/5
Let v be ((-616)/(-847))/((-18)/(-33)). Let d(q) be the first derivative of 0*q**2 + 0*q + 1/2*q**4 + v*q**3 + 26. Let d(o) = 0. Calculate o.
-2, 0
Solve -669*a**3 - 3300 + 16924*a**5 - 39*a**4 - 4920*a - 2697*a**2 - 16927*a**5 - 36*a**4 = 0.
-11, -5, -2
Factor -2/9 - 32768/9*r**2 + 512/9*r.
-2*(128*r - 1)**2/9
Let g = -20/63 - 134023/63. Let o = 2129 + g. Let -4/3*j**4 + 0*j + o*j**2 + 4/9*j**5 - 4/9*j**3 + 0 = 0. Calculate j.
-1, 0, 1, 3
Let d(n) be the first derivative of n**6/15 + n**5/5 + n**4/6 + 26*n + 101. Let c(y) be the first derivative of d(y). Factor c(f).
2*f**2*(f + 1)**2
Let b(v) = -v**2 + 73*v - 72. Let g(x) = -x**2 + 145*x - 144. Suppose 0 = 2*j + 19 - 5. Let n(r) = j*b(r) + 3*g(r). Solve n(c) = 0 for c.
1, 18
Let d(r) be the third derivative of r**5/60 + 497*r**4/6 + 494018*r**3/3 + 2780*r**2. Suppose d(k) = 0. Calculate k.
-994
Let l be (765/(-18))/(-17)*378/315. Let -16/3*h**4 + 8/3*h**l - 14/3*h + 2*h**5 + 4/3 + 4*h**2 = 0. What is h?
-1, 2/3, 1
Let x = 22 - 16. Let u(t) = -30*t - 3*t + x*t**2 - 12 - 45*t**2 + 15*t**2. Let n(m) = -m**3 - 23*m**2 - 33*m - 13. Let w(h) = -3*n(h) + 2*u(h). Factor w(c).
3*(c + 1)**2*(c + 5)
Suppose 192*f - 3042 = -10*f - 32*f. Let q(t) be the first derivative of -1/5*t**5 + t**3 + 1/2*t**4 - 2*t**2 - f - 4*t. Solve q(j) = 0 for j.
-1, 2
Let n(m) = 5*m**4 - 32*m**3 - 532*m**2 - 951*m - 456. Let u(y) = -5*y**4 + 33*y**3 + 533*y**2 + 949*y + 454. Let p(r) = 2*n(r) + 3*u(r). Factor p(c).
-5*(c - 15)*(c + 1)**2*(c + 6)
Let j(r) be the first derivative of r**3 - 36*r**2 - 316. Factor j(k).
3*k*(k - 24)
Let q be (-2)/6 - (-44)/(-3). Let b = -11 - q. Find t, given that 9*t - 8*t - b*t**2 + 11*t + 7*t**2 = 0.
-4, 0
Solve -1456/5*x**2 - 2/5 - 106/5*x - 1352/5*x**3 = 0.
-1, -1/26
Suppose 0 = -2*m + 127*x - 129*x - 8, 4*x + 18 = -3*m. Find t, given that 11/3*t + 5/6*t**m + 4/3 - 3/2*t**3 = 0.
-1, -4/9, 2
Let k(s) = s**3 - 20*s**2 - 4*s + 11. Let o(n) = 3*n**3 + 23*n - 3*n**3 - 120 - 12*n**3 + 28*n + 222*n**2 - 5*n. Let r(p) = -68*k(p) - 6*o(p). Solve r(w) = 0.
-7, -1, 1
Let n(m) be the first derivative of -5/3*m**3 + 5/4*m**4 - 25/2*m**2 - 15*m + 11. Determine q so that n(q) = 0.
-1, 3
Let j(u) be the second derivative of 3*u**7/70 + u**6/8 + u**5/20 - u**4/8 - 21*u**2/2 + 82*u. Let s(t) be the first derivative of j(t). Solve s(y) = 0.
-1, 0, 1/3
Let p(f) be the first derivative of 1331*f**6/54 + 1573*f**5/45 - 616*f**4/9 - 536*f**3/27 + 40*f**2/9 + 16*f/9 + 389. Solve p(b) = 0 for b.
-2, -2/11, 2/11, 1
Let h(g) be the first derivative of 129 - 15*g**4 - 420*g**2 - 392*g - 2/5*g**5 - 506/3*g**3. Determine v so that h(v) = 0.
-14, -1
Suppose -13*d = -12*d - 4*q - 24, 10*d = q + 45. Let x(c) be the first derivative of -8*c - 4 - 2*c**2 + 2/3*c**3 + 1/4*c**d. What is p in x(p) = 0?
-2, 2
Factor 2542644/11*b**3 + 7848/11*b**4 + 6/11*b**5 - 15468408/11*b**2 + 0 + 23309046/11*b.
6*b*(b - 3)**2*(b + 657)**2/11
Let q(l) be the first derivative of -5*l**3/3 + 2135*l**2 + 4275*l - 6427. Suppose q(a) = 0. Calculate a.
-1, 855
Let i be (-8 + -1514)/(5/10*-8). Let z = i - 376. Factor 3/2*n**2 - z + 3*n.
3*(n - 1)*(n + 3)/2
Let 0 - 4/7*d**3 - 112*d**2 + 788/7*d = 0. Calculate d.
-197, 0, 1
Let x(n) be the second derivative of 3*n**7/14 + 11*n**6/30 + n**4/4 + 31*n. Let j(f) = 5*f**5 + 6*f**4 + 2*f**2. Let r(t) = 5*j(t) - 3*x(t). Factor r(s).
-s**2*(s + 1)**2*(2*s - 1)
Let c be (5/(-90)*69 - -5)*(7 - 4). Factor -3*i + c*i**2 - 1/2*i**3 + 0.
-i*(i - 6)*(i - 1)/2
Factor 4*k**2 + 19128088 - 16*k**2 + 10*k**2 + 8116*k + 3*k**2 - 2660724.
(k + 4058)**2
Let j = 98 - 45. Let a be (-6)/(-1 + 3 + -4). What is f in -2 + 5 + 4*f**5 + 24*f**4 + 24*f + 1 + 53*f**a + j*f**2 = 0?
-2, -1, -1/2
Let 270*j + 189/2*j**2 + 3/2*j**3 + 0 = 0. Calculate j.
-60, -3, 0
Let l(v) = 45*v**3 - 100*v**2 + 235*v + 555. Let h(k) = -11*k**3 + 25*k**2 - 56*k - 138. Let m(j) = 25*h(j) + 6*l(j). Factor m(z).
-5*(z - 4)*(z - 3)*(z + 2)
Let o be ((-1)/(-4) - 0)*(-64)/(-1). Let j(d) be the first derivative of 25 + o*d - 20/3*d**3 + 16*d**2. Factor j(b).
-4*(b - 2)*(5*b + 2)
Let b(o) be the first derivative of 2*o**3/9 - o**2/9 - 1488. Factor b(v).
2*v*(3*v - 1)/9
Factor 128*u**4 - 23*u**4 + 12*u - 77173*u**3 + 192*u**2 + 76864*u**3.
3*u*(u - 2)*(u - 1)*(35*u + 2)
Let f(g) be the first derivative of 57 - 3/4*g**4 + 12*g**2 - 2*g**3 + 0*g. Factor f(k).
-3*k*(k - 2)*(k + 4)
Let y be (1/(-5))/((173/(-3460))/((-5)/(-25))). Determine x, given that -4/3*x**2 + 8/15*x**4 - 2/15*x**5 + 0*x**3 + 2/15*x + y = 0.
-1, 1, 2, 3
Suppose 6*g = -9*g + 6*g - 18*g. Factor 7/6*a + g + 1/6*a**2.
a*(a + 7)/6
Factor 0 + 76/17*n**2 + 2/17*n**3 + 0*n.
2*n**2*(n + 38)/17
Factor 1088/5 - 1/5*m**2 + 542/5*m.
-(m - 544)*(m + 2)/5
Let t(q) = -q**3 - 18*q**2 + 450*q + 64. Let y be t(-32). Let a(j) be the second derivative of 1/80*j**5 + 14*j + 1/4*j**2 + y*j**4 - 1/8*j**3 + 0. Factor a(f).
(f - 1)**2*(f + 2)/4
Suppose -2*w - g = g, -6*w + 7*w + 5*g = 0. Let b(l) be the first derivative of 4*l**2 + w*l - 5 - 4/3*l**3. Factor b(j).
-4*j*(j - 2)
Suppose 2*m - l - 1 = 0, 0 = -126*m + 116*m - 5*l + 35. Determine d so that 7/2*d**m + 1/2*d**3 - 4*d + 0 = 0.
-8, 0, 1
Let c(q) be the third derivative of -q**9/393120 - q**8/43680 - q**7/16380 - 57*q**5/20 + 140*q**2. Let t(k) be the third derivative of c(k). Factor t(w).
-2*w*(w + 1)*(w + 2)/13
Let g(n) = 1022*n + 3079. Let v be g(-3). Let w(b) be the third derivative of -v*b**2 + 0*b + 0 + 1/420*b**5 + 0*b**3 + 0*b**4. Factor w(y).
y**2/7
Let f(p) = -11*p**2 - 83*p - 122. Let j(v) = v**2 + 5*v + 3. Let z(b) = f(b) + 6*j(b). Factor z(s).
-(s + 8