- 89/15*c**3. Find g, given that h(g) = 0.
-1/6, 1/3, 10
Let k(c) be the third derivative of c**6/480 - 9*c**5/20 + 71*c**4/32 - 53*c**3/12 + 18*c**2 - 14*c. Factor k(t).
(t - 106)*(t - 1)**2/4
Suppose -14 - 321 = -5*l. Let o be (210/33)/(-2) + l + -62. Suppose 24/11*m**2 + 2/11*m**4 + o*m + 6/11 + 12/11*m**3 = 0. What is m?
-3, -1
Let b(l) be the third derivative of 85/24*l**4 + 5/6*l**5 + 20/3*l**3 + 1/24*l**6 + 52*l**2 + 0*l + 0. Factor b(c).
5*(c + 1)**2*(c + 8)
Suppose 3*f = 5*o + 3, 6*f - f - 4*o - 5 = 0. Let g(w) be the first derivative of 10*w**3 - 3*w**2 - w + 15*w**3 - f - 28*w**3. Factor g(t).
-(3*t + 1)**2
Let y(k) be the second derivative of -5*k**7/14 + 371*k**6/6 + 499*k**5/4 + 625*k**4/12 - 31*k - 15. Determine s, given that y(s) = 0.
-1, -1/3, 0, 125
Suppose 9*m - 300 = 5*m. Find l, given that -70*l + m + 152*l**2 - 311*l**2 + 154*l**2 = 0.
-15, 1
Let u(x) = -4*x**3 - 588*x**2 - 85260*x + 85849. Let g(j) = -15*j**3 - 2351*j**2 - 341041*j + 343396. Let c(n) = -6*g(n) + 22*u(n). Find b such that c(b) = 0.
-293, 1
Let x(y) be the third derivative of y**8/168 - 31*y**7/105 + y**6/2 - 2*y**2 - 1306*y + 1. Solve x(g) = 0 for g.
0, 1, 30
Let r(o) be the second derivative of o**6/30 + 587*o**5/20 + 86435*o**4/12 + 85849*o**3/6 - 3*o + 557. Find y such that r(y) = 0.
-293, -1, 0
Let s = 3929 - 3929. Let x(u) be the first derivative of 3/8*u + s*u**3 + 22 - 3/8*u**2 + 3/16*u**4 - 3/40*u**5. Suppose x(w) = 0. What is w?
-1, 1
Suppose -18 = -10*s + 13*s. Let m be (-5 - s)/((-2)/(-102)). Determine c, given that -m*c**3 - 4 - 3*c**2 + 50*c**3 + 6*c**2 = 0.
-1, 2
Factor 872*j + 4/5*j**2 + 237620.
4*(j + 545)**2/5
Let i(y) be the second derivative of -y**4/18 - 22*y**3/3 + 69*y**2 + 1355*y. Factor i(d).
-2*(d - 3)*(d + 69)/3
Let c(m) be the second derivative of -m**7/3150 - 7*m**6/900 + 3*m**4/2 + 24*m + 1. Let s(d) be the third derivative of c(d). Factor s(y).
-4*y*(y + 7)/5
Let p(g) be the second derivative of 12*g**3 + 27/20*g**5 - 6*g**2 - 6*g - 29/4*g**4 + 5. Determine o so that p(o) = 0.
2/9, 1, 2
Let u(h) be the third derivative of 7*h**7/30 - 259*h**6/24 + 773*h**5/10 + 743*h**4/6 + 220*h**3/3 + 36*h**2 - 106. Find z, given that u(z) = 0.
-2/7, 5, 22
Let r(i) = -5*i**2 + 15*i - 21. Let v(p) = -4*p**2 + 14*p - 20. Let c(q) = -q + 12. Let d be c(6). Let j = 4 - d. Let y(h) = j*r(h) + 3*v(h). Factor y(s).
-2*(s - 3)**2
Let b = -127526/39 - -42513/13. Let 0 - c - 2/3*c**2 + b*c**3 = 0. What is c?
-1, 0, 3
Let j = 3827/458 - 1799/229. Find y, given that 3*y + 0 + j*y**2 - 1/6*y**3 = 0.
-3, 0, 6
Let q(t) = 13*t**2 + t - 1. Let l(i) = -144*i**2 - 107*i - 612. Let y(h) = l(h) + 11*q(h). Let y(v) = 0. Calculate v.
-89, -7
Let q be 61 + -60 - 4/((-2)/1). Let u(k) = 8*k - 22. Let n be u(q). Factor 24*v - 12*v**3 - 4*v**n + 2*v**4 - 58 + 4*v**3 + 76.
2*(v - 3)**2*(v + 1)**2
Let r(y) be the third derivative of -y**6/60 + y**5/6 + 3*y**4 - 901*y**2. Suppose r(c) = 0. What is c?
-4, 0, 9
Let r(p) be the first derivative of 21*p**2/2 - 19*p + 187. Let j be r(1). Suppose -j*z**3 - 4/3*z**5 + 8/3*z - 14/3*z**4 + 0 + 16/3*z**2 = 0. What is z?
-2, -1/2, 0, 1
Let s = 32 - 44. Let u = -9 - s. Solve 24*o**2 - u*o - 8*o**2 - 3*o**2 - 12*o**2 = 0 for o.
0, 3
Suppose 20/7*t + 2/7*t**5 + 2/7*t**4 - 16/7 + 2*t**2 - 22/7*t**3 = 0. What is t?
-4, -1, 1, 2
Find o such that -324/7*o**2 + 8/7*o**4 + 46/7*o**3 - 432/7 - 2/7*o**5 + 648/7*o = 0.
-6, 2, 3
Suppose 3*p - 118 = 4*f, -p = 26*f - 30*f - 50. Let v be (-4)/p - (-551)/1938. Let -v*j - 1/3*j**2 + 1/3 + 1/6*j**3 = 0. What is j?
-1, 1, 2
Let g = -296 - -298. Factor -4493 - 2*i + 4493 + i**g + i**3.
i*(i - 1)*(i + 2)
Suppose 50*w**2 - 2*w**3 - 14*w - 15*w + 0*w**3 - 792 - 67*w = 0. Calculate w.
-3, 6, 22
Let n be (20/(-12))/(80/(-672)). Let i(v) be the third derivative of n*v**2 - 25/9*v**3 + 0*v - 1/90*v**5 + 0 - 5/18*v**4. Factor i(o).
-2*(o + 5)**2/3
Let m(t) be the third derivative of 75/8*t**3 + 102*t**2 + 0 - 65/32*t**4 + 0*t - 1/96*t**6 + 11/48*t**5. Determine l, given that m(l) = 0.
3, 5
Let w(x) be the third derivative of -6*x + 0 - 23/20*x**5 + 18*x**3 - 6*x**2 + 3*x**4 - 9/70*x**7 - 1/112*x**8 - 27/40*x**6. Let w(z) = 0. What is z?
-3, -2, 1
Let 50/11*u + 228/11 + 2/11*u**2 = 0. What is u?
-19, -6
Let d(m) = 13*m**3 - 85*m**2 + 143*m - 71. Let k = 468 - 454. Let i(s) = 6*s**3 - 41*s**2 + 71*s - 35. Let z(p) = k*i(p) - 6*d(p). Let z(j) = 0. Calculate j.
2/3, 2, 8
Let w(r) be the first derivative of r**5/5 + 3*r**4 - 61*r**3/3 + 24*r**2 - 7020. Determine g so that w(g) = 0.
-16, 0, 1, 3
Let l(w) = w**2 - 6*w + 10. Let m(y) = 2*y - 15. Let j be m(10). Let a be l(j). Factor q + 0*q - 3*q**2 - 8*q - 12 - a*q.
-3*(q + 2)**2
Factor 324/5*i**2 + 642/5*i + 64 + 2/5*i**3.
2*(i + 1)**2*(i + 160)/5
Suppose 6*w = -7*w + 22*w - 189. Let q(y) be the third derivative of -1/90*y**5 + 0*y + 1/18*y**4 + 0 + 4/9*y**3 + w*y**2 - 1/360*y**6. Factor q(v).
-(v - 2)*(v + 2)**2/3
Find t, given that 1/6*t**2 + 266/3 + 47/6*t = 0.
-28, -19
Factor -1/6*a**2 - 28*a - 167/6.
-(a + 1)*(a + 167)/6
Let c(m) be the first derivative of 34 + 0*m**5 - 9/2*m**2 + 2*m**3 - 1/2*m**6 + 3*m**4 - 6*m. Factor c(t).
-3*(t - 2)*(t - 1)*(t + 1)**3
Solve -108/5 + 2/5*y**3 - 24/5*y**2 + 18*y = 0 for y.
3, 6
Let f(w) be the first derivative of w**5/5 - 43*w**4 + 170*w**3 - 254*w**2 + 169*w + 2126. Determine c, given that f(c) = 0.
1, 169
Let q = 1219/16 + -20627/272. Let a = 1 - -1. Factor q*p - 4/17 - 2/17*p**a.
-2*(p - 2)*(p - 1)/17
Factor 1/4*h**5 + 40*h - 19/4*h**4 - 12 - 193/4*h**2 + 99/4*h**3.
(h - 12)*(h - 4)*(h - 1)**3/4
Let f(m) be the second derivative of m**4/6 - 241*m**3 - 724*m**2 - 72*m + 7. Suppose f(c) = 0. What is c?
-1, 724
Suppose 327*y = 348*y - 105. Let f(n) be the second derivative of -16*n + 0 + 7/30*n**4 - 3/50*n**y - 2/15*n**3 + 0*n**2. Suppose f(g) = 0. What is g?
0, 1/3, 2
Let n(s) be the first derivative of 3/2*s**2 + 1/9*s**3 + 8/3*s - 59. Find x such that n(x) = 0.
-8, -1
Suppose 3*m + 4*b = 9737 - 9675, -5*m = 2*b - 38. Factor 0*d**m + 0 + 0*d - 1/5*d**4 + 4/5*d**3.
-d**3*(d - 4)/5
Let y(r) be the third derivative of -r**7/140 + 137*r**6/80 - 4623*r**5/40 - 4761*r**4/16 + 535*r**2. Find k such that y(k) = 0.
-1, 0, 69
Let x be (2 - 0) + 50/5. Let l(y) = -y**3 + 12*y**2 + y - 7. Let t be l(x). Determine g so that t - g**2 - 10*g + 4 + 4*g - 2*g**2 = 0.
-3, 1
Suppose -2*y - 4*o = -268, 4*o - 533 = -4*y - o. Find u, given that -y*u + 3*u**2 + 69*u + 69*u - 9 = 0.
-3, 1
Let o(w) be the second derivative of -w**5/5 - 11*w**4 + 224*w**3/3 + 288*w**2 + 346*w. Factor o(b).
-4*(b - 4)*(b + 1)*(b + 36)
Let u(x) be the first derivative of -x**4/24 - x**3/9 + 11*x**2/12 + 2*x + 844. Factor u(w).
-(w - 3)*(w + 1)*(w + 4)/6
Suppose 13*w = -3*i - 46, 4*w + 16 + 4 = 2*i. Let h(k) be the third derivative of 0 + 2*k**3 - 1/15*k**5 - 20*k**i - 1/3*k**4 + 0*k. Factor h(y).
-4*(y - 1)*(y + 3)
Suppose -3*f - 5*m + 228 - 133 = 0, -5*f + 55 = -2*m. Let 0*h - 18*h**5 - 3/2*h**2 - f*h**3 + 0 + 69/2*h**4 = 0. What is h?
-1/12, 0, 1
Let z(u) = -42 - 3*u + 2*u**2 + 37 - 8*u. Let p(v) = 9 - 3*v**2 + 20*v + 5*v**2 + v - 5*v**2. Let g(m) = 5*p(m) + 9*z(m). Factor g(b).
3*b*(b + 2)
Let x(a) be the first derivative of -a**5 + 6 + 5/3*a**3 + 0*a - 1/6*a**6 + 2*a**2 - 3/4*a**4. Factor x(l).
-l*(l - 1)*(l + 1)**2*(l + 4)
Let a(s) be the third derivative of 571787*s**6/40 - 20667*s**5 + 12450*s**4 - 4000*s**3 - 3009*s**2. Solve a(b) = 0 for b.
20/83
Let o(m) = 9*m**2 + 34*m**2 - 7*m**4 - 21*m**3 - 10*m - 13 + 18. Let k(s) = 7*s**4 + 20*s**3 - 43*s**2 + 10*s - 6. Let i(f) = -5*k(f) - 6*o(f). Factor i(r).
r*(r - 1)*(r + 5)*(7*r - 2)
Let u(f) = -f**3 - 10*f**2 - 4*f + 53. Let j be u(-9). Suppose -31 = -2*k + j*b - 11, 5*k + 4*b - 2 = 0. Factor -64/5 + 32/5*n - 4/5*n**k.
-4*(n - 4)**2/5
Let h(v) = -286*v**3 + 1246*v**2 - 46660*v + 294584. Let a(i) = 10*i**3 - 43*i**2 + 1609*i - 10158. Let f(p) = -172*a(p) - 6*h(p). Let f(x) = 0. Calculate x.
-42, 11
Let g(l) be the third derivative of l**6/540 + l**5/18 + 13*l**4/54 - 40*l**3/9 - 2644*l**2. Factor g(o).
2*(o - 2)*(o + 5)*(o + 12)/9
Solve 136/7*m**2 + 2/7*m - 278/7*m**3 + 20*m**4 + 0 = 0 for m.
-1/70, 0, 1
Let n(s) be the first derivative of s**7/210 + s**6/120 - s**5/60 - s**4/24 - 41*s**2/2 - 71. Let q(k) be t