*i*(i + 1)*(i + 2)**3
Factor -1/7*u**4 - 15625/7*u - 75/7*u**3 - 1875/7*u**2 + 0.
-u*(u + 25)**3/7
Let -26*g**2 - 2366*g + 245*g**2 - 1939*g + 0*g**3 + 11025 - 3*g**3 = 0. Calculate g.
3, 35
Let q(w) be the first derivative of -3/35*w**5 + 0*w + 42 + 3/14*w**4 - 3/7*w**2 + 1/7*w**3. Factor q(s).
-3*s*(s - 2)*(s - 1)*(s + 1)/7
Factor -6*c + 14 - 15/2*c**2 - 1/2*c**3.
-(c - 1)*(c + 2)*(c + 14)/2
Let z(p) = 7*p**2 - 8*p - 8. Let j be z(2). Solve -2*f - 674 - 7*f - j*f**2 - 3*f + 666 + 0*f = 0 for f.
-2, -1
Let c = 12/9185 - -91694/119405. Suppose 0 - 12/13*y**4 + 0*y**2 + 0*y + c*y**3 + 2/13*y**5 = 0. Calculate y.
0, 1, 5
Let r(h) = -5*h**3 + 62*h**2 - 187*h - 12. Let g be r(7). Let -1/8 + 1/8*o**3 + 3/8*o - 3/8*o**g = 0. Calculate o.
1
Let l(x) be the first derivative of x**6/15 + 4*x**5/25 - x**4/10 - 4*x**3/15 + 5595. Find m such that l(m) = 0.
-2, -1, 0, 1
Let h be (-1 - 18/(-21))*35364/(-8420). Determine p, given that 1/10*p**4 - 7/10*p**2 + h + 1/10*p**3 - 1/10*p = 0.
-3, -1, 1, 2
Let m = 5686519/920 - 6181. Let n = 231/920 + m. Let 1/4*f**4 + 1/4 - 1/8*f - 1/2*f**2 + n*f**3 - 1/8*f**5 = 0. Calculate f.
-1, 1, 2
Let s(y) be the first derivative of y**4/24 - 2*y**3 - 13*y**2/4 + 37*y/3 - 1784. Suppose s(h) = 0. Calculate h.
-2, 1, 37
Let n be 570/950 + 12/5. Let l(m) be the second derivative of -3*m + 10*m**n + 23/6*m**4 + 25/2*m**2 + 3/5*m**5 + 4 + 1/30*m**6. Solve l(x) = 0 for x.
-5, -1
Let t = 912/13 - 8171/130. Let k = 231/20 - t. Solve -k*y**4 - 1 + 3/4*y**5 - 39/4*y**2 + 5*y + 37/4*y**3 = 0.
2/3, 1, 2
Let u(t) be the second derivative of 2*t**7/189 + 2*t**6/27 - 89*t**5/45 + 65*t**4/9 + 15*t - 50. Determine y, given that u(y) = 0.
-13, 0, 3, 5
Let b(p) be the second derivative of 0*p**2 + 1/3*p**6 + 0*p**3 - 5/6*p**4 + 1/4*p**5 - 3*p - 5/42*p**7 + 15. What is x in b(x) = 0?
-1, 0, 1, 2
Suppose 4*d - d + 4*r = -2, 5*d = 4*r + 18. Factor 5*u + u - 32 - 7*u - 11*u + d*u**2.
2*(u - 8)*(u + 2)
Let a(n) be the second derivative of -n**6/225 + n**5/25 - 2*n**4/15 + 8*n**3/45 - 478*n. Find i such that a(i) = 0.
0, 2
Let h(i) be the first derivative of -i**5/15 - 17*i**4/12 + i**3/3 + 53*i**2/6 + 34*i/3 + 1369. Let h(a) = 0. What is a?
-17, -1, 2
Let j(s) be the third derivative of 5/24*s**4 - s**2 - 1/24*s**6 + 0*s + 6 + 0*s**5 + 0*s**3. What is b in j(b) = 0?
-1, 0, 1
Suppose 0 = -2*k - k - 2*w + 25, 3*w - 10 = k. Factor -14*j**2 - 10*j**2 - 2*j**4 + 16*j**3 - 5*j + k*j.
-2*j**2*(j - 6)*(j - 2)
Let c(a) be the first derivative of a**4/32 + a**3/3 + 5*a**2/4 + 2*a - 4563. Solve c(w) = 0.
-4, -2
Let s(q) = -q**4 + 39*q**3 + 61*q**2 + 3*q. Let p(k) = -41*k**3 - 60*k**2 - 4*k. Let w(i) = 6*p(i) + 5*s(i). Factor w(j).
-j*(j + 1)*(j + 9)*(5*j + 1)
Let v = 314 - 354. Let n(h) = -7*h**3 - 18*h**2 + 8*h - 8. Let t(g) = -g**3 + g - 1. Let x(k) = v*t(k) + 5*n(k). Solve x(a) = 0 for a.
0, 18
Suppose -1142*d + 1140*d = -198. Factor d*c**2 + 80 - 35*c**3 + 373*c - 39*c**2 - 73*c.
-5*(c - 4)*(c + 2)*(7*c + 2)
Let d(a) be the third derivative of -a**6/40 + 63*a**5/20 + 33*a**4 + 134*a**3 - 66*a**2 + 7. Factor d(f).
-3*(f - 67)*(f + 2)**2
Factor 832/9*y + 1/9*y**4 + 1/9*y**3 - 64/3*y**2 + 1024/9.
(y - 8)**2*(y + 1)*(y + 16)/9
Let i(o) be the second derivative of 10*o**6/3 - 49*o**5/4 - 305*o**4/6 - 85*o**3/6 + 90*o**2 - 6256*o. Determine v, given that i(v) = 0.
-1, 9/20, 4
Let k(q) be the third derivative of q**8/40320 + 11*q**7/10080 + q**6/144 + q**5/60 - 10*q**4/3 - 3*q**2. Let w(z) be the third derivative of k(z). Factor w(j).
(j + 1)*(j + 10)/2
Let h(a) be the first derivative of -a**7/70 - 5*a**6/8 + 13*a**5/10 - 53*a**2/2 - 8. Let c(l) be the second derivative of h(l). Factor c(k).
-3*k**2*(k - 1)*(k + 26)
Let h(w) be the third derivative of -11*w**6/300 - 7*w**5/25 - 3*w**4/5 + 8*w**3/15 - 1060*w**2 + 2. Factor h(l).
-2*(l + 2)**2*(11*l - 2)/5
Let v be 39*18/5850*5. Factor -3/5*f**4 + 9/5 + v*f**5 + 3*f - 18/5*f**3 - 6/5*f**2.
3*(f - 3)*(f - 1)*(f + 1)**3/5
Let k be (-7 + 6104/8)*-1. Let r = -754 - k. Suppose 3/2*x - r + 1/2*x**2 = 0. What is x?
-4, 1
Let x(q) be the first derivative of -q**6/1260 + q**4/84 - 208*q**3/3 - 144. Let k(t) be the third derivative of x(t). Factor k(d).
-2*(d - 1)*(d + 1)/7
Find g such that 61 - g**2 + 3*g**2 - 66*g - 10*g - 26*g + 227 = 0.
3, 48
Solve -175*l - 5*l**4 + 575*l**2 - 570 + 5369*l**3 - 2706*l**3 - 2488*l**3 = 0 for l.
-3, -1, 1, 38
Let y(c) = -11*c**5 - 3*c**4 - 9*c**3 - c**2 - 4*c + 4. Let p(o) = -13*o**5 - 2*o**4 - 10*o**3 - o**2 - 5*o + 5. Let k(b) = -4*p(b) + 5*y(b). Factor k(l).
-l**2*(l + 1)**2*(3*l + 1)
Let q(n) = -85*n**4 + 99*n**3 + 288*n**2 + 272*n + 93. Let d(i) = 200*i**4 - 196*i**3 - 577*i**2 - 543*i - 187. Let j(r) = 3*d(r) + 7*q(r). Factor j(z).
5*(z + 1)**3*(z + 18)
Factor -10*k + 52*k - 32161 + 32085 - 2*k**2.
-2*(k - 19)*(k - 2)
Let s = -199 - -199. Suppose -29*c + s*c = -116. What is y in 60/7*y**3 - 36/7*y**2 + 0 + 4/7*y**5 + 0*y - c*y**4 = 0?
0, 1, 3
Let r(n) be the third derivative of 0*n - 1/54*n**4 + 1/270*n**5 + 98*n**2 + 0*n**3 + 0. Solve r(i) = 0.
0, 2
Suppose -3*g = 2*q - 44, 24 = g + 9*q - 13*q. Suppose -6*x + 11*x**2 - 44*x**2 - 2*x**3 + 5*x**2 + 52 - g*x = 0. Calculate x.
-13, -2, 1
Let a be (-137)/(-7) + 36/84. Find t, given that 12*t**2 - 7289*t + 4*t**4 - 4*t**5 + 7289*t + a*t**3 = 0.
-1, 0, 3
Suppose 20*q - 27*q + 21 = 0. Suppose 23*f + 3*f**2 - 5*f + 0*f**q - 15*f**2 - 8 + 2*f**3 = 0. What is f?
1, 4
Let m(d) be the second derivative of 0 - 1/7*d**3 + 59*d + 1/42*d**4 - 4/7*d**2. Solve m(r) = 0.
-1, 4
Suppose 0*t - 1056/5*t**4 - 84*t**3 - 3*t**5 + 0 + 0*t**2 = 0. Calculate t.
-70, -2/5, 0
Solve 278*f**2 + 435*f**3 - 409*f**3 - 2*f**4 - 174*f**2 - 104*f - 384 = 0.
-3, -2, 2, 16
Let n(b) be the first derivative of b**5/50 - 11*b**4/10 + 159*b - 156. Let y(i) be the first derivative of n(i). Factor y(f).
2*f**2*(f - 33)/5
Suppose -29 - 29*z - 204*z**2 + 51*z + 11*z - 37*z + 233 + 4*z**3 = 0. What is z?
-1, 1, 51
Let j = -4980 + 4980. Let x(q) be the second derivative of -2/3*q**3 - 3*q + 0*q**4 + 0*q**2 + j + 1/5*q**5. Let x(u) = 0. What is u?
-1, 0, 1
Suppose -5*g + 27*g = 550. Factor 31*d**4 - 10*d**2 - 11*d**4 - 20*d**3 + g*d + 10 - 6*d**5 - 20 + d**5.
-5*(d - 2)*(d - 1)**3*(d + 1)
Let k(h) = -5363*h - 5360. Let g be k(-1). Suppose -17/4*w**2 + w**g + 4*w - 3/4 = 0. What is w?
1/4, 1, 3
Let a(u) = 15*u + 423. Let t be a(-6). Let i = t + -328. Determine l, given that 6/5*l**3 + 2/5*l**i + 0*l + 2/5*l**2 + 0 + 6/5*l**4 = 0.
-1, 0
Let p(f) be the first derivative of f**6/42 - 11*f**5/35 - 3*f**4/7 - 140. Determine d, given that p(d) = 0.
-1, 0, 12
Let t(j) = -10*j**4 - 531*j**3 - 1982*j**2 - 1898*j. Let g(m) = 2*m**4 + 106*m**3 + 396*m**2 + 380*m. Let b(d) = 11*g(d) + 2*t(d). Factor b(r).
2*r*(r + 2)**2*(r + 48)
Let r = 8 + -4. Let j = -5354 + 5357. Factor -3*c**r + 61*c**3 + 24*c + 9*c**2 + 12 - 119*c**3 + 52*c**j.
-3*(c - 2)*(c + 1)**2*(c + 2)
Let g(x) = -2*x**2 + 2*x. Let d be g(1). Let p(a) = 209*a - 11495. Let c be p(55). Factor 0 - 1/4*b**2 + 1/4*b**4 + c*b + d*b**3.
b**2*(b - 1)*(b + 1)/4
Suppose 2*g - 12 = -s + g, 5*g = 5*s - 110. Let i(n) be the first derivative of -6*n + s + 2*n**3 - n**3 - n + 4*n. Factor i(u).
3*(u - 1)*(u + 1)
Determine w, given that -61*w**3 + 139*w**2 - 524*w**2 + w**4 + 85*w**3 = 0.
-35, 0, 11
Let k(r) be the first derivative of 0*r**2 + 0*r**4 + 1/30*r**5 + 0*r**3 + 13*r - 3 + 1/90*r**6. Let l(q) be the first derivative of k(q). Factor l(h).
h**3*(h + 2)/3
Let n(s) = 3*s**3 - 6*s**2 + 7*s - 2. Let h be n(1). Suppose 0 = 2*a - 3*t, -h*a - 7 = -7*a + 4*t. Factor -5/2*j - 1/2*j**2 - a.
-(j + 2)*(j + 3)/2
Let u(t) be the third derivative of t**5/20 - 13*t**4/4 + 14*t**2 - 112. Solve u(c) = 0 for c.
0, 26
Factor -9*b**2 - 381*b - 21 - 31 + 16 + 660*b - 339*b.
-3*(b + 6)*(3*b + 2)
Let d(u) be the second derivative of u**6/70 - 9*u**4/28 - 2*u**3/7 + 18*u**2/7 + 7*u + 29. Solve d(m) = 0.
-2, 1, 3
Factor -5*s**2 + 1538*s + 86 + 31*s**2 + 230 - 80.
2*(s + 59)*(13*s + 2)
Let w = -29148443/731158 - 44/19241. Let f = -102/19 - w. Let -21/2*t**2 - 9 - f*t = 0. What is t?
-3, -2/7
Let s be (-27)/9 + 34/(-2). Let a = -14 - s. Determine l, given that a*l + 49 + 53 - 2*l**3 - 9*l**2 - 97 = 0.
-5, -1/2, 1
Let s(v) = v**4 - 49*v**3 - 28*v**2 + 39*v + 32. Let 