 + p*v**3 + 44*v**2 - 11*v**2 + 18*v - 18*v**4.
3*v*(v + 1)*(v + 2)*(v + 3)
Let p(d) be the first derivative of 1/12*d**3 - 5/2*d + 3/8*d**2 + 120. Factor p(u).
(u - 2)*(u + 5)/4
Let j = -2/3419 - -54710/10257. Let q(m) be the first derivative of j*m + 19 + 16/3*m**2 + 4/3*m**3. What is o in q(o) = 0?
-2, -2/3
Let p = 99 - 32. Let -p*l - l**3 - 3*l + 16*l**2 + 6*l = 0. Calculate l.
0, 8
Suppose -21*z + 20*z + 45 = 0. Let a = z - 43. Suppose -2*p**2 + 2*p**2 - 2*p**a + 2*p + 0*p**2 = 0. Calculate p.
0, 1
Let s(f) be the third derivative of 3*f**5/100 + 401*f**4/24 - 223*f**3/15 - f**2 + 3*f + 364. Find m, given that s(m) = 0.
-223, 2/9
Let w(y) be the first derivative of y**3/15 - 229*y**2/5 + 52441*y/5 - 4161. Factor w(d).
(d - 229)**2/5
Let z(m) be the second derivative of 0*m**2 + 0 + 48*m - 2/11*m**3 + 7/165*m**6 - 3/11*m**5 + 29/66*m**4. Find o, given that z(o) = 0.
0, 2/7, 1, 3
Let q be (3/(-54))/(10/(-54)*6). Let i(j) be the third derivative of 8*j**2 + 0*j + q*j**5 + 0 + 0*j**3 - 1/8*j**4. What is l in i(l) = 0?
0, 1
Factor 30*m - 115*m**3 - 20*m - 2*m**4 - 570*m**2 - 10*m + 47*m**3.
-2*m**2*(m + 15)*(m + 19)
Let b(q) be the second derivative of -7/24*q**4 - 9*q - 2 - 1/40*q**5 + 4*q**2 - 2/3*q**3. Factor b(u).
-(u - 1)*(u + 4)**2/2
Suppose -128*u + 209*u - 486 = 0. Let w(g) = -g - 6. Let o be w(-6). Let 4*i**3 + 3*i**2 - 2*i + o*i - u*i**3 + i**2 = 0. What is i?
0, 1
Let q be ((-341172)/(-312))/(-243)*(-4)/63. Factor -4*c**2 + 0*c + 0 - 18/7*c**3 - q*c**4.
-2*c**2*(c + 2)*(c + 7)/7
Let c(w) be the first derivative of -2*w**3/21 - 51*w**2/7 - 540*w/7 + 800. Suppose c(d) = 0. What is d?
-45, -6
Suppose 206*j + n + 1 = 205*j, -11*j + 2*n = -28. Solve 15/2*f**j - 5/2*f**3 + 15*f - 20 = 0 for f.
-2, 1, 4
Let u(w) = -w + 1. Let t(o) = -2*o**3 - 3*o + 11. Suppose 132*f + 12 = 126*f. Let x(s) = f*t(s) + 22*u(s). Factor x(v).
4*v*(v - 2)*(v + 2)
Let r(n) = -2*n - 22. Let k be r(-6). Let u = 12 + k. Factor -7*p + 4 - 2*p**u + 4*p + p.
-2*(p - 1)*(p + 2)
Let i(v) = v**2 - 1159*v + 41479. Let z(p) = 2*p**2 - 1738*p + 62218. Let m(a) = -10*i(a) + 7*z(a). Factor m(u).
4*(u - 72)**2
Let i = -190683 + 190683. Factor i - 2/11*k + 2/11*k**3 + 0*k**2.
2*k*(k - 1)*(k + 1)/11
Let c(t) be the second derivative of -2/7*t**4 + 0 + 47*t + 4/21*t**3 + 13/70*t**5 - 2/35*t**6 + 0*t**2 + 1/147*t**7. Solve c(d) = 0.
0, 1, 2
Let p be 37/(-35) + 5*42/150. Let n(m) be the first derivative of p*m**5 + 2/7*m**2 + 24/7*m - 5/7*m**4 - 19 - 52/21*m**3. Let n(u) = 0. What is u?
-1, 2/3, 3
Suppose -14*g + 3*m = -19, -1500*g + 1498*g - 4*m + 16 = 0. Suppose 5/6*t**4 + 7/3*t**3 - 10/3*t + 2/3 - 1/2*t**g = 0. Calculate t.
-2, 1/5, 1
Let n(w) = -2*w + 52. Let c be n(6). Suppose 0 = 7*u + 3*u - c. Factor 5*y**2 + y**3 + 3*y**2 - u*y**3 + 9*y - 2*y**2.
-3*y*(y - 3)*(y + 1)
Suppose 5*t - 528 = -2*z, -3*z - 17037 = -3*t - 16653. Solve -1/7*c**2 - 8*c - t = 0.
-28
Let -9 - 9/2*i**3 + 3/4*i**4 + 27/4*i**2 + 3*i = 0. Calculate i.
-1, 2, 3
Suppose -2*t = -h - 13, -5*t + 3*h + 27 = -2*t. Suppose -28 = -t*z - 12. Suppose -7*a**3 + 6*a**3 + 3*a**2 + 11*a**3 - a**3 + 6*a**z = 0. Calculate a.
-1, -1/2, 0
Let o = -33 - -35. Suppose o*j - 30 = -5*w, -4*w + 0*j = 2*j - 26. Factor 31 + 17 + 23*z**2 + 3*z**2 + 64*z + 2*z**2 + w*z**3.
4*(z + 2)**2*(z + 3)
Let u(s) be the second derivative of s**6/15 + 41*s**5/5 - 167*s**4/6 + 28*s**3 - 1766*s. Solve u(b) = 0.
-84, 0, 1
Let t = 931030 + -931028. Factor -1/6*g**t - 5/2 + 4/3*g.
-(g - 5)*(g - 3)/6
Let t(o) = 3600*o**2 - 3616*o - 22. Let k(y) = -480*y**2 + 482*y + 3. Let u(x) = 38*k(x) + 5*t(x). Determine w so that u(w) = 0.
-1/60, 1
Suppose -2*j - o + 12 = 0, j - 2*o + 5 = 1. Determine u, given that 71*u + 14*u**2 + 2*u**j + 11*u - 88*u - 10*u**3 = 0.
0, 1, 3
Let 0*w + 2/15*w**4 - 8/5*w**3 + 0 + 24/5*w**2 = 0. What is w?
0, 6
Let c(m) be the third derivative of m**5/100 - 39*m**4/40 - 41*m**3/5 + 526*m**2 + 1. Factor c(g).
3*(g - 41)*(g + 2)/5
Suppose 0 = -4*g + 2*t + 18, -209*t + 205*t = 3*g - 8. Let v(b) be the second derivative of 0*b**2 - 10*b - 1/20*b**5 - 1/4*b**g + 0*b**3 + 0. Factor v(o).
-o**2*(o + 3)
Let l(b) be the first derivative of b**6/180 - 13*b**5/60 + 11*b**4/6 + b**3/3 + 31*b**2 - 68. Let i(n) be the third derivative of l(n). What is y in i(y) = 0?
2, 11
Let o(w) be the third derivative of -w**6/660 + 4*w**5/165 - 5*w**4/132 - 50*w**3/33 + 561*w**2. Factor o(h).
-2*(h - 5)**2*(h + 2)/11
Let x be (18/27)/(2/9). Suppose 7053*q + 18 + 4*q**2 + 26*q**2 + x*q**2 - 6948*q = 0. What is q?
-3, -2/11
Let u(l) be the first derivative of 225 - 2/75*l**5 - 1/10*l**4 - 2/45*l**3 + 1/5*l**2 + 4/15*l. What is b in u(b) = 0?
-2, -1, 1
Let z be 3 + -1 - ((-4 - -2) + 2). Factor 4332*v**z + 10 - 114*v - 7 - 114*v.
3*(38*v - 1)**2
Let 119/4*z**3 + 1417/4*z**2 + 1/2*z**4 + 2205/4 + 5089/4*z = 0. Calculate z.
-45, -7, -1/2
Factor -201*c**2 - 151*c**2 - 228*c**2 - 43*c**3 - 138*c - 101*c**3 + 122*c.
-4*c*(c + 4)*(36*c + 1)
Find a such that -15/2*a**2 + 3/2*a**3 + 3*a + 12 = 0.
-1, 2, 4
Let b(d) be the first derivative of -2*d**3/15 + d**2/5 + 12*d/5 - 1014. Determine n, given that b(n) = 0.
-2, 3
Let h(a) = -a. Suppose -7*r = -10*r - 18. Let y be h(r). Let 3*d - 6*d**2 + y*d**2 - d**2 - d = 0. Calculate d.
0, 2
Let b(h) be the second derivative of -h**6/10 + 351*h**5/10 - 13209*h**4/4 - 28322*h**3 - 5070*h. Factor b(v).
-3*v*(v - 119)**2*(v + 4)
Let o be 28/(-126) + (-112)/(-18). Factor -o*w**2 + w + 33*w - 3*w**4 + 15 - 6*w**2 - 18*w**3 - 16*w.
-3*(w - 1)*(w + 1)**2*(w + 5)
Let y(t) be the first derivative of -t**4 - 20*t**3/3 + 72*t**2 - 3038. Suppose y(d) = 0. Calculate d.
-9, 0, 4
Let s = -44822 + 44826. Let p be 1/3*(2 + -1). Determine l, given that 0*l**3 + 1/6*l**s - p*l**2 + 1/6 + 0*l = 0.
-1, 1
Let r = -667 - -669. Let a be 5/(-15) + (r - 1). Factor 1/9*x**4 - 5/9*x**2 + 0 - a*x + 2/9*x**3.
x*(x - 2)*(x + 1)*(x + 3)/9
Let m(s) be the second derivative of -s**7/2520 + s**6/20 - 27*s**5/10 + 53*s**4/12 + 54*s. Let u(g) be the third derivative of m(g). Factor u(x).
-(x - 18)**2
Let o = 56 + -52. Let r(n) = 5*n - 17*n - 4*n**o + 12*n**3 + 5*n**2 + 7*n**2 + 5 + 3. Let k(y) = -y**3 - y**2 + y - 1. Let t(m) = -8*k(m) - r(m). Factor t(d).
4*d*(d - 1)**2*(d + 1)
Suppose 0*u - 4*u = 4*o - 672, 5*u - 890 = 5*o. Let z = u - 121. Factor -8*h**2 - 140*h + z*h**2 + 164 - 4*h**3 - 64.
-4*(h - 5)**2*(h - 1)
Let x be (81/5*-4)/((-1400)/500). Factor x + 3*g**3 - 3/7*g**4 - 81/7*g - 27/7*g**2.
-3*(g - 3)**3*(g + 2)/7
Let b(l) be the first derivative of -l**4/4 - l**3/2 + 3*l + 4. Let g(s) be the first derivative of b(s). Find u, given that g(u) = 0.
-1, 0
Let h(i) = 325*i**3 + 385*i**2 - 565*i - 145. Let g = 268 + -270. Let b(u) = -27*u**3 - 32*u**2 + 47*u + 12. Let w(f) = g*h(f) - 25*b(f). Factor w(r).
5*(r - 1)*(r + 2)*(5*r + 1)
Let y = -7 + -48. Let d = y + 57. Factor 26*s**2 - 5*s**3 + s**3 + s**4 - 4*s + 1 - 20*s**d.
(s - 1)**4
Suppose -66923416/9 + 164836/3*c + 1/9*c**3 - 406/3*c**2 = 0. Calculate c.
406
Let f(m) be the first derivative of -m**5 + 55*m**4/4 - 185*m**3/3 + 225*m**2/2 - 90*m + 966. What is o in f(o) = 0?
1, 3, 6
Let v be 572/910 - 6/14. Let m(y) be the third derivative of -10*y**2 + 1/40*y**4 - 1/100*y**5 + v*y**3 + 0*y + 0. Factor m(w).
-3*(w - 2)*(w + 1)/5
Let w(t) be the third derivative of 2*t**5/15 - 11*t**4/24 + 10*t**3/3 - 2*t**2 + 20*t. Let d(z) = -2*z**2 + z. Let v(n) = 10*d(n) + 2*w(n). Factor v(k).
-4*(k - 2)*(k + 5)
Let z be 4/(-10)*(864/720 + 1028/(-440)). Let 0*a + 1/11*a**4 + 6/11*a**2 + 0 - z*a**3 = 0. What is a?
0, 2, 3
Let d(m) be the third derivative of -m**8/2520 - m**7/420 + m**6/54 - 47*m**3/6 + 147*m**2. Let f(g) be the first derivative of d(g). Solve f(s) = 0 for s.
-5, 0, 2
Let 97579*y**2 - 69*y**3 + 1 + y**4 - 97799*y**2 + 266*y + 22*y - 1 = 0. Calculate y.
-4, 0, 1, 72
Suppose -64/3*k - 8 + 214/3*k**2 - 24*k**4 + 56/3*k**3 = 0. What is k?
-3/2, -2/9, 1/2, 2
Let u(f) be the second derivative of -f**6/60 + 3*f**5/8 - 35*f**4/24 - 5*f**3/4 + 9*f**2 + 58*f + 2. What is k in u(k) = 0?
-1, 1, 3, 12
Solve -5*d**4 - 607*d**3 - 115520*d**2 + 0*d + 4*d - 913*d**3 - 4*d = 0 for d.
-152, 0
Determine q, given that -2/13*q**3 - 64798/13*q + 722/13*q**2 - 65522/13 = 0.
-1, 181
Let v(y) be the first derivative of 3*y**5/5 + 93*y