**4 + 0*h + 0. Determine w so that d(w) = 0.
-1, 0, 3
Suppose 20 + 10 = 6*k. Suppose -2*b + 10 = 2*i + b, 0 = -2*i - k*b + 2. Suppose -3*j**2 - 19 - i*j - j**3 + 12*j + 22 = 0. What is j?
-3, -1, 1
Suppose 3*g + 1 = y - 0*y, y + 2*g + 24 = 0. Let o = y - -16. Factor 36*u - 2*u**2 - 27*u**o + 4*u**3 + 5*u**2.
4*u*(u - 3)**2
Let w(u) be the first derivative of -3*u**4/4 + 800*u**3 + 4809*u**2/2 + 2406*u - 10050. Factor w(f).
-3*(f - 802)*(f + 1)**2
Let i(v) be the first derivative of -v**5/5 + v**4/4 + v**3 - v**2/2 - 2*v + 1094. Determine u, given that i(u) = 0.
-1, 1, 2
Factor 0 - 1/5*i**2 - 239/5*i.
-i*(i + 239)/5
Let g(z) be the first derivative of -16/17*z + 166 - 5/34*z**4 + 2/85*z**5 + 4/17*z**2 + 4/17*z**3. Factor g(q).
2*(q - 2)**3*(q + 1)/17
Let b(v) be the first derivative of -1/22*v**4 - 1932/11*v**2 - 308 + 60/11*v**3 - 8464/11*v. Suppose b(w) = 0. What is w?
-2, 46
Let j(m) be the second derivative of -m**4/3 + 8*m**3 + 216*m**2 - 4*m - 22. Factor j(k).
-4*(k - 18)*(k + 6)
Find t, given that -35 + t**2 + 1454*t - 735*t - 721*t = 0.
-5, 7
Suppose -56*m + j = -53*m + 94, 0 = 2*j - 2. Let x be ((3/8)/(m/310))/(-3). Find k, given that -1/2 - k**2 - 1/4*k**3 - x*k = 0.
-2, -1
Let o(a) be the first derivative of -a**3/7 - 3*a**2 - 135*a/7 - 5650. Suppose o(l) = 0. What is l?
-9, -5
Let g(d) be the second derivative of 8*d**7/21 - 2*d**6/3 - 83*d**5/5 + 185*d**4/3 - 242*d**3/3 + 40*d**2 - 270*d. Solve g(z) = 0.
-5, 1/4, 1, 4
Let i(j) = -5*j**3 + 31*j**2 - 75*j + 65. Let v = -484 - -489. Let z(d) = 5*d**3 - 30*d**2 + 75*d - 70. Let c(s) = v*i(s) + 4*z(s). Factor c(o).
-5*(o - 3)**2*(o - 1)
Let d(p) = 4*p**2 - 349*p + 941. Let o(t) = 2*t**2 - 173*t + 471. Let f(x) = 3*d(x) - 7*o(x). Solve f(s) = 0.
3, 79
Suppose -10*j**2 + 32*j**2 + 140*j**2 + 5*j**3 + 0*j**3 - 3*j**3 - 4752*j + 30240 = 0. What is j?
-105, 12
Let m(o) be the second derivative of o**5/120 - 5*o**4/24 + o**3 - 3*o + 199. Factor m(n).
n*(n - 12)*(n - 3)/6
Let m = 2666 + -2666. Let h(t) be the first derivative of m*t - t**3 + 21 - t**2 - 1/4*t**4. Determine j so that h(j) = 0.
-2, -1, 0
Let b be (36/(-52))/(1944/(-8424)). Factor 2/13 - 2/13*c**b + 6/13*c**2 - 6/13*c.
-2*(c - 1)**3/13
Let j = 2093943 - 2093939. Let y = -2/1659 - -59734/8295. Suppose 0 - m**j + y*m**2 + 16/5*m - 12/5*m**3 = 0. What is m?
-4, -2/5, 0, 2
Suppose -4*g + 4*r = 576, -3*g - 14*r + 16*r - 430 = 0. Let j = g + 145. Find h, given that 0*h + 0 - 7/3*h**j - 2*h**2 + h**4 = 0.
-2/3, 0, 3
Let q(p) be the first derivative of 5/12*p**4 + 0*p**2 - 8*p - 5/6*p**3 + 15. Let i(x) be the first derivative of q(x). Let i(l) = 0. What is l?
0, 1
Let o(y) = -3*y**2 + 11*y - 8. Suppose -9*l = -5*l - 8. Suppose -l*h - 20 = -32. Let q(u) = u**2 - 4*u + 3. Let z(c) = h*o(c) + 17*q(c). Factor z(t).
-(t - 1)*(t + 3)
Let l(a) be the second derivative of a**5/20 + 23*a**4/4 + 529*a**3/2 - 24*a**2 + 80*a. Let p(v) be the first derivative of l(v). What is c in p(c) = 0?
-23
Let w be (6/15)/((-39 - -31) + 1 + (-796)/(-110)). Find p, given that 30/13*p + 48/13*p**2 + 4/13 + w*p**3 = 0.
-1, -2/11
Let i = 1599 + -1595. Let l(p) be the second derivative of 1/6*p**i + 1/3*p**3 + 0*p**2 + 0 - 18*p. Factor l(r).
2*r*(r + 1)
Let u(o) = o**2 + o - 3. Let z be u(-3). Suppose -p = 3*d - 7, 12*p - 2*d - 2 = 11*p. Factor -4*x - x**z - 6*x**2 + 3*x**3 - p*x**3.
-2*x*(x + 1)*(x + 2)
Let k = -339266 + 339287. Solve 94/5*q**3 - 118/5*q - 24/5 - 3*q**4 - k*q**2 = 0.
-2/5, -1/3, 3, 4
Suppose -6*x = -x - 2*a - 588, -4*a + 594 = 5*x. Let d be -1 - ((-12)/(-36))/((-6)/x). Factor -20/9*n + d + 2/9*n**2.
2*(n - 5)**2/9
Let r be 24/27 - (-1610)/1449. Factor -44/3 - 40/3*s + 4/3*s**r.
4*(s - 11)*(s + 1)/3
Let b(d) be the third derivative of -d**8/2184 - 2*d**7/105 - 197*d**6/780 - 22*d**5/39 + 121*d**4/13 - 1553*d**2. Find r such that b(r) = 0.
-11, -6, 0, 2
Let s(l) be the first derivative of 0*l - 7*l**3 - 15*l**2 + 184 - 3/4*l**4. Suppose s(m) = 0. Calculate m.
-5, -2, 0
Suppose -5*y = s - 85, 5*s + 174*y = 177*y - 51. Let 16/11*g - 10/11*g**4 - 60/11*g**2 + s + 54/11*g**3 = 0. Calculate g.
0, 2/5, 1, 4
Let u(t) be the second derivative of -19*t**5/100 - 511*t**4/60 + 293*t**3/15 - 28*t**2/5 - 1284*t. Suppose u(r) = 0. Calculate r.
-28, 2/19, 1
Let l = 408 - 478. Let v be (245/l)/(1/(-2)). Factor 1/4 - v*h**2 + 5/4*h - 8*h**3.
-(h + 1)*(4*h - 1)*(8*h + 1)/4
Let f(t) be the second derivative of 5*t**7/42 + 4*t**6/3 + 9*t**5/2 + 20*t**4/3 + 25*t**3/6 - 898*t. Factor f(m).
5*m*(m + 1)**3*(m + 5)
Let k(m) be the third derivative of 0*m + 1/3*m**4 + 58 - 13/25*m**5 - 2/75*m**6 + 0*m**3 + m**2. Determine i so that k(i) = 0.
-10, 0, 1/4
Let f(h) be the third derivative of h**6/24 - 7*h**5/2 + 135*h**4/8 - 100*h**3/3 - 4752*h**2. Factor f(s).
5*(s - 40)*(s - 1)**2
Let d = -451 + 453. Factor -249 - 125*u + 21*u - 190 - 4*u**d - 237.
-4*(u + 13)**2
Let i(s) be the second derivative of -s**8/960 - 11*s**7/1120 + s**6/144 - s**3/2 - 9*s**2/2 + 14*s. Let x(k) be the second derivative of i(k). Factor x(b).
-b**2*(b + 5)*(7*b - 2)/4
Let v(s) be the second derivative of 1/15*s**6 - 51*s - 2/5*s**5 + 4/3*s**3 + 1/3*s**4 + 0 - 3*s**2. Find g such that v(g) = 0.
-1, 1, 3
Solve 1/2*g**4 - 33 - 127/2*g**2 + 29/2*g**3 + 163/2*g = 0 for g.
-33, 1, 2
Factor 3/2*m**4 + 90*m**2 + 57/2 - 33*m**3 - 87*m.
3*(m - 19)*(m - 1)**3/2
Let s(f) = -178*f**2 + 11314*f - 3192222. Let k(l) = 38*l**2 - 2263*l + 638444. Let o(v) = -14*k(v) - 3*s(v). Determine p so that o(p) = 0.
565
Let t(k) be the third derivative of 7/660*k**6 - 5/12*k**4 + 0 - 1/1155*k**7 - 50/33*k**3 + 1/110*k**5 - 24*k**2 + 0*k. Find b, given that t(b) = 0.
-2, -1, 5
Let r = 3742 - 29933/8. Let m(n) be the first derivative of -r*n**4 + 12*n + 15/2*n**2 + 1/2*n**3 - 26. Let m(u) = 0. What is u?
-2, -1, 4
Let s = -175877 - -1407025/8. Factor 0 + 7/8*z**5 + 0*z**2 - s*z**4 + 1/4*z**3 + 0*z.
z**3*(z - 1)*(7*z - 2)/8
Let u(i) be the third derivative of i**5/360 + 5*i**4/144 - 26*i**3/9 - 141*i**2 - 3. Factor u(a).
(a - 8)*(a + 13)/6
Solve 157*h**3 + 175*h - 4*h**5 + 96 - 24*h**4 + 128 - 17*h**3 + 769*h + 720*h**2 + 160 = 0 for h.
-8, -2, -1, 6
Factor -1/3*z**3 - 103/3*z**2 + 0 + 0*z.
-z**2*(z + 103)/3
Let l(a) be the third derivative of a**7/150 + 311*a**6/200 + 119*a**5/30 + 11*a**4/5 - 2*a**2 - 11507. Suppose l(i) = 0. Calculate i.
-132, -1, -2/7, 0
Suppose -2*z = 0, -h = -3*z - 5 + 3. Suppose 0 = -c - 0*c + 4*b + 2, -3*b = -c + h. Find p, given that -p**c - 184 + 181 - 4*p + 0*p**2 = 0.
-3, -1
Let a(z) be the second derivative of -1/10*z**5 - 32*z + 0 + 0*z**2 + 0*z**3 + 5/6*z**4. Factor a(p).
-2*p**2*(p - 5)
Let i(o) = 2625*o**2 - 353725*o + 1037540. Let l(z) = z**3 - 4*z**2 + 2*z + 1. Let w(c) = -i(c) + 5*l(c). Determine j so that w(j) = 0.
3, 263
Let t(c) be the second derivative of 5*c**4/24 - 140*c**3/3 - 580*c**2 + 2191*c. Factor t(q).
5*(q - 116)*(q + 4)/2
Let q(o) be the second derivative of o**5/50 + 101*o**4/30 + 20*o**3/3 - 25*o + 15. Factor q(f).
2*f*(f + 1)*(f + 100)/5
Let i be 95/(-38)*(1 - -1). Let z(b) = 14*b + 73. Let d be z(i). What is y in 0 - 3/5*y**5 - 6/5*y**2 + 6/5*y**4 + 0*y**d + 3/5*y = 0?
-1, 0, 1
Let b be 2/4 + 5/(-18) - (6272/(-144))/98. Let y(u) = -u - 3. Let t be y(-6). Suppose 0*n**2 - 2/3*n + 0 + b*n**t = 0. What is n?
-1, 0, 1
Let m(l) be the second derivative of l**5/80 - 3*l**4/16 - 5*l**3 + 16*l**2 - 57*l + 29. Factor m(t).
(t - 16)*(t - 1)*(t + 8)/4
Let d be -2 + (-24)/14 + 2/(-7). Let r be d/(-30) - 3248/(-840). Determine h so that 350/3*h**r + 136/3*h**2 + 0 - 98/3*h**5 - 124*h**3 - 16/3*h = 0.
0, 2/7, 1, 2
Let n be 3336/(-11520)*-32 - 6*(-3)/(-2). What is p in 4/3 - 26/15*p + n*p**2 + 2/15*p**3 = 0?
-5, 1, 2
Factor -212*p + 1/2*p**2 - 856.
(p - 428)*(p + 4)/2
Let a be 4/(-12) - 134/3. Let r be 1/(-2) - (a/6 - -7). Suppose x**2 - 1/2*x**5 + r + 0*x**3 + 1/2*x - x**4 = 0. What is x?
-1, 0, 1
Solve -57/7*y**3 + 54/7*y + 9/7*y**4 + 0 - 9/7*y**2 + 3/7*y**5 = 0 for y.
-6, -1, 0, 1, 3
Let w(x) be the third derivative of 0*x + 0*x**3 + 0 + 1/12*x**5 - 35/24*x**4 + 74*x**2. Determine n, given that w(n) = 0.
0, 7
Let c(d) be the third derivative of -d**8/112 + 13*d**7/70 - 57*d**6/40 + 103*d**5/20 - 41*d**4/4 + 12*d**3 + 577*d**2. Factor c(k).
-3*(k - 6)*(k - 4)*(k - 1)**3
Let b(n) be the s