40*x**5 - 3/4*x**p - 1/4*x**4 + 3*x**2. Factor z(b).
-3*(b + 1)*(b + 3)/2
Let i(b) = 239*b**2 - 1432*b + 2. Let p(a) = -359*a**2 + 1432*a - 3. Let o(f) = 3*i(f) + 2*p(f). Factor o(v).
-v*(v + 1432)
Let l be (12/(-10))/((-6)/20). Suppose -3*x = 4*c - 3*c - 11, 0 = 5*c - l*x - 74. Factor 65*y + 8 + 8 + 19*y**4 + 75*y**2 + 4 + 35*y**3 - c*y**4.
5*(y + 1)**3*(y + 4)
Let o(m) = m**2 - 2*m + 1. Let u be o(4). Let f be 660/220 - 12/8. Determine b, given that f*b**2 + u*b + 15/2 = 0.
-5, -1
Let b(i) be the first derivative of -389*i**3/5 - 1164*i**2/5 + 12*i/5 - 781. Determine u so that b(u) = 0.
-2, 2/389
Solve -174 + 103*k**3 - 2064*k + 446*k**3 + 195*k**4 - 1317*k**2 - 942 - k**5 + 726*k**2 + 4*k**5 = 0.
-62, -3, -1, 2
Suppose -11 = 3*z - 41. Suppose 12*w - 16*w = -4*o - 20, -w + 11 = -4*o. Suppose 7*p**2 + z*p**w - 3*p**2 - 9*p**2 - 5*p**4 = 0. What is p?
0, 1
Let q(c) be the second derivative of c**5/4 - 10*c**4 - 5*c**3/6 + 60*c**2 + c + 113. Determine z so that q(z) = 0.
-1, 1, 24
Suppose 2*g - 5*r - 69 = 0, -4*r + 46 = 4*g - g. Let z be 42/2 - (-25 + g). Solve -52*d**3 + 26*d**2 - 16*d - 28*d**2 + 50*d**2 + z*d**4 - 4*d**5 = 0.
0, 1, 2
Suppose -8*n = 155 - 155. Let y(q) be the first derivative of -17 + 1/9*q**3 + 0*q + n*q**2 - 1/12*q**4. Determine h, given that y(h) = 0.
0, 1
Let t = -7528 + 7532. Let b(l) be the second derivative of 160*l**2 - 13*l + 40/3*l**3 + 5/12*l**t + 0. Solve b(v) = 0.
-8
Let u be 455/260 + ((-11)/4 - -1). Let k(c) be the second derivative of 20*c + 2/9*c**2 + u + 0*c**3 - 1/27*c**4. Solve k(j) = 0.
-1, 1
Let z(h) be the first derivative of h**6/33 + 42*h**5/55 + 67*h**4/11 + 148*h**3/11 - 135*h**2/11 - 486*h/11 - 104. Suppose z(g) = 0. What is g?
-9, -3, -1, 1
Suppose 5*y = 5*l - 90, 38 = 2*l - 3*y + 3. Suppose -4*r = -2*r + 2, -l = -4*g + 3*r. Let -1/5*m**g + 1/5*m**2 - 2/5*m**3 + 2/5*m + 0 = 0. What is m?
-2, -1, 0, 1
Let -1728/5*q - 17802*q**3 - 94154/5*q**2 + 36980*q**4 - 8/5 = 0. Calculate q.
-1/2, -2/215, 1
Let m be (-2)/7*(4/(-3) - (-45 + 53)). Let u(d) be the first derivative of -6/5*d**2 + m*d**3 - 16 + 24/25*d**5 + 0*d - 12/5*d**4 - 2/15*d**6. Factor u(s).
-4*s*(s - 3)*(s - 1)**3/5
Suppose 131*q**2 + 45*q**2 - 203*q**2 - 1056 - 3*q**3 + 93*q**2 + 993*q = 0. Calculate q.
-11, 1, 32
Let u(l) be the third derivative of -l**6/1080 - l**5/10 - 9*l**4/2 - 47*l**3/2 + 19*l**2. Let v(d) be the first derivative of u(d). Factor v(r).
-(r + 18)**2/3
Let i(s) be the third derivative of 5*s**8/588 - 38*s**7/735 - s**6/14 + 67*s**5/105 - 19*s**4/21 - 4*s**2 + 15*s - 2. Solve i(v) = 0 for v.
-2, 0, 1, 19/5
Let y = 30863/13 + -11201891/4719. Let r = y + 5/121. Factor q**3 + 0 - 4/3*q - r*q**5 + 2/3*q**4 - 4/3*q**2.
-q*(q - 2)**2*(q + 1)**2/3
Factor 0 + 7/2*o**2 - 5*o - 1/2*o**4 + 2*o**3.
-o*(o - 5)*(o - 1)*(o + 2)/2
Let s(a) = -36*a**2 + 448*a - 2896. Suppose -6*v = -7 + 25. Let q(l) = 7*l**2 - 90*l + 579. Let y(i) = v*s(i) - 16*q(i). Factor y(n).
-4*(n - 12)**2
Let j(d) be the second derivative of d**7/12600 + d**6/720 - d**5/12 - 9*d**4 + 240*d. Let l(p) be the third derivative of j(p). What is z in l(z) = 0?
-10, 5
Let s(p) = -2*p**3 - 22*p**2 - 22*p + 2. Let y(f) = 2*f**3 + 21*f**2 + 22*f - 3. Let c(d) = 3*s(d) + 2*y(d). Factor c(w).
-2*w*(w + 1)*(w + 11)
Let r(q) be the first derivative of -q**3/21 + 1144*q**2/7 - 1308736*q/7 + 3028. Solve r(y) = 0 for y.
1144
Let r(n) be the first derivative of -n**3/15 - 20*n**2 - 199*n/5 - 3403. What is u in r(u) = 0?
-199, -1
Let s(t) be the third derivative of -t**5/30 + 71*t**4/12 - 340*t**3 - 1447*t**2. Suppose s(f) = 0. What is f?
20, 51
Let h(o) be the first derivative of -o**6/150 - o**5/50 + 64*o - 2. Let l(v) be the first derivative of h(v). Factor l(u).
-u**3*(u + 2)/5
Let i be (18 + -6)/(6/(-788)) - 2. Let f = 7892/5 + i. Factor 0*p**2 + 0*p - f*p**3 + 0.
-2*p**3/5
Suppose 0 = -119*b + 102*b + 34. Suppose 2*h = -w + 46, h - 9 - 20 = w. Find a, given that 10*a**2 + a**2 - h*a**3 + 0*a**b - a**2 = 0.
0, 2/5
Let p(t) be the third derivative of t**6/210 + 17*t**5/35 - 27*t**4/7 - 2129*t**2 - 1. Suppose p(j) = 0. What is j?
-54, 0, 3
Suppose 2*h - j - 181 = 0, -5*j - 450 = -5*h - 2*j. Let s = -89 + h. Factor 0 + 2/11*f - 2/11*f**3 + 2/11*f**s - 2/11*f**2.
2*f*(f - 1)**2*(f + 1)/11
Suppose -1167*w + 4*s - 38 = -1169*w, 5*s - 52 = -4*w. Find f such that -2/9*f**2 - 2/9*f**5 + 0*f + 0 - 2/3*f**4 - 2/3*f**w = 0.
-1, 0
Let d = 601094/7 - 85864. Let -286/7*l**2 - 2/7 + 242/7*l**3 + d*l = 0. Calculate l.
1/11, 1
Suppose 17*r = 30*r + 1092. Let l be 34/14 + -2 + (-76)/r. Factor l*w**2 + 2/9*w**4 + 8/9*w**3 + 2/9 + 8/9*w.
2*(w + 1)**4/9
Factor -20972*r - 6700 + 8537*r**2 - 8521*r**2 + 802 + 654.
4*(r - 1311)*(4*r + 1)
Solve -4680/7*c + 5475600/7 + 1/7*c**2 = 0.
2340
Let p = 875 + -321. Let z = -358 + p. Determine l so that -4*l**3 + 103 + 18*l**2 - 20*l + 99 - z = 0.
1/2, 1, 3
Let f(n) be the third derivative of -2*n**7/21 - 193*n**6/24 - 35*n**5 - 1385*n**4/24 - 115*n**3/3 - 291*n**2 - 5*n. Solve f(s) = 0.
-46, -1, -1/4
Let o = 6114 + -6110. Let a(x) be the first derivative of -13 - x**2 + 10/27*x**3 + 1/2*x**o + 4/9*x - 14/45*x**5. Determine b, given that a(b) = 0.
-1, 2/7, 1
Suppose -81*y + 57*y + 1971 = 597*y - 513. Suppose -16/5*b**3 + 8/5*b**y + 2/5*b**5 - 28/5*b**2 + 14/5*b + 4 = 0. Calculate b.
-5, -1, 1, 2
Suppose 2*p + d - 1 = -4, p + d = -2. Let m be 27/6 - p - (-5 + 5). What is o in -m*o - 2*o**3 + 13/2*o**2 + 1 = 0?
1/4, 1, 2
Let v(i) be the first derivative of 57/2*i**2 + 1 - 3*i + 243/4*i**4 - 99*i**3. What is k in v(k) = 0?
1/9, 1
Factor -2/5*h**3 + 0 + 594/5*h - 592/5*h**2.
-2*h*(h - 1)*(h + 297)/5
Let w(s) = -3*s**2 - 72048*s + 62126448. Let x(u) = u**2 + 20584*u - 17750414. Let f(i) = -7*w(i) - 24*x(i). Factor f(v).
-3*(v - 1720)**2
Let p(q) be the second derivative of -6*q + 26/3*q**3 + 676*q**2 + 1/24*q**4 + 21. Solve p(f) = 0 for f.
-52
Let a(x) be the second derivative of x**7/1890 - x**6/135 + 11*x**5/270 - x**4/9 - 107*x**3/6 - 33*x. Let j(i) be the second derivative of a(i). Factor j(p).
4*(p - 3)*(p - 2)*(p - 1)/9
Let y(j) be the third derivative of -j**7/840 + j**6/18 - 5*j**5/6 - 5*j**3/2 + 4*j**2 + 2*j. Let b(u) be the first derivative of y(u). Factor b(g).
-g*(g - 10)**2
Let q(t) be the second derivative of -1350*t**6 - 2160*t**5 - 1080*t**4 - 256*t**3 - 32*t**2 + 965*t. Factor q(f).
-4*(3*f + 2)*(15*f + 2)**3
Let n(i) = 16*i**3 + 269*i**2 + 212*i + 26. Let o(y) = y**3 - y**2 + 1. Suppose 8*j - 46 = -62. Let d(g) = j*o(g) - n(g). Determine u, given that d(u) = 0.
-14, -2/3, -1/6
Let f be (86/36 - (-85)/(-34))*-5087. Let l = -563 + f. Factor -22/9*j**4 + 212/9*j**2 - 2/9*j**5 + 98/9 - l*j**3 - 266/9*j.
-2*(j - 1)**3*(j + 7)**2/9
Let f be 1/(-1)*(4 + -6 + 2). Let s(m) be the second derivative of -1/144*m**4 - 7*m + 0*m**2 + f*m**3 + 0. Factor s(d).
-d**2/12
Let g(u) be the third derivative of 0*u + 1/525*u**7 + 0 + 40*u**2 + 1/30*u**4 - 1/50*u**5 + 0*u**6 + 0*u**3. Find k, given that g(k) = 0.
-2, 0, 1
Let g be (0 - (-5)/4)*12832/(-240). Let s = 205/3 + g. Factor -3/4*f**2 + s*f - 3/4.
-3*(f - 1)**2/4
Let q = 7 + -5. Let w(l) = -2*l**3 + 13*l**2 - 23*l + 22. Let d be w(4). Solve -2/5*m**q + 4*m - d = 0.
5
Let w(y) be the third derivative of y**6/160 - y**5/16 - 31*y**4/8 + 65*y**3/2 + 10*y**2 + 14*y + 12. What is t in w(t) = 0?
-10, 2, 13
Let j(g) = 45*g + 138. Let d be j(-6). Let f be (-110)/d + (-3)/6. Factor f*v - 1/3*v**2 + 0.
-v*(v - 1)/3
Let k(y) be the second derivative of 1/126*y**4 - 13/63*y**3 + 1 + 31*y + 4/7*y**2. Solve k(r) = 0.
1, 12
Let k = -149 - -194. Suppose k - 48 = -o. Suppose -a**4 - a - 2*a**o - 5*a - 2 + 3 + 8*a = 0. Calculate a.
-1, 1
Let d(z) be the third derivative of -z**6/90 - 4*z**5/15 - 7*z**4/6 - 53*z**3/6 + 2*z**2 - 6*z. Let x(m) be the first derivative of d(m). Factor x(v).
-4*(v + 1)*(v + 7)
Let n be -14*(-13)/3640 + 0. Let f(q) be the second derivative of 5/6*q**3 + 6*q + 0 + q**2 + n*q**5 + 1/3*q**4. Factor f(w).
(w + 1)**2*(w + 2)
Let n = 7400909/22120 + -27/3160. Let g = -334 + n. Find r such that 0*r - g + 4/7*r**2 = 0.
-1, 1
Let x(k) be the first derivative of k**3/4 - 288*k**2 + 110592*k + 1003. Factor x(c).
3*(c - 384)**2/4
Let f = 1563667 - 1563667. Let p(u) = -u**2 + 5*u + 8. Let l be p(6). Find g, given tha