*(k - 2)**2
Determine k so that -60*k - 3/4*k**2 + 0 = 0.
-80, 0
Suppose 2*z - 41 = -3*c, -4*c + 120 = -9*z + 14*z. Let s(t) be the second derivative of 1/9*t**4 + z*t + 0 + 6*t**2 + 4/3*t**3. What is p in s(p) = 0?
-3
Suppose -2*p - 4*o = -128, 0 = -4*p - 5*o + 2*o + 261. Let q be (-33)/p*(-8 + 2). Factor 1/9*w**q + 0*w - 4/9 + 1/3*w**2.
(w - 1)*(w + 2)**2/9
Suppose -2*u - 116*u = -17*u - 303. Factor 0 - 92/13*v**u - 4/13*v + 186/13*v**2.
-2*v*(v - 2)*(46*v - 1)/13
Let p(d) = 5*d**3 - 4680*d**2 + 9371*d - 4800. Let m(x) = 2*x**3 - 2340*x**2 + 4686*x - 2396. Let z(y) = -13*m(y) + 6*p(y). Factor z(f).
4*(f - 1)**2*(f + 587)
Let v be ((-3528)/(-35))/(-3)*(-10)/40. Factor v*j**2 - 18*j + 46/5 + 2/5*j**3.
2*(j - 1)**2*(j + 23)/5
Let m be 1/(-1)*(-4)/(0 - -4). Suppose -p + m = -3. Factor -24*r**p + 3*r**3 + 5*r + 12*r**4 - 8*r**3 + 7*r**4 + 5*r**2.
-5*r*(r - 1)*(r + 1)**2
Let k(i) be the first derivative of -2*i**3/15 - 232*i**2 - 2318*i/5 - 893. Factor k(c).
-2*(c + 1)*(c + 1159)/5
Factor 535/3*h + 0 + 5/3*h**2.
5*h*(h + 107)/3
Let m(k) be the third derivative of k**8/20160 + k**7/2772 - k**6/1980 + k**5/12 - k**4/12 + 74*k**2. Let q(w) be the third derivative of m(w). Factor q(y).
(y + 2)*(11*y - 2)/11
Let x(j) be the first derivative of j**3/5 - 1473*j**2/10 + 4392*j/5 - 7519. Factor x(b).
3*(b - 488)*(b - 3)/5
Let q(u) = 23*u**4 + 1986*u**3 - 892*u**2 - 12*u + 4. Let x(y) = -116*y**4 - 9930*y**3 + 4459*y**2 + 57*y - 19. Let n(i) = 19*q(i) + 4*x(i). Factor n(d).
-3*d**2*(d + 74)*(9*d - 4)
Let d(q) be the second derivative of 7*q**5/24 - 1175*q**4/24 - 505*q**3/18 - 3526*q. Solve d(h) = 0 for h.
-2/7, 0, 101
Let j(h) be the first derivative of -2*h**5/25 - 71*h**4/10 - 1102*h**3/5 - 12029*h**2/5 + 27508*h/5 + 5032. Solve j(l) = 0 for l.
-26, -23, 1
Solve -33/4*u**3 - 27/2 + 33/4*u + 51/4*u**2 + 3/4*u**4 = 0 for u.
-1, 1, 2, 9
Let d(q) = -12*q - 8. Let v be d(-1). Let g be 104/(-130)*(-10)/v. Solve -5/2*a + 0 - 5/4*a**3 - 15/4*a**g = 0 for a.
-2, -1, 0
Suppose z = -w + 4, 3*z + 24*w = 25*w + 8. Let p(n) be the second derivative of 1/12*n**4 + 0 + 10/3*n**z + 39*n + 50*n**2. Suppose p(r) = 0. Calculate r.
-10
Let t = 10021/21 + -3338/7. Factor -14/3*w**3 - 53/6*w**2 + 7/6*w + t.
-(w + 2)*(4*w - 1)*(7*w + 1)/6
Let g(o) = 2*o**4 - 32*o**3 - 168*o**2 - 292*o - 180. Let h(p) = -3*p**4 + 31*p**3 + 168*p**2 + 289*p + 177. Let v(x) = -5*g(x) - 4*h(x). Solve v(b) = 0.
-12, -2
Let q(u) be the second derivative of -1/20*u**5 + 0*u**2 + 1/120*u**6 - 1/12*u**4 + 1/168*u**7 + 32*u + 1 + 0*u**3. Factor q(s).
s**2*(s - 2)*(s + 1)*(s + 2)/4
Let r(i) be the third derivative of i**7/70 - 9*i**6/40 + 19*i**5/20 + 9*i**4/8 - 10*i**3 - 1352*i**2. Determine f so that r(f) = 0.
-1, 1, 4, 5
Let r(o) be the second derivative of -o**6/1200 - o**5/600 + o**4/120 + 67*o**2/2 - 99*o. Let i(u) be the first derivative of r(u). Factor i(s).
-s*(s - 1)*(s + 2)/10
Suppose -2/3*u**4 - 556/3 - 554/3*u**3 + 554/3*u + 186*u**2 = 0. What is u?
-278, -1, 1
Suppose -7*p + 12 = -p. Determine l so that l**3 + p*l - 7*l - 3*l**3 + 3*l**3 - 4*l**2 = 0.
-1, 0, 5
Let z = -121/125 - -146/125. Factor t**2 - 4/5*t**3 - z*t + 0.
-t*(t - 1)*(4*t - 1)/5
Let k(z) be the first derivative of 2*z**3 - 47*z**2 + 294*z + 99. Let l(v) = -2*v**2 + 31*v - 98. Let a(b) = 6*k(b) + 20*l(b). Let a(c) = 0. What is c?
7
Let b = -3324 + 3329. Let n(j) be the first derivative of -4/3*j**3 - 12/5*j**b - 26 - 3*j**4 - 2/3*j**6 + 0*j + 0*j**2. Factor n(u).
-4*u**2*(u + 1)**3
Suppose 5*i - 640 = -5*z, 506 = 9*i - 5*i - 2*z. Let u = -1391/11 + i. Factor 2/11*y**2 - 2/11*y**3 + 10/11*y + u.
-2*(y - 3)*(y + 1)**2/11
Let c(m) be the second derivative of -4/21*m**3 - 2 + 1/105*m**6 + 2/35*m**5 + 1/14*m**4 - 4/7*m**2 - 17*m. Factor c(n).
2*(n - 1)*(n + 1)*(n + 2)**2/7
Let 5*c**3 - 1437*c - 8*c**3 - 791*c - 3211*c + 24642 + 240*c**2 = 0. Calculate c.
6, 37
Let z(c) be the second derivative of -c**6/165 + c**5/11 - 29*c**4/66 + 32*c**3/33 - 12*c**2/11 - 382*c. Suppose z(x) = 0. Calculate x.
1, 2, 6
Let a(y) be the second derivative of -45/2*y**2 + 5/2*y**3 - 4*y + 0 + 1/4*y**5 + 25/12*y**4. Determine p so that a(p) = 0.
-3, 1
Let g(f) be the first derivative of -f**4/10 + 8*f**3/5 + 31*f**2/5 - 84*f/5 - 623. Factor g(m).
-2*(m - 14)*(m - 1)*(m + 3)/5
Let g(i) be the second derivative of i**3/6 - i. Let o(l) = 13*l - 4 - 4*l + 0 - 14*l**2 + 13*l**2 - 8*l. Let p(b) = 10*g(b) - 2*o(b). Factor p(x).
2*(x + 2)**2
Let u be -3 - (-198)/105*(-305)/(-122). Let 291/7*y**4 - 33/7*y**2 + 246/7*y**3 + u + 12*y**5 - 60/7*y = 0. What is y?
-2, -1, 1/4, 2/7
Let u(p) be the second derivative of -p**4/12 + 8*p**3/3 + 2*p - 336. Factor u(z).
-z*(z - 16)
Let p(t) be the third derivative of -t**6/6 + 41*t**5/5 - 335*t**4/3 - 192*t**3 - 120*t**2. Factor p(j).
-4*(j - 16)*(j - 9)*(5*j + 2)
Let w be (2/(-9))/((-45)/405). Suppose -b - w*o + 11 = 10, 0 = -5*o. Find x such that -b - 7/4*x**2 + 4*x = 0.
2/7, 2
Let z = 111 - -223. Suppose -15*h + z - 304 = 0. Find l, given that -2 + 0*l**h - 7/3*l + 1/3*l**3 = 0.
-2, -1, 3
Let -13/5*g**3 - 1/5*g**4 + 6*g**2 + 0 + 0*g = 0. What is g?
-15, 0, 2
Factor -4/7*m**4 + 0 + 24/7*m**2 - 12/7*m**3 + 32/7*m.
-4*m*(m - 2)*(m + 1)*(m + 4)/7
Let b(i) = -6*i**3 - 122*i**2 - 296*i - 48. Let d(w) = 2*w**3 + 41*w**2 + 99*w + 18. Let a(f) = -3*b(f) - 8*d(f). Determine h, given that a(h) = 0.
-16, -3, 0
Let w be (-27)/(-36) - (-53)/4. Factor 9*y**3 + w - 23 + 63 - 12*y**2 - 12*y**3 + 9*y.
-3*(y - 2)*(y + 3)**2
Factor 1/9*r**2 - 14/9*r - 527/9.
(r - 31)*(r + 17)/9
Let n(l) be the first derivative of l**4/30 - 17*l**3/15 + 16*l**2/5 - 97*l + 111. Let b(j) be the first derivative of n(j). Find m, given that b(m) = 0.
1, 16
Let p = -2872099/140 - -20515. Let z(a) be the third derivative of -3/7*a**3 - 1/8*a**4 - p*a**5 + 0*a + 0 + 11*a**2. Factor z(j).
-3*(j + 1)*(j + 6)/7
Let a = 1194 + -1196. Let f be 3 - (-32)/16*(-1)/a. Determine b so that 6*b**f - 64/3*b**3 + 112/3*b**2 + 32/3 - 32*b - 2/3*b**5 = 0.
1, 2
Let f(y) be the second derivative of -y**5/40 - 4*y**4 - 256*y**3 + 58*y**2 + 4*y - 19. Let k(s) be the first derivative of f(s). Let k(i) = 0. What is i?
-32
Factor 16/7*x**2 + 46/7*x - 2/7*x**3 - 60/7.
-2*(x - 10)*(x - 1)*(x + 3)/7
Solve 1003*w + 280 + 1213*w + 4805*w**2 + 40 - 315*w + 579*w = 0 for w.
-8/31
Let i(r) = 2*r**2 + 8674*r + 9513512. Let w(m) = 2*m**2 + 8669*m + 9513511. Let q(o) = 11*i(o) - 10*w(o). Determine l so that q(l) = 0.
-2181
Let c be (-2292)/48 + 1*(-10)/8. Let t be 2 - (6/(-14) + (-21)/c). Find d, given that 0*d - 1/3*d**5 - 1/3*d**t + 1/3*d**3 + 1/3*d**4 + 0 = 0.
-1, 0, 1
Factor 1/6*v + 7 - 1/6*v**2.
-(v - 7)*(v + 6)/6
Factor -2*c**3 - 56*c**2 - 157*c**2 - 10050*c - 79*c**2 + 45000.
-2*(c - 4)*(c + 75)**2
Find s, given that 540*s**2 - 2326*s**5 + 740*s**3 + 770*s**5 + 1541*s**5 + 115*s**4 - 720*s = 0.
-3, -2, 0, 2/3, 12
Factor 297/2*t + 150 - 3/2*t**2.
-3*(t - 100)*(t + 1)/2
Let p(b) be the second derivative of 5*b**4/24 - 785*b**3/12 - 795*b**2/2 - 11492*b. Determine f so that p(f) = 0.
-2, 159
Let r(n) = 28*n**2 - 388*n - 960. Let p be r(16). Factor p + 9/7*v - 3/7*v**2.
-3*v*(v - 3)/7
Let f(w) = 19294*w - 73822. Let p be f(4). Factor -p*v - 2028 - 2001*v**2 - 3/2*v**5 - 1011/2*v**3 - 48*v**4.
-3*(v + 2)**3*(v + 13)**2/2
Suppose 42 = 64*b - 86. Factor 771*v - 1172 - 428*v**b + 41 - 1150*v**2 - 192 - 132*v**3 - 3*v**4 - 3543*v.
-3*(v + 1)**2*(v + 21)**2
Let k(c) be the third derivative of 0*c**4 + 0*c + 0 + 3/14*c**7 - 146*c**2 - 1/2*c**5 + 0*c**3 - 7/24*c**6 - 5/168*c**8. Suppose k(l) = 0. What is l?
-1/2, 0, 2, 3
Let v(q) = 16*q**2 + 10*q + 16. Let z be -2*50/(-4) + (-9 - -6). Let s(c) = 2 - 3 - 2*c - 2 - 3*c**2. Let t(h) = z*s(h) + 4*v(h). Factor t(n).
-2*(n + 1)**2
Let h(y) = -11*y**2 - 6598*y - 6629. Let x(v) = 20*v**2 + 13195*v + 13245. Let k(n) = -5*h(n) - 3*x(n). Find b such that k(b) = 0.
-1318, -1
Let f(m) = -15*m - 50 + 10*m - 13*m - 23*m - 114. Let w be f(-4). Factor 3/5*l**3 - 3/5*l**5 + 0*l - 3/5*l**2 + 3/5*l**4 + w.
-3*l**2*(l - 1)**2*(l + 1)/5
Let z(x) = 2*x**2 + 31*x + 79. Suppose 0 = -5*o + 7*o + 6. Let v(b) = -b**2 - 15*b - 39. Let g(n) = o*z(n) - 7*v(n). Factor g(d).
(d + 6)**2
Let b(s) = -s + 3*s**4 - 3*s**4 + s**3 - 3 + 5 - s**4. Let y(g) = 4*g**4 - 2*g**3 - 2*g**2 + 3*g -