 1288*m - 14. Let p(r) be the first derivative of -19 - 1/2*r**4 + 9*r**2 + m*r**3 + 10*r. Factor p(x).
-2*(x - 5)*(x + 1)**2
Let y(v) be the first derivative of -11/8*v**4 - 86 - v - 15/4*v**2 - 4*v**3. Factor y(x).
-(x + 1)**2*(11*x + 2)/2
Suppose 3*s = 3*d + 84, 0*d + 5*s = -d - 52. Let q = -32 - d. Factor -3*r**2 + 2*r**2 + q*r + 3*r**2 - 2*r.
2*r*(r - 1)
Let i(g) be the third derivative of g**5/60 + g**4/4 - 8*g**3/3 - 302*g**2. Factor i(l).
(l - 2)*(l + 8)
Factor 0*q + 0 - 55/4*q**2 + 1/4*q**3.
q**2*(q - 55)/4
Let g(b) be the first derivative of 2*b**6/15 - 172*b**5/25 + 162*b**4/5 - 952*b**3/15 + 314*b**2/5 - 156*b/5 + 617. Suppose g(z) = 0. What is z?
1, 39
Let f(n) = -6*n**2 - 39*n + 72. Let g be f(-8). Let m(v) be the first derivative of 0*v**3 - 1/4*v**2 + g*v + 1/8*v**4 - 1. What is q in m(q) = 0?
-1, 0, 1
Let o(i) be the first derivative of -16200*i**5 + 78300*i**4 - 151380*i**3 + 146334*i**2 - 707281*i/10 - 2724. Factor o(z).
-(30*z - 29)**4/10
Let u(z) be the third derivative of -z**7/15 - 113*z**6/30 - 43*z**5/2 + 323*z**4/6 + 232*z**3/3 - 562*z**2 - 8. Suppose u(n) = 0. Calculate n.
-29, -4, -2/7, 1
Factor 27/7*z**2 - 48/7*z - 180/7 + 3/7*z**3.
3*(z - 3)*(z + 2)*(z + 10)/7
Let y(u) be the first derivative of u**7/42 - u**6/24 - 11*u**5/4 - 105*u**4/8 - 63*u**2 + 71. Let j(n) be the second derivative of y(n). Factor j(q).
5*q*(q - 7)*(q + 3)**2
Let f(c) = -2*c**2 + 42*c + 16. Suppose y = -4*y + 140. Let p(t) = -164 + 2*t + 79 + 85. Let s(b) = y*p(b) - 2*f(b). Factor s(i).
4*(i - 8)*(i + 1)
Let u be (-2 - -4)/(-1 - -3). Suppose 3*n + 2*w = -3*w, 0 = -2*n - 3*w + u. Suppose 15*x - 5*x**n - 15*x - 4*x**4 - 6*x**4 = 0. Calculate x.
-2, 0
Let y(x) be the second derivative of 1/6*x**4 + 0 + 0*x**5 - 1/15*x**6 + 0*x**2 + 38*x + 0*x**3. Factor y(r).
-2*r**2*(r - 1)*(r + 1)
Suppose 11*p - 90 = 5*p. Let l be 3 - 6/p*75/(-20). Factor 3/4*t**5 + 3/4*t - 3*t**2 + l*t**3 + 0 - 3*t**4.
3*t*(t - 1)**4/4
Let s(l) be the third derivative of 1/16*l**4 - l**2 + 1/40*l**5 - 8*l + 0*l**3 + 0. Determine y, given that s(y) = 0.
-1, 0
Let 0 + 64/19*z**5 - 2/19*z - 100/19*z**4 + 6/19*z**3 + 32/19*z**2 = 0. What is z?
-1/2, 0, 1/16, 1
Let u(s) be the first derivative of s**3/3 - 56*s**2 - 113*s - 4710. Suppose u(p) = 0. Calculate p.
-1, 113
Let m = -189154/5 - -37419. Let a = m + 412. Factor 0*k - 3/5*k**3 - 2/5*k**2 - a*k**4 + 0.
-k**2*(k + 1)*(k + 2)/5
Let q(w) be the third derivative of -w**8/1960 - 11*w**7/490 - w**6/3 - 10*w**5/7 + 41*w**3/6 + 303*w**2. Let u(r) be the first derivative of q(r). Factor u(f).
-6*f*(f + 2)*(f + 10)**2/7
Let h(y) = 359*y - 2133. Let a be h(6). Let x(u) be the first derivative of 0*u + 0*u**2 - 4*u**5 + 0*u**3 - a - 5/6*u**6 - 5*u**4. Solve x(w) = 0 for w.
-2, 0
Let i = -3786 - -7563. Factor 3777*g - 12*g**2 + 48*g**3 - i*g + 27*g**4.
3*g**2*(g + 2)*(9*g - 2)
Let y be 4/72*(-180)/(-110)*11/2. Determine n, given that -y*n**3 - 3/2*n**2 + 0*n + 0 = 0.
-3, 0
Let r be 466/(-8) - ((-10)/8 - -1). Let o = -56 - r. Factor -2*q**4 + 4*q**o - 2*q**2 + 1 - 1 - q**5 + q.
-q*(q - 1)*(q + 1)**3
Let i = -70427 + 915553/13. Factor -2/13*d + 0 - 4/13*d**2 - i*d**3.
-2*d*(d + 1)**2/13
Let h(d) = -5*d**4 + 108*d**3 + 249*d**2 + 130*d. Let o(t) = 10*t**4 - 214*t**3 - 497*t**2 - 260*t. Let w(v) = 13*h(v) + 6*o(v). Factor w(f).
-5*f*(f - 26)*(f + 1)**2
Let u(r) be the second derivative of -6*r**2 + 9/20*r**5 - 46 - 11/4*r**4 + 6*r**3 - 3*r. Factor u(q).
3*(q - 2)*(q - 1)*(3*q - 2)
Suppose -166 - 17 + 8 = -35*f. Let b(r) be the first derivative of -51/2*r**4 - 3*r**6 + 3*r - 12*r**2 + 69/5*r**f - 23 + 24*r**3. Find t such that b(t) = 0.
1/3, 1/2, 1
Let k be 38/(-5) + -2 + (-30)/18*(-99 + 93). Factor 2*c**3 - k + 2/5*c**2 - 2*c.
2*(c - 1)*(c + 1)*(5*c + 1)/5
Let v(j) be the second derivative of -2*j**4/15 - 2747*j**3/15 + 687*j**2/5 + 2*j - 2085. Let v(o) = 0. What is o?
-687, 1/4
Let s be ((-27636)/(-35))/(-21) - -38. Factor s*d**3 + 4/5*d**2 + 8/5 - 14/5*d.
2*(d - 1)**2*(d + 4)/5
Solve 4/5*w**3 + 1/10*w**4 + 2/5*w + 22/5 - 33/10*w**2 = 0.
-11, -1, 2
Let n(y) be the second derivative of 5*y**7/84 + 7*y**6/6 + 8*y**5 + 295*y**4/12 + 475*y**3/12 + 35*y**2 + 560*y. Factor n(h).
5*(h + 1)**3*(h + 4)*(h + 7)/2
Factor 206/3*q + 264 + 2/3*q**2.
2*(q + 4)*(q + 99)/3
Let a be (-1480)/(-1260) + (-56)/63. Let w be (2 - 5)/(9/(-6)). Factor -6/7*u - a*u**w + 0.
-2*u*(u + 3)/7
Suppose o + l = 327, 0 = -11*o + 7*o + 5*l + 1299. Factor 55 + 332*j**2 - 28 - 27*j - o*j**2.
3*(j - 3)*(2*j - 3)
Let v(x) be the first derivative of x**3/24 - 627*x**2/16 + 313*x/4 - 8989. Factor v(y).
(y - 626)*(y - 1)/8
Let v(m) be the second derivative of -m**5/4 + 41*m**4/6 - 176*m**3/3 + 64*m**2 + 689*m + 1. Determine j so that v(j) = 0.
2/5, 8
Let z(b) = 7*b**4 - 17*b**3 - 13*b**2 - 7*b + 2. Let x(c) = 5*c - 31*c**3 - 4*c - c**4 + c**5 - 2*c**2 + 32*c**3 + c**2. Let d(q) = -4*x(q) - z(q). Factor d(s).
-(s - 2)*(s + 1)**3*(4*s - 1)
Let r = 66 - 64. Suppose -3*y + r*f = -24, -8 - 30 = -5*y + 4*f. Factor 16*c + 0*c**3 + 26*c**2 + 4*c**3 - y*c**2.
4*c*(c + 2)**2
Let z = 489562/5 + -97912. Factor 34/5*r**2 + z*r**4 + 34/5*r + 14/5*r**3 + 12/5.
2*(r + 1)**2*(r + 2)*(r + 3)/5
Let b(f) be the first derivative of -2*f**3/9 - 80*f**2/3 - 296*f - 2802. Determine k, given that b(k) = 0.
-74, -6
Let l(v) be the first derivative of -5*v**4/8 - 35*v**3/6 - 10*v**2 + 221*v + 146. Let w(a) be the first derivative of l(a). Suppose w(x) = 0. What is x?
-4, -2/3
Let x(c) = c**3 - 13*c**2 + 16*c - 1. Let v be x(12). Let j = 62 - v. Factor s**2 + 18*s + 0*s**2 - j - 4*s**2.
-3*(s - 5)*(s - 1)
Let k(p) be the third derivative of -1/15*p**6 - 2 - 31*p**2 + 3/2*p**4 + 0*p - 1/2*p**5 + 0*p**3 + 1/105*p**7. Factor k(b).
2*b*(b - 6)*(b - 1)*(b + 3)
Let r = 15503 - 1085209/70. Let n(v) be the third derivative of 1/735*v**7 - 3/7*v**3 + 0 + 0*v - 15*v**2 - 4/35*v**5 + r*v**6 + 13/42*v**4. Factor n(c).
2*(c - 1)**3*(c + 9)/7
Let b(y) be the second derivative of y**5/110 - 3*y**4/22 - 172*y**3/33 + 180*y**2/11 + 89*y - 4. Find h such that b(h) = 0.
-10, 1, 18
Let z(t) = -16*t - 2*t**2 - 6 - 15*t**2 - 4*t**2 - 6*t**2. Let j(k) = -110*k**2 - 65*k - 25. Let p(d) = -6*j(d) + 25*z(d). Solve p(i) = 0 for i.
-2/3, 0
Let v be (906510/(-6027) + 150)/((-10)/(-14) + -1). Suppose 4*a**4 + v*a**2 + 0*a - 38/7*a**3 + 0 = 0. Calculate a.
0, 5/14, 1
Let k be 1*-7 - ((-14)/4)/((-64)/(-128)). Let x(v) be the second derivative of 0*v**2 + k + 2*v + 1/27*v**3 - 1/54*v**4. Factor x(s).
-2*s*(s - 1)/9
Factor -2/3*y**2 + 0 + 4*y - 2/3*y**3.
-2*y*(y - 2)*(y + 3)/3
Let m(w) be the first derivative of 18 - 12*w**2 + 32*w + 4/3*w**3. Solve m(o) = 0.
2, 4
Let m(i) = 368*i - 3310. Let n be m(9). Determine d so that -30*d**3 - 130*d + 10*d**4 - 30 - 315/2*d**n = 0.
-2, -1/2, 6
Let r(b) = -1203*b + 1205. Let s be r(1). Let -7/10 + 17/10*t**3 + 21/10*t**s + 1/5*t**4 - 1/10*t = 0. What is t?
-7, -1, 1/2
Let -32/3*k**2 - 28/9*k**4 + 0 + 1/9*k**5 + 100/9*k**3 + 0*k = 0. Calculate k.
0, 2, 24
Let g(k) be the first derivative of 12*k**5/5 + 22*k**4 + 148*k**3/3 + 20*k**2 - 1316. Suppose g(f) = 0. Calculate f.
-5, -2, -1/3, 0
Let p = 2582/5 + -514. Let w be 3*(-36)/27 + 11 + (-459)/85. Factor -4/5*c**4 + p*c**3 + 0*c - w*c**2 + 0.
-4*c**2*(c - 2)*(c - 1)/5
Let h be 4/10 + 252/225*5. Suppose -3*a**3 - h*a**4 + 3*a**5 + 3*a**4 + 3*a**2 + a**5 - a**5 = 0. Calculate a.
-1, 0, 1
Let b be 3*(16/(-72))/((-6)/45). Solve -3*d - 5 - 65 + 43*d + b*d**2 - 65*d = 0 for d.
-2, 7
Let c = -5522/51 - -1886/17. Let q(v) be the second derivative of -27*v + 0 + c*v**3 + 1/5*v**5 + 0*v**2 + 5/3*v**4. Factor q(a).
4*a*(a + 1)*(a + 4)
Let d(r) be the first derivative of r**5/10 + 15*r**4/4 + 9*r**3/2 - 29*r**2/2 - 3295. What is i in d(i) = 0?
-29, -2, 0, 1
Let q = -336 + 343. Let d be 77/(-1078)*(q/(-4) + 0). Find i such that 1/4*i - d*i**2 - 1/8 = 0.
1
Let p = 1654997/18 + -169325/2. Find w such that -64/3*w**2 - 2048/3*w - p - 2/9*w**3 = 0.
-32
Let o(z) be the second derivative of 0*z**3 + 1/126*z**7 + 13/45*z**6 + 0*z**5 - 9*z + 0*z**4 + 0*z**2 + 1. Determine u so that o(u) = 0.
-26, 0
Suppose 380*p + 3 = 377*p. Let v be (6*p - -2)*19/(-190). Find x such that 8/5*x**3 + 8/5*x - v*x**4 - 2/5 - 12/5*x**2 = 0.
1
Let q be -3 + -1 - (3 - -39)/(-6). Determine l, give