56*r - 68/3*r**3. Factor o(v).
4*(v - 8)**2*(v - 1)
Let k(f) be the first derivative of f**3/12 + 137*f**2/8 + 258*f + 4637. Factor k(q).
(q + 8)*(q + 129)/4
Let p = 194/21 - -1949/105. Let x = -898/35 + p. Solve 0*f + 3*f**4 - 9/7*f**5 - x*f**3 + 0 + 3/7*f**2 = 0.
0, 1/3, 1
Let x be (-2 - (-3 - -1))/(10/(-5)). Let o be (1 + x)/(-13*13/(-676)). Factor -1/7*l**2 + 0 + 1/7*l**o + 2/7*l - 2/7*l**3.
l*(l - 2)*(l - 1)*(l + 1)/7
Let u(b) be the second derivative of -b**6/6 - 107*b**5/2 - 1055*b**4/3 - 700*b**3 + 1901*b. Factor u(k).
-5*k*(k + 2)**2*(k + 210)
Let g(j) = j**5 - j**4 - 1. Let v(x) = -18*x**2 + 6*x**4 - 3*x**5 + 2 + 27*x - 21 - 12*x**3 + 23. Let z(r) = -4*g(r) - v(r). Determine t so that z(t) = 0.
-3, 0, 1, 3
Let f = -346 + 348. Suppose 30 + 9*d - d**f - 4*d**2 - 3 - 12*d**3 - 19*d**2 = 0. Calculate d.
-3/2, 1
Let m be ((-1287)/(-4))/((-133)/8 - -17). Let y = 858 - m. What is o in -1/2*o**3 + 0 - 1/6*o**2 + y*o = 0?
-1/3, 0
Let j(p) = -232*p**2 + 321*p. Let l(q) = -199*q**2 + 320*q. Let v(s) = 6*j(s) - 7*l(s). Find c, given that v(c) = 0.
0, 314
Let q(u) be the third derivative of u**5/20 + 319*u**4/2 + 203522*u**3 + 1801*u**2. Suppose q(o) = 0. Calculate o.
-638
Let c = -36822 - -36824. Let o(n) be the second derivative of -n**c - 2/7*n**3 + 7*n + 0 + 1/42*n**4. Find x, given that o(x) = 0.
-1, 7
Let k(a) be the first derivative of 3*a**6/10 - 492*a**5/25 + 6381*a**4/20 + 638*a**3 - 1008*a**2/5 - 4704*a/5 - 3498. Suppose k(q) = 0. What is q?
-1, 2/3, 28
Let f(l) be the second derivative of -l**7/168 + 23*l**6/30 - 2377*l**5/80 + 6067*l**4/24 - 5719*l**3/6 + 1849*l**2 + 153*l + 2. Factor f(b).
-(b - 43)**2*(b - 2)**3/4
Let x(l) be the second derivative of -l**4/18 + 6200*l**3/9 - 9610000*l**2/3 + 6*l - 10. Solve x(s) = 0 for s.
3100
Let y(x) be the third derivative of 2*x**7/105 + x**6/15 - 11*x**5/15 - 2*x**4 + 24*x**3 - 1023*x**2. Solve y(f) = 0 for f.
-3, 2
Let o be ((-380)/150 + 8/6)*72/(-144). Factor 1/5*j**4 - 1/5*j**3 - o*j**2 + 1/5*j + 2/5.
(j - 2)*(j - 1)*(j + 1)**2/5
Let j(m) be the third derivative of m**7/840 + m**6/480 - 11*m**5/80 + 59*m**4/96 - 7*m**3/6 - 233*m**2. Find n, given that j(n) = 0.
-7, 1, 4
Let v(i) = i**3 - 10*i**2 + 20*i - 4. Let o be v(2). Let z be 6 - -1*o/(-2). Factor -2/3*g**2 - z*g - 6.
-2*(g + 3)**2/3
Let x(m) = -7*m**4 - 79*m**3 - 448*m**2 - 824*m. Let t(v) = 20*v**4 + 236*v**3 + 1346*v**2 + 2470*v. Let l(q) = 4*t(q) + 11*x(q). Suppose l(j) = 0. What is j?
-17, -4, 0
Suppose 47/2*u**3 - 1/2*u**4 + 75*u**2 + 2*u - 100 = 0. What is u?
-2, 1, 50
Let o(x) be the second derivative of 0 + 64*x + 6*x**4 + 1/10*x**6 - 16*x**3 - 6/5*x**5 + 24*x**2. Factor o(q).
3*(q - 2)**4
Suppose 2*h - 65 = -i, 14*i + 2*h = 11*i + 183. Solve 17 + i*u**4 - 35 - 25*u**5 - 170*u**3 + 10 - 45*u + 130*u**2 + 13 + 46*u**4 = 0 for u.
1/5, 1
Suppose 12*f + 732*f = -213*f + 3828. Factor -3/2*c**2 - 3/4*c**5 + 9/4*c**3 + 0*c + 0*c**f + 0.
-3*c**2*(c - 1)**2*(c + 2)/4
Solve -28/15*u**2 + 0 - 98/15*u - 2/15*u**3 = 0 for u.
-7, 0
Let j = 1 + -1. Let c be 162/20 + 12/(-16)*((-1350)/(-125) - 10). Determine k so that c*k**4 + j + 21/2*k**2 - 3/2*k**5 - 3*k - 27/2*k**3 = 0.
0, 1, 2
Find i, given that 27/7*i**3 - 4*i**2 + 8/7*i**4 + 20/7 - 27/7*i = 0.
-4, -1, 5/8, 1
Let l(s) be the third derivative of -11/8*s**4 + 35*s**2 + 3*s**3 + 1/112*s**8 + 0 + 1/4*s**6 + 0*s**5 - 3/35*s**7 + 0*s. Solve l(t) = 0 for t.
-1, 1, 2, 3
Let v be (108 - 2 - -1) + 6 + -3. Suppose -60*y = -10 - v. Factor 0*b**3 - 1/2*b**y + 0*b + 1/2*b**4 + 0.
b**2*(b - 1)*(b + 1)/2
Solve -363609/8 - 603/4*z - 1/8*z**2 = 0 for z.
-603
Let p be (-4)/(-3) - 4/(-6). Let h = -464668 - -464668. Let h + 2/3*w**p - 1/3*w - 1/3*w**3 = 0. What is w?
0, 1
Let d(v) = 6*v**3 - v**2 + 1. Let n be d(1). Suppose -n*w - 16 = -10*w. Let 35*j - 5 + 9*j**2 + 5*j**w - 84*j**2 + 65*j**3 - 25*j**4 = 0. Calculate j.
1/4, 1
Suppose -2*f + 11 = 5*t, 0*f - 4*f - t + 31 = 0. Let m be 2/f*1*(-3)/(-3). Suppose -m*z**2 + 0 + 1/2*z = 0. What is z?
0, 2
Let k(y) be the third derivative of y**6/60 - 23*y**5/30 - 469*y**4/12 - 1813*y**3/3 + 2*y**2 - 144. Factor k(c).
2*(c - 37)*(c + 7)**2
Let a(x) be the third derivative of x**5/60 - 18*x**4 - 433*x**3/6 + 4017*x**2. Factor a(b).
(b - 433)*(b + 1)
Let d(q) be the second derivative of -q**4/48 - 2*q**3/3 - 39*q**2/8 + q + 276. Factor d(y).
-(y + 3)*(y + 13)/4
Let j(p) = -4*p**2 + 57*p - 63. Let k be j(13). Let a(y) be the first derivative of -1/6*y**3 + 0*y + 0*y**k - 1/4*y**4 - 1/10*y**5 - 23. Factor a(s).
-s**2*(s + 1)**2/2
Solve 2/5*u**2 + 664*u + 275560 = 0 for u.
-830
Let b be (-497)/(-142)*(-2)/(-6). Let q(a) be the first derivative of -13 + 1/12*a**4 + b*a**2 + 5/9*a**3 + a. Factor q(z).
(z + 1)**2*(z + 3)/3
Let k(n) = 2*n**3 - 18*n**2 + 52*n - 36. Let u = -16 + 11. Let r(d) = 2*d**3 - 18*d**2 + 53*d - 37. Let f(m) = u*k(m) + 4*r(m). Factor f(w).
-2*(w - 4)**2*(w - 1)
Let l(c) be the second derivative of c**5/10 - 19*c**4 - 115*c**3/3 + 5694*c. Suppose l(w) = 0. Calculate w.
-1, 0, 115
Let z(x) be the third derivative of x**6/480 - 11*x**5/120 - 85*x**4/96 + 125*x**3/12 + 6170*x**2. Factor z(u).
(u - 25)*(u - 2)*(u + 5)/4
Find b such that -100*b**2 + 112*b**3 - 5254664*b + 3*b**3 - 35*b**4 + 5254684*b = 0.
0, 2/7, 1, 2
Let c be (1792/154 + -12)/(2/3*(-39)/143). Factor 9/7*j + 0 + 3/7*j**3 - 12/7*j**c.
3*j*(j - 3)*(j - 1)/7
Suppose -4*s + 16 = 5*n, 4*s + 3 + 1 = 0. Let o be 279/36 - 28/n. Suppose -o*x**2 + 3/4*x**3 - 3/4*x + 3/4 = 0. What is x?
-1, 1
Suppose 1672/21*s + 0 + 2/21*s**3 + 558/7*s**2 = 0. What is s?
-836, -1, 0
Let f = 1721 + -1672. Let d be (8/(-5))/(f/(1470/(-36))). Factor -2 + 11/3*m - 1/3*m**3 - d*m**2.
-(m - 1)**2*(m + 6)/3
Let v(a) be the first derivative of a**3/9 - 47*a**2/2 + 2341. Factor v(s).
s*(s - 141)/3
Let v = 46989 - 46989. Factor 1/6*u**3 + v + 0*u + 7/6*u**2.
u**2*(u + 7)/6
Let f = 294 + -292. Let 14*n**3 - 270*n**4 + 58*n + 268*n**4 + 24*n**2 + 20 + 30*n**f = 0. What is n?
-1, 10
Let r(z) be the second derivative of -z**6/135 - 43*z**5/45 + 455*z**4/54 + 339*z + 11. Factor r(c).
-2*c**2*(c - 5)*(c + 91)/9
Find w such that -915*w + 36*w**4 - w**5 + 64 + 159*w**3 + 202*w**2 + 791*w - 8*w**4 - 280 - 48 = 0.
-2, 1, 33
Suppose 14 = -m + 4*o, -4*m + 7*m - o = 2. Suppose -3*f = -h + 101, -6*h + m*f = -h - 479. Solve -h - 67*c - 28*c**2 - 41*c + 151 - 80*c = 0 for c.
-7, 2/7
Let f be (2/4 - (-9)/(-2)) + -2. Let c be -1*f/3 + 32/2. Find u such that -12 + 27*u**2 - 5*u**2 + 8*u - c*u**2 = 0.
-3, 1
Suppose 20*u = -430 + 2810. Let k be (-1)/(-4)*-2 - u/(-34). Factor 3/7*h**2 + 0*h + 0 + 3/7*h**k.
3*h**2*(h + 1)/7
Let q(k) be the first derivative of -k**3/15 - 466*k**2/5 - 931*k/5 + 9945. Factor q(s).
-(s + 1)*(s + 931)/5
Let s(i) be the first derivative of 34*i**5/5 - 41*i**4/2 + 14*i**3 + 13*i**2 - 20*i - 619. Factor s(p).
2*(p - 1)**3*(17*p + 10)
Let u(d) be the second derivative of -9/7*d**2 + 69*d + 8/21*d**3 + 0 + 1/42*d**4. Find f such that u(f) = 0.
-9, 1
Let j(q) be the first derivative of -q**5/20 + 3*q**4/2 - 18*q**3 - 11*q**2 - 6*q - 137. Let u(k) be the second derivative of j(k). Suppose u(g) = 0. What is g?
6
Factor 152/3 - 224/3*j + 2/3*j**3 + 70/3*j**2.
2*(j - 2)*(j - 1)*(j + 38)/3
Let p be (-3)/(6 - 3) + (-4)/(-1). Let m be ((-57783)/(-21) - p) + (-4)/7. Factor 5*d**2 + 3*d - m*d**3 - 5*d**4 + 2743*d**3 + 2*d.
-5*d*(d - 1)*(d + 1)**2
Let k = -12344281/984 - -12545. Let z = k - -159415/6888. Suppose z*h**3 + 0 + 72/7*h**2 + 8/7*h = 0. Calculate h.
-2/9, 0
Let x(w) = -w**2 - 5*w - 1. Let a(h) = -7*h**2 - 9251*h - 2645. Let j(k) = 2*a(k) + 14*x(k). What is p in j(p) = 0?
-663, -2/7
Let p(c) be the first derivative of 1058*c - 1012*c**2 + 2/5*c**5 + 292*c**3 - 215 + 22*c**4. Determine k, given that p(k) = 0.
-23, 1
Let a be ((-5)/(-20))/(1 + (-3)/(10 - -2)). Let z(n) be the second derivative of 0 + a*n**4 + 13*n - 1/3*n**3 - 2*n**2 + 1/10*n**5. Let z(l) = 0. What is l?
-2, -1, 1
Let h be (-40)/(-15)*261/348. Let r(b) be the second derivative of 2/21*b**7 - 4/5*b**6 + 0 - 8*b**3 - 2/3*b**4 - 15*b + 16*b**h + 11/5*b**5. Factor r(d).
4*(d - 2)**3*(d - 1)*(d + 1)
Let d be (-2400)/(-3520)*(3 + 8). Factor 5/4*m**3 + 55/4*m - 15/2*m**2 - d.
5*(m - 3)*(m - 2)*(m - 1)/4
Find j, given that 14797 + 13532 + 200*j - 3*j**2 + 248*j - 2