 - 11 - s*m**3. Determine c so that j(c) = 0.
-2, 0, 2
Let b(m) be the second derivative of -m**6/30 - 4*m**5/15 + 19*m**4/6 - 28*m**3/3 - 86*m**2 + 157*m. Let d(j) be the first derivative of b(j). Solve d(v) = 0.
-7, 1, 2
Let k(o) = o**3 + 2*o + 41. Let q be k(0). Determine v, given that 11*v - 5*v**3 - 9*v**4 - 24*v**3 - 1 - q*v - 43*v**2 - v**5 - 7 = 0.
-4, -2, -1
Let w = 387353/5 + -77467. Factor -w*m**3 - 13/5*m - 1/5*m**5 + 7/5*m**4 + 3/5 + 22/5*m**2.
-(m - 3)*(m - 1)**4/5
Let t(n) be the first derivative of n**5/300 + 3*n**4/4 + 135*n**3/2 + 85*n**2 + 86. Let b(p) be the second derivative of t(p). Factor b(s).
(s + 45)**2/5
Let -720*h - 36 - 451*h - 14878*h**2 - 729*h - 53621*h**3 + 607*h = 0. Calculate h.
-4/29, -3/43
Let u = -13899 + 41698/3. Let d(q) be the third derivative of -3*q**2 - 1/48*q**4 - 1/240*q**5 + 0 + u*q**3 + 0*q. Factor d(f).
-(f - 2)*(f + 4)/4
Suppose 0 = -0*p - p - 2*p. Let w(c) = c**2 + 2*c + 2. Let i be w(p). Solve 34 - 34 - 5*h**i = 0.
0
Let f(x) be the second derivative of 1/15*x**6 + 11/8*x**4 - 6*x + 5/6*x**3 + 6 - 27/40*x**5 + 0*x**2. Let f(l) = 0. What is l?
-1/4, 0, 2, 5
Suppose -42*i - 195 = -47*i. Solve 17 - 42*f**2 - 14 + 15 - 9*f**3 - i*f = 0.
-3, -2, 1/3
Let m = 1338622 - 4015834/3. Factor -4/3*t**2 + 8*t - m.
-4*(t - 4)*(t - 2)/3
Let x = 67601 + -337997/5. Find o such that x*o + 24/5 - 2/5*o**2 = 0.
-2, 6
Let t(d) be the third derivative of -d**8/336 - d**7/105 + 3*d**6/40 + d**5/30 - d**4/3 - 2*d**2 + 633. Solve t(h) = 0.
-4, -1, 0, 1, 2
Let q = -15909 - -15911. Let j(l) be the first derivative of -l**4 - 7 + 20/3*l**3 - 6*l**q - 36*l. Let j(g) = 0. What is g?
-1, 3
Suppose 271*n - 265*n - 2994 = 0. Let h = n - 2491/5. Factor -h*b**2 + 0 - 2/5*b - 2/5*b**3.
-2*b*(b + 1)**2/5
Suppose -18*q + 13*q + r = -3300, -5*r = -4*r. Factor 5*d**2 + q*d**4 + 0*d + 605/2*d**5 + 0 + 225/2*d**3.
5*d**2*(d + 2)*(11*d + 1)**2/2
Let g(j) = j**2 + 1. Let f(x) = -8*x**2 - 29*x + 12. Let o(m) = f(m) + 6*g(m). Let q be o(-15). Factor -2*p**q + 0*p**3 + 2*p**2 - 4*p - 4*p**2 + 8*p**2.
-2*p*(p - 2)*(p - 1)
Let i(r) be the second derivative of r**6/900 + 7*r**5/150 + 49*r**4/60 + 27*r**3/2 + r**2/2 + 2*r - 48. Let c(p) be the second derivative of i(p). Factor c(d).
2*(d + 7)**2/5
Let a(o) be the second derivative of 0 + 1/108*o**4 + 361/18*o**2 - 77*o - 19/27*o**3. Factor a(i).
(i - 19)**2/9
Let c = 808/6035 - 2/3621. Let q(z) be the second derivative of 4/3*z**3 + 0 + c*z**6 + 5/3*z**4 + 4/5*z**5 + 0*z**2 + 4*z. Factor q(d).
4*d*(d + 1)**2*(d + 2)
Suppose -4*m - 5 = 7. Let u(t) = -t**3 - 4*t**2 - 3*t + 2. Let l be u(m). Factor 63*v - 26*v - 13*v**l - 31*v + 3*v**3 + 4*v**2.
3*v*(v - 2)*(v - 1)
Let c(a) be the second derivative of a**5/100 - a**4/10 - a**3/30 + 3*a**2/5 - 95*a - 51. Factor c(q).
(q - 6)*(q - 1)*(q + 1)/5
Let p(x) be the third derivative of 161*x**5/480 - 85*x**4/48 + 7*x**3/4 - 878*x**2. Factor p(u).
(7*u - 2)*(23*u - 42)/8
Let x(z) = z**2 - 13*z + 8. Let v be x(-6). Suppose -130 = -4*d - v. Determine m, given that -22/3*m + 4/3 - 8/3*m**3 + 26/3*m**d = 0.
1/4, 1, 2
Suppose -2*d - 4*h = -72, 12*d - 92 = 9*d - 2*h. Solve -18*t**3 + 396*t + 484 + d*t**2 - 5025*t**4 + 9*t**2 + 5026*t**4 = 0 for t.
-2, 11
Solve 1722368/15 + 3712/15*v + 2/15*v**2 = 0 for v.
-928
Factor 3456/5 + 30*a**3 + 4296*a**2 - 17256/5*a.
6*(a + 144)*(5*a - 2)**2/5
Let p(c) be the first derivative of c**2 + 12 + 2/3*c**3 - 4*c. Suppose p(w) = 0. Calculate w.
-2, 1
Let m(s) be the third derivative of s**5/120 - 205*s**4/12 + 42025*s**3/3 - 69*s**2. Factor m(d).
(d - 410)**2/2
Let t(j) = -2*j + 10. Let a be t(3). Let 122*y**2 - a - 40*y**2 - 38*y**2 - 43*y**2 - 3*y = 0. Calculate y.
-1, 4
Let m(c) = c**2 + 11. Let l be (2/((-2)/(-3)))/(72/48). Let n(j) = 5 - 3 - 2 - 1. Let g(w) = l*m(w) + 22*n(w). Find v, given that g(v) = 0.
0
Let o = 6641 + -20488/3. Let q = -187 - o. Determine i, given that 2/3*i**4 + q*i**2 + 2/15 + 2/15*i**5 + 4/3*i**3 + 2/3*i = 0.
-1
Let z = -284716 - -569453/2. Factor -z*k**2 - 3/2*k**3 + 0 + 0*k.
-3*k**2*(k + 7)/2
Let o(f) be the first derivative of -f**4/16 + 3*f**3 + 75*f**2/8 - 86*f + 107. Let h(n) be the first derivative of o(n). Suppose h(c) = 0. What is c?
-1, 25
Factor 1/3*q**2 - 140/3 - 4/3*q.
(q - 14)*(q + 10)/3
Let g(w) be the first derivative of -18 + 10*w + 4*w**4 + 2/5*w**5 + 16*w**2 + 12*w**3. Factor g(p).
2*(p + 1)**3*(p + 5)
Suppose -5615 = 1103*s - 21057. What is u in 20/3*u**4 - s*u**5 + 0 + 40/3*u**3 - 20/3*u**2 + 2/3*u = 0?
-1, 0, 1/7, 1/3, 1
Let k(g) be the second derivative of -8/3*g**3 + 7 + 1/3*g**4 + 2*g + 6*g**2. Suppose k(q) = 0. Calculate q.
1, 3
Let u(p) = p**3 - p**2 + p - 4. Let x be u(2). Suppose 9*g**3 - 3*g**4 - 355*g**x + 3*g**4 - 15*g**5 - 4*g**4 + 353*g**2 = 0. Calculate g.
-1, 0, 1/3, 2/5
Factor -4*n**3 - 2 + 32/3*n + 26/3*n**2.
-2*(n - 3)*(n + 1)*(6*n - 1)/3
Let 75/7 + 85/7*q**4 + 54/7*q**3 - 912/7*q**2 + 10*q - 12/7*q**5 = 0. What is q?
-3, -1/4, 1/3, 5
Let u(c) be the second derivative of -c**5/50 - 47*c**4/15 - 37*c**3/3 - 92*c**2/5 + 2620*c. Find n such that u(n) = 0.
-92, -1
Let r = 617 + -608. Let u be (r/(-4))/9*8/(-15). Solve -u*x**2 + 0*x + 0 = 0 for x.
0
Let w(q) = q**3 - 8*q**2 - 26*q - 15. Let x be w(11). Factor 66*f**3 + 2*f**5 + x*f - 62*f + 72*f**2 + 20*f**4.
2*f**2*(f + 3)**2*(f + 4)
Let x(c) be the first derivative of -6*c**6/7 - 1752*c**5/35 - 7201*c**4/7 - 55360*c**3/7 - 50688*c**2/7 - 16384*c/7 - 292. Solve x(f) = 0 for f.
-16, -1/3
Solve -4225 + 181*u**2 - 20*u**3 - 76*u**2 - 31*u + 25*u**3 + 226*u = 0 for u.
-13, 5
Let s(q) be the second derivative of -138*q + 6/7*q**3 - 1/7*q**4 + 0 - 3/140*q**5 + 0*q**2. Factor s(h).
-3*h*(h - 2)*(h + 6)/7
Let d(r) be the second derivative of r**5/450 - 4*r**3/45 + 225*r**2/2 + 283*r. Let i(b) be the first derivative of d(b). Find j, given that i(j) = 0.
-2, 2
Let f(a) be the third derivative of -5*a**8/336 - 11*a**7/42 - 5*a**6/12 + 53*a**5/6 - 665*a**4/24 + 245*a**3/6 + 8*a**2 + 124. Factor f(j).
-5*(j - 1)**3*(j + 7)**2
Suppose -2568*u = -2921*u - 3128*u - 3183*u - 50*u. Factor b**2 + 1/3*b + b**3 + u + 1/3*b**4.
b*(b + 1)**3/3
Let s(o) be the second derivative of -o**4/48 - 649*o**3/12 - 421201*o**2/8 + 107*o - 1. Factor s(f).
-(f + 649)**2/4
Let n(y) be the second derivative of 8*y**7/63 + 68*y**6/15 + 889*y**5/60 - 245*y**4/12 - 509*y**3/18 - 23*y**2/2 - 363*y + 6. Solve n(p) = 0.
-23, -3, -1/4, 1
Suppose -6*b + 130 = 257 - 145. Let q(h) be the first derivative of -18*h + 10/3*h**3 - b*h**2 - 1/2*h**4 + 24. Determine a so that q(a) = 0.
-1, 3
Let v(m) be the third derivative of 943*m**6/540 - 314*m**5/45 - m**4/27 - 127*m**2 - 38. Factor v(k).
2*k*(k - 2)*(943*k + 2)/9
Let x(o) = -o**3 - 2*o**2 - 4*o + 6. Let d be x(0). Suppose l - 10 = 5*a - 9*a, l + d = 4*a. Factor 4*q - 10/3*q**a - 2/3.
-2*(q - 1)*(5*q - 1)/3
Suppose -2031*r + 1039*r - 74 = -1029*r. Let 18 - 9/2*p**r + 24*p = 0. Calculate p.
-2/3, 6
Let h(m) be the first derivative of m**4/18 + 44*m**3/3 + 260*m**2/3 + 1552*m/9 - 333. Find n, given that h(n) = 0.
-194, -2
Let r(t) be the third derivative of 7*t**2 + 0*t**5 + 0*t**4 + 1/42*t**7 + 0*t**3 + 2*t - 1/8*t**6 + 0. Let r(l) = 0. Calculate l.
0, 3
Let n(q) be the second derivative of 5*q**7/42 - 467*q**6/6 + 36269*q**5/2 - 1551030*q**4 - 3285360*q**3 + 18982080*q**2 + 5038*q - 1. Factor n(z).
5*(z - 156)**3*(z - 1)*(z + 2)
Let p(i) = 12*i**3 - 11*i**2 + 24*i - 23. Let q be p(1). Let s be (-9)/(-10)*48/36. Factor -s*d**q - 6/5*d + 36/5.
-6*(d - 2)*(d + 3)/5
Let g be ((-22)/(-33))/(4/3*1). Suppose d = -1, 17 = 5*v - 0*v + 3*d. Suppose 1/4*r**5 + 1/4*r**3 + 0 - 3/4*r**v + 3/4*r**2 - g*r = 0. What is r?
-1, 0, 1, 2
Let f(a) = -11*a**2 - 77*a + 4. Let o be f(-7). Let p(n) be the first derivative of 6*n - 9 - 13/2*n**2 - 1/5*n**5 + 1/4*n**o + 7/3*n**3. Factor p(m).
-(m - 2)*(m - 1)**2*(m + 3)
Let i be 990/(-12)*64/6. Let l be i/(-88) - 16/2. Let 1/4 + 1/2*h + 1/4*h**l = 0. Calculate h.
-1
Let v = -1053 + 113725/108. Let w(b) be the third derivative of 1/270*b**5 - v*b**4 + 0*b + 0*b**3 + 0 - b**2. What is p in w(p) = 0?
0, 1
Let a = -1294 - -949. Let r be (5/(-2))/(a/(-18) + -20). Find u, given that -2/3*u + 2/15*u**r + 2/15*u**2 + 2/5 = 0.
-3, 1
Suppose 29 = 36*i - 43. Factor 25*v**4 - 90 + 67156*v + 153*v**