 + 13*c**3 + 11*c**2. Let d(h) = -2*h**4 - 16*h**3 - 14*h**2. Let z(r) = 2*d(r) + 3*x(r). Factor z(q).
q**2*(q + 1)*(2*q + 5)
Let s(d) = -33*d**2 - 1650*d + 5. Let n be s(-50). Let o(q) be the first derivative of 0*q + 4/5*q**n + 7*q**4 + 44/3*q**3 + 10*q**2 - 42. Solve o(i) = 0 for i.
-5, -1, 0
Suppose -i - 54*r + 49*r = -22, -3*i + 3*r - 6 = 0. Factor 3*o**i - 7*o**4 + 8*o**2 + 0*o**2 + 2*o**3 - 5*o**2 - o**2.
-o**2*(o - 1)*(7*o + 5)
What is v in 46/3 - 25/3*v + 1/3*v**2 = 0?
2, 23
What is u in -6180/7*u - 648/7*u**2 - 4/7*u**3 - 15200/7 = 0?
-152, -5
Let b be (-2 - -2)/(-417 - -388). Factor -4/7*y**4 - 4/7*y + b + 4/7*y**2 + 4/7*y**3.
-4*y*(y - 1)**2*(y + 1)/7
Determine k so that -144*k + 576 - 4*k**4 + 4890*k**3 - 352*k**2 - 9796*k**3 + 4830*k**3 = 0.
-12, -6, -2, 1
Factor 65/9*s - 64/9 - 1/9*s**2.
-(s - 64)*(s - 1)/9
Let t(u) be the third derivative of u**7/350 + 103*u**6/200 - 21*u**5/10 + 320*u**2 - u. Factor t(x).
3*x**2*(x - 2)*(x + 105)/5
Suppose -2*b = x - 105, 0 = 2*x - 3 - 7. Factor 41 - b*h + 75*h**2 + 11 - 7 + 10*h**3 - 80*h.
5*(h - 1)*(h + 9)*(2*h - 1)
Suppose 7*k = 23 + 26. Let c be (-2)/k + 15*12/420. Find u such that 0*u**2 - 2/7*u**3 + c*u**4 - 1/7 + 2/7*u = 0.
-1, 1
Let a(m) be the second derivative of 5/18*m**4 + 1/15*m**5 + 0 + 0*m**2 + 5/3*m**3 - 19*m + 1/270*m**6. Let n(o) be the second derivative of a(o). Factor n(v).
4*(v + 1)*(v + 5)/3
Factor -33 + 9/2*b**3 - 93/4*b**2 + 47*b - 1/4*b**4.
-(b - 11)*(b - 3)*(b - 2)**2/4
Let y be (-65)/(260/48) + 97/8. Solve y*z**2 - 61/8*z + 15/2 = 0.
1, 60
Let x be (-39 + 17 - -15) + 142/20. Let y(d) be the first derivative of 1/5*d**3 + 18 - 1/20*d**4 - 3/5*d + x*d**2. Factor y(k).
-(k - 3)*(k - 1)*(k + 1)/5
Factor -255*b - 5*b**4 + 11570*b**3 - 15*b + 360*b**2 - 675 - 11620*b**3.
-5*(b - 3)**2*(b + 1)*(b + 15)
Let m = 1127 - 675. Let i = 455 - m. What is t in -i*t**3 + 0 - 9/2*t**4 + 3*t**5 + 0*t**2 + 0*t = 0?
-1/2, 0, 2
Let v(s) = -215*s**2 - 700*s - 465. Let u(a) = 71*a**2 + 233*a + 156. Let b(h) = -10*u(h) - 3*v(h). Find c, given that b(c) = 0.
-33/13, -1
Let h(d) = d**2 + 2*d - 7. Let y be h(-3). Let m = y - -6. Let 65*a**4 + 7*a**m - 70*a**4 + 0*a**3 + 10*a**5 - 10*a**3 - 2*a**2 = 0. What is a?
-1, 0, 1/2, 1
Let l = 1523911 + -10667309/7. Solve -68/7*q**3 + 16/7*q**5 + 52/7*q**4 + 52/7*q - l*q**2 + 16/7 = 0.
-4, -1, -1/4, 1
Let a(c) be the first derivative of 3*c**5 - 95*c**4/4 + 20*c**3/3 + 30*c**2 - 2318. Factor a(h).
5*h*(h - 6)*(h - 1)*(3*h + 2)
Let w(q) be the second derivative of q**4/18 - 265*q**3/9 + 2056*q**2/3 + 1467*q. Find p, given that w(p) = 0.
8, 257
Let s(f) be the second derivative of 29*f**3/3 + 29*f**2 + 166*f. Let h(g) = g**2 + 118*g + 117. Let n(p) = -4*h(p) + 10*s(p). Factor n(t).
-4*(t - 28)*(t + 1)
Let i(l) be the third derivative of l**5/240 - 145*l**4/32 - 109*l**3/6 - 10*l**2 - 253*l. Factor i(x).
(x - 436)*(x + 1)/4
Let h(q) = -9*q**2 + 411*q + 1204. Let j(n) = -64*n**2 + 2880*n + 8424. Let r(g) = 36*h(g) - 5*j(g). Let r(m) = 0. Calculate m.
-3, 102
Let f(o) be the third derivative of -o**5/15 + 117*o**4/2 + 704*o**3/3 - 42*o**2 + 2*o - 17. Factor f(q).
-4*(q - 352)*(q + 1)
Let c be 40/8 - (-3)/3. Factor 113*b**2 + 4*b - 10*b - 110*b**2 + c - 15.
3*(b - 3)*(b + 1)
Factor -14/5 - 4/3*s - 2/15*s**2.
-2*(s + 3)*(s + 7)/15
Suppose 3*u - 4 = s, 2*u = 5*s - 2 - 4. Suppose 2*w**2 - 18 + 18 + 105*w - 7*w**u = 0. What is w?
0, 21
Factor -30 - 2/5*l**2 - 56/5*l.
-2*(l + 3)*(l + 25)/5
Let -5/3*v**4 + 0 - 5*v**3 + 20/3*v + 0*v**2 = 0. What is v?
-2, 0, 1
Let q = -7983863/11 + 725809. Suppose 0*b + 8/11 - 34/11*b**2 - q*b**3 - 10/11*b**4 = 0. Calculate b.
-2, -1, 2/5
Let w(d) be the second derivative of 2 - 1936/3*d**2 - 86*d - 1/18*d**4 + 88/9*d**3. Factor w(x).
-2*(x - 44)**2/3
Let a(s) be the third derivative of -s**5/60 - 5*s**4/6 - 2*s**2 - 144*s. Let k be a(0). Find i, given that -12/5*i**2 - 6/5 + 16/5*i + k*i**3 + 2/5*i**4 = 0.
-3, 1
Solve 12/13*f + 2/13*f**3 + 0 - 14/13*f**2 = 0.
0, 1, 6
Suppose 3*z + 2*t - 14 = 0, 73*z = 74*z + t - 7. Let v be 1 - (-10)/(-28)*2. Factor z - 4/7*a - 8/7*a**3 + 10/7*a**2 + v*a**4.
2*a*(a - 2)*(a - 1)**2/7
Let j(a) be the second derivative of a**6/30 - 7*a**5 + 139*a**4/12 + 3670*a. Factor j(z).
z**2*(z - 139)*(z - 1)
Let f(l) be the first derivative of -l**5/60 - 13*l**4/6 - 213*l**2/2 + 50. Let y(u) be the second derivative of f(u). Suppose y(r) = 0. Calculate r.
-52, 0
Suppose 19*i = 17*i + 8. Find h, given that -h**3 + 91*h**2 + 2*h - 2 - 4*h**4 - h + 3*h**i - 177*h**2 + 89*h**2 = 0.
-2, -1, 1
Factor 1/2*z + 1/8*z**2 - 77/8.
(z - 7)*(z + 11)/8
Factor 6*t + 0 - 6*t**3 - 2/7*t**2 + 2/7*t**4.
2*t*(t - 21)*(t - 1)*(t + 1)/7
Let h = 1 + -2. Let g(t) = -t**4. Let p(k) = 56*k - 44*k + 5*k**3 - 23*k**2 - 17*k**3 + 21*k**2 - k**4. Let q(s) = h*p(s) + 3*g(s). Factor q(j).
-2*j*(j - 6)*(j - 1)*(j + 1)
Suppose -15*c + 11*c + 4*m + 32 = 0, -c = 3*m + 4. Factor 10*x**2 - 19*x**3 + 0*x**4 - 4*x - 2*x**4 - 3*x**c + 5*x**5 + 13*x**3.
2*x*(x - 1)**3*(x + 2)
Let w(t) be the third derivative of -125*t**8/336 - 1405*t**7/42 + 103*t**6/2 + 1348*t**5/3 - 2840*t**4/3 + 760*t**3 + 7*t**2 + 39. Find k, given that w(k) = 0.
-57, -2, 2/5, 2
Let f(m) be the first derivative of 0*m**4 + 0*m - 1/12*m**5 + 0*m**3 - 9 + 13*m**2. Let b(g) be the second derivative of f(g). What is k in b(k) = 0?
0
Suppose -41*c - 830 = -51*c. Solve -31*x**2 - 34*x**2 + c*x**2 + 4*x**3 - 3*x**3 = 0.
-18, 0
Let d(w) be the first derivative of w**6/18 + 28*w**5/15 + 15*w**4/4 - 202*w**3/9 - 266*w**2/3 - 104*w + 1631. Suppose d(r) = 0. What is r?
-26, -2, -1, 3
Let i(m) = 5*m**3 - 11*m**2 - 28*m + 306. Let c be 1 + 0 + (3 - 17). Let b(p) = -11*p**3 + 21*p**2 + 54*p - 613. Let r(w) = c*i(w) - 6*b(w). Factor r(q).
(q - 3)*(q + 10)**2
Let z(n) be the first derivative of -n**3/3 + 33*n**2 + 847*n - 11273. Factor z(k).
-(k - 77)*(k + 11)
Suppose 0 = -6*j + 71 + 1. Suppose q = 4*f + 10, 2*q - j = -3*q + f. What is g in -6 + 5*g**2 - q*g - 5*g + 2*g + 5*g**3 + 1 = 0?
-1, 1
Let w = -2754/35 - -555/7. Suppose -28 = -2*u - 12*u. Suppose 12/5*m**3 - 12/5*m**u - w*m**4 + 0*m + 0 = 0. Calculate m.
0, 2
Suppose 5*i - 27 = t, -4*t - i = 4 - 22. Let a(n) be the first derivative of 2/15*n**5 + 10 + 0*n**4 + 0*n - 2/9*n**t + 0*n**2. Solve a(h) = 0 for h.
-1, 0, 1
Let s(a) be the third derivative of a**6/60 + 13*a**5/5 + 71*a**4/12 - 154*a**3 + 1616*a**2. Find u such that s(u) = 0.
-77, -3, 2
Let w(y) = -5*y**2 + 41*y + 78. Let f(n) = 4*n**2 - 41*n - 43. Let j(v) = 6*f(v) + 5*w(v). Factor j(m).
-(m - 3)*(m + 44)
Let p(x) be the first derivative of 4*x**5/5 - 9*x**4 + 20*x**3 + 50*x**2 + 1523. Factor p(k).
4*k*(k - 5)**2*(k + 1)
Let v(c) be the first derivative of -11*c**6/3 + 34*c**5/5 + 117*c**4/2 + 278*c**3/3 + 50*c**2 + 4753. Factor v(h).
-2*h*(h + 1)**3*(11*h - 50)
Suppose -28 - 1421*l - 79*l**4 + 107*l**2 + 755*l + 774*l - 99*l**3 - 9*l**5 = 0. What is l?
-7, -2, -1, 2/9, 1
Let x(b) = -b**3 - 3*b**2 - 4*b - 13. Let r be x(-3). Let a be r/2*(-40)/(7 - 2). What is q in -4*q**2 - a*q**2 - 12*q + 6*q**2 = 0?
-6, 0
Let w(y) = 2*y**2 + y + 2. Let x(r) = -r**3 - 105*r**2 - 3244*r - 3128. Let m(t) = -12*w(t) + 3*x(t). Find d, given that m(d) = 0.
-56, -1
Let p(b) be the first derivative of -b**3/3 - b**2/2 + 92. Let t be p(0). Solve 5/4*d**2 + d + 1/4*d**3 + t = 0.
-4, -1, 0
Let x(n) = -n**3 + n**2 - 5. Let l(w) = w**4 + 138*w**3 + 332*w**2 + 349*w + 211. Let h(i) = -2*l(i) - 38*x(i). Find c, given that h(c) = 0.
-116, -1
Suppose -10*h + 96*h = 4*o + 48, 4*h - o - 12 = 0. Factor -2*c + h + 1/4*c**2.
c*(c - 8)/4
Let u(z) be the first derivative of -21*z**3/8 + 291*z**2/16 - 57*z/2 + 1720. Solve u(h) = 0 for h.
1, 76/21
Let m(h) be the third derivative of -2/15*h**5 - 2/105*h**7 + 0 + 0*h**4 - 1/10*h**6 + 0*h**3 + 0*h - 91*h**2. Determine l, given that m(l) = 0.
-2, -1, 0
Let a(y) = y**4 + 146*y**3 - 780*y**2 - 1411*y + 1989. Let q(h) = 30*h**3 - 156*h**2 - 282*h + 398. Let t(w) = -2*a(w) + 11*q(w). Let t(n) = 0. What is n?
-2, 1, 10
Let w(u) be the third derivative of -u**6/40 - 23*u**5/20 - 59*u**4/4 - 48*u**3 - 3354*u**2. Suppose w(v) = 0. What is v?
-16, -6, -1
Let s(f) = 2*f**3 + 8*f**2 + 2 - f**4 - 9*f**2 - 3. Let a(t) = -5*t**4 + 12*t**3 + 7*t**2 + 6*t - 4. Let u(p) = -5*a(p) + 20*s(p)