 = 9*s**3 - 174*s**2 - 375*s + 294. Suppose -24*t - 10*t = -34. Let z(j) = t*b(j) + 18*a(j). Factor z(q).
-3*(q + 7)**2*(3*q - 2)
Let w(q) be the second derivative of -5*q**5/4 + 195*q**4/2 - 520*q**3 + 880*q**2 - 31*q - 3. Let w(p) = 0. What is p?
4/5, 2, 44
Find k such that 23/3*k**2 + 0 - 8*k**3 - 5/2*k - 1/6*k**5 + 3*k**4 = 0.
0, 1, 15
Suppose -12*l + 2077 + 72011 = 0. Suppose 6166*x = l*x. Factor 1/2*c**2 + 0*c + x - 1/4*c**3.
-c**2*(c - 2)/4
Suppose 2*n + 2*n + 2*r - 548 = 0, -4*n - r + 550 = 0. Let y be n/8 + (-18)/(-24). Factor -7 - 15*x**2 + 46 + 77*x + 31 + y*x.
-5*(x - 7)*(3*x + 2)
Suppose -2*b + 6 = b. Let c be (17437/(-282) + 62)*0. Factor c + 1/2*y**3 + y**b + 0*y.
y**2*(y + 2)/2
Factor -290/3*g + 0 + 2/3*g**2.
2*g*(g - 145)/3
Let v(d) be the second derivative of 0 + 2/35*d**6 - 11/14*d**4 + 1/98*d**7 + 36/7*d**2 - 96*d - 2/7*d**3 - 9/140*d**5. Find n, given that v(n) = 0.
-3, -2, 1, 2
Factor -27*l**2 - 69 + 50 + 37*l - l**3 + 10*l**2.
-(l - 1)**2*(l + 19)
Let t(k) be the third derivative of k**6/180 - k**4/12 + 28*k**3 + 8*k**2 - 9. Let o(a) be the first derivative of t(a). Determine u so that o(u) = 0.
-1, 1
Let z(n) be the first derivative of -n**5/210 - 3*n**4/28 - 8*n**3/21 - 67*n**2/2 - 146. Let d(o) be the second derivative of z(o). Factor d(m).
-2*(m + 1)*(m + 8)/7
Suppose -4*n + 3*y = 7, 10 + 14 = 2*n + 4*y. Factor -34*v**2 + 67*v**n - 58*v**2 - 95*v + 20.
-5*(v + 4)*(5*v - 1)
Let 0*x + 0 - 44/9*x**3 + 1/9*x**4 + 41/3*x**2 = 0. What is x?
0, 3, 41
Let j be (-2)/(-3)*(-6 + 9). Let l = 13049 + -13045. Factor -32/3*x + 16/3 + l*x**j.
4*(x - 2)*(3*x - 2)/3
Let s be 168/18 + (-1080)/324. Let u(g) be the third derivative of 4*g + 1/180*g**s + 3*g**2 - 1/36*g**4 + 0 + 1/60*g**5 + 0*g**3. Find o such that u(o) = 0.
-2, 0, 1/2
Let k(a) be the second derivative of a**5/60 + a**4/6 + 47*a**2 - 60*a. Let c(j) be the first derivative of k(j). Find q, given that c(q) = 0.
-4, 0
Find x such that -240*x**2 - 5*x**5 - 151/3*x**4 - 508/3*x**3 - 416/3*x - 80/3 = 0.
-5, -2, -2/3, -2/5
Suppose -120 - 79 + 145*o**3 + 159 - 143*o**2 + 5*o**5 - 45*o**4 + 71*o**2 + 150*o - 143*o**2 = 0. Calculate o.
1, 2, 4
Let q(c) be the second derivative of c**6/36 + 7*c**5/24 + 25*c**4/36 + 17*c - 36. What is a in q(a) = 0?
-5, -2, 0
Let b(f) be the first derivative of 3/5*f**5 + 0*f**2 + 3*f**4 - 5*f**3 + 0*f + 21. Determine d so that b(d) = 0.
-5, 0, 1
Suppose -7 = -41*j + 44*j + 4*u, 0 = -2*j + 5*u + 26. Let b(d) be the first derivative of 4/3*d**j + 1/2*d**4 - 18 + 0*d**2 - 2/5*d**5 + 0*d. Factor b(h).
-2*h**2*(h - 2)*(h + 1)
Let i(r) be the third derivative of -254*r**7/735 + 2*r**6/105 + 127*r**5/105 - 2*r**4/21 + 740*r**2. Suppose i(s) = 0. What is s?
-1, 0, 4/127, 1
Suppose 4*p - 11 = -d + 31, 12*d = p + 14. Let 1/6*v + 1 - 1/6*v**3 - v**d = 0. Calculate v.
-6, -1, 1
Let v = -64872 + 64875. Factor -120*r - 236/3*r**2 - 54 - 2/3*r**4 - 40/3*r**v.
-2*(r + 1)**2*(r + 9)**2/3
Suppose -l - 3*l = -5*l. Let a be ((l - 1) + 2)*(-2 + 4). Solve -3*s**2 + 7*s**a - 3*s**3 + 7*s**2 + 6*s - 8*s**2 = 0 for s.
-1, 0, 2
Let a(f) be the first derivative of f**4/30 + 1364*f**3/45 + 116281*f**2/15 - 2895. Determine j so that a(j) = 0.
-341, 0
Let h(l) be the third derivative of -l**5/180 + 53*l**4/8 + 239*l**3/9 + 139*l**2 + 2*l. Determine v so that h(v) = 0.
-1, 478
Factor 50/3*b**3 + 8 - 64*b**2 + 118/3*b.
2*(b - 3)*(b - 1)*(25*b + 4)/3
Let f(o) be the third derivative of o**7/168 + o**6/6 + 3*o**5/2 + 20*o**4/3 - 47*o**3/2 - 131*o**2. Let g(d) be the first derivative of f(d). Factor g(k).
5*(k + 2)**2*(k + 8)
Find f, given that -1179/5*f**4 + 81/5*f**5 + 1347*f**2 + 3271/5*f**3 + 2456/5*f + 252/5 = 0.
-1, -2/9, 7, 9
Let o(w) = -67*w**4 - 64*w**3 - 42*w**2 - 52. Let p(g) = -32*g**4 - 32*g**3 - 20*g**2 - 24. Let q(k) = -6*o(k) + 13*p(k). Factor q(d).
-2*d**2*(d + 2)*(7*d + 2)
Let w(u) = -15*u**3 - 1107*u**2 - 745*u - 119. Let q(a) = a**3 - 4*a**2 - a - 1. Let f(y) = -6*q(y) - w(y). Factor f(c).
(c + 125)*(3*c + 1)**2
Factor 43*w + 1/2*w**4 - 85/2 + 42*w**2 - 43*w**3.
(w - 85)*(w - 1)**2*(w + 1)/2
Let c be (-68757)/195 - (-4)/(-10). Let j = -349 - c. Factor 2/9*i**3 + 0*i**j + 0 - 2/9*i**5 + 0*i + 0*i**2.
-2*i**3*(i - 1)*(i + 1)/9
Suppose -52*u + 35*u + 34 = 0. Let -911 - u*n**3 + 911 - 2*n**4 + 12*n**5 = 0. Calculate n.
-1/3, 0, 1/2
Let c(r) = -60*r**3 - 294*r**2 - 2016*r - 1712. Let k(o) = 269*o**3 + 1173*o**2 + 8065*o + 6846. Let h(u) = 18*c(u) + 4*k(u). Suppose h(t) = 0. Calculate t.
-143, -6, -1
Let g(u) be the first derivative of u**3/12 + 59*u**2/4 + 3481*u/4 - 923. Solve g(j) = 0.
-59
Suppose 2*h - k = -1, -3520*h = -3516*h - 3*k + 7. Find z such that 0 - 1/5*z**3 + 0*z**h + 1/5*z = 0.
-1, 0, 1
Suppose 5*x + 0*x + 124 = -4*f, -5*f - 138 = 2*x. Let j = -24 - f. Let -18*a**3 + 30*a**5 - 7*a**3 + 5*a**4 + 15*a**j - 25*a**5 = 0. What is a?
-3, 0, 1
Let q(y) be the third derivative of 2209*y**6/200 - 6721*y**5/100 + 283*y**4/40 - 3*y**3/10 + y**2 + 132*y + 8. Factor q(c).
3*(c - 3)*(47*c - 1)**2/5
Let t(o) be the third derivative of -o**9/20160 + o**8/1344 + 59*o**5/60 + 5*o**2. Let r(z) be the third derivative of t(z). Let r(i) = 0. Calculate i.
0, 5
Let u(v) be the first derivative of -16*v**4 - 129 + 296/15*v**3 + 18/5*v - 12*v**2 + 128/25*v**5. Factor u(r).
2*(2*r - 1)**2*(4*r - 3)**2/5
Let d(i) = 1966*i**3 - 2380*i**2 + 944*i - 149. Let s(t) = -7865*t**3 + 9520*t**2 - 3775*t + 600. Let r(h) = 25*d(h) + 6*s(h). Let r(a) = 0. What is a?
5/14, 1/2
Let n(r) be the second derivative of -10*r**7/63 + 34*r**6/45 + 28*r**5/5 - 16*r**4/9 - 256*r**3/9 + 32*r**2 + 2*r + 1. Let n(h) = 0. What is h?
-2, 2/5, 1, 6
Let x = 652 + -650. Determine k so that 9*k**2 + 10*k**2 - 58 - 4*k**x + 10*k + 58 + 5*k**3 = 0.
-2, -1, 0
Suppose -16*i + 18*i = 8. Suppose i*m + 4828 = 8*m. Factor 6*z**2 + m*z**3 - 21*z**2 - 45*z + 135 - 1202*z**3.
5*(z - 3)**2*(z + 3)
Let a(d) be the third derivative of -d**8/840 + 113*d**7/525 - 1679*d**6/150 + 4703*d**5/75 - 1837*d**4/12 + 605*d**3/3 + 3*d**2 + 120*d. Solve a(b) = 0 for b.
1, 55
Factor 3/4*b**2 + 585 + 231/4*b.
3*(b + 12)*(b + 65)/4
Factor 352*q - 296/3*q**2 - 384 + 2*q**3 - 1/3*q**5 + 3*q**4.
-(q - 4)**3*(q - 3)*(q + 6)/3
Suppose 10*g + 12 = t + 6*g, -g = 4. Let i be (t/(-7))/(101 - 99). Factor 4/7 - i*w - 2/7*w**2.
-2*(w - 1)*(w + 2)/7
Suppose -35*w = 14*w + w. Let i(d) be the third derivative of -9*d**3 + w + 0*d - 1/40*d**5 - 3/4*d**4 + 14*d**2. Factor i(q).
-3*(q + 6)**2/2
Let 4/3*f**4 + 0 + 4/3*f**5 + 0*f - 4/3*f**2 - 4/3*f**3 = 0. What is f?
-1, 0, 1
Let q(j) be the first derivative of -j**3/3 + 31*j**2/2 + 312*j + 320. Factor q(l).
-(l - 39)*(l + 8)
Let o be (-31 - -23) + 23960/2996. Let r = o + 755/2247. Let -1/3 - r*a - a**3 + 5/3*a**2 = 0. What is a?
-1/3, 1
Let z be (-4)/6*756/(-56). Find p such that -68 + 68 + 4*p + 6*p**3 - z*p**2 - p**4 = 0.
0, 1, 4
Let n = -203480/3 + 67827. Let -h**3 + 5/3*h**2 - 2/3*h - 1/3*h**4 + 0 + n*h**5 = 0. Calculate h.
-2, 0, 1
Determine k so that 4558/11*k - 2224/11*k**2 - 36 + 2*k**3 = 0.
1/11, 2, 99
Find h, given that -2937888 - 1212*h - 1/8*h**2 = 0.
-4848
Factor 1/3*n**2 + 452929/3 + 1346/3*n.
(n + 673)**2/3
Suppose -18*r + 16*r = -140. Let h = r + -35. Factor -4 + 493*z**2 + 55*z + h*z**3 - 413*z**2 + 14.
5*(z + 1)**2*(7*z + 2)
Factor 170 - 3*k**2 - 13*k**2 + 126*k - 36*k**2 + 2*k**3 + 8*k**2 + 2*k**2.
2*(k - 17)*(k - 5)*(k + 1)
Let l(v) = 9*v**2 - 40653*v - 34394841. Let s(d) = 2*d**2 - 10163*d - 8598712. Let k(y) = 5*l(y) - 21*s(y). Factor k(z).
3*(z + 1693)**2
Let t be (21/(-14))/(4/(-48)). Let v be ((-3)/(-2))/((-2)/(-4)). Factor -2*b + 32*b**3 - 5*b**4 - 10*b**2 + 15 - t*b - 12*b**v.
-5*(b - 3)*(b - 1)**2*(b + 1)
Factor -968/15*q + 12/5*q**3 - 2/15*q**4 - 22/5*q**2 + 0.
-2*q*(q - 11)**2*(q + 4)/15
Suppose 16 = 9*h - 11. Factor -13*y**h - 1386*y + 3920 + 8*y**3 - 417*y - 275*y**2 - 1837*y.
-5*(y - 1)*(y + 28)**2
Suppose 24*b = 2*h + 19*b + 25, 2*h + 49 = -3*b. Let z be (-155)/(-90) - (-30)/h. Factor 2/9*m**5 - z*m**4 - 4/9*m**3 + 0*m**2 + 0 + 0*m.
2*m**3*(m - 2)*(m + 1)/9
Suppose 0 = -d - 3*i + 10, 12*d - 70 = 8*d - 2*i. Determine o, given that -d + 15 + 52 + 312*o + 507*o**2 = 0.
-4/13
Let k(m) be the third derivative of 0 + 64*m**2 + 0*m**4 - 1/540*m**5 + 1/1080*m**6 + 0*m**3 + 0*m. Wh