0 + 10/3*v**2 - 2*v**3.
-2*v*(v - 2)*(3*v + 1)/3
Let q(i) be the first derivative of i**7/1960 + i**6/42 + 19*i**5/40 + 21*i**4/4 - 60*i**3 - 300. Let h(l) be the third derivative of q(l). Solve h(t) = 0.
-7, -6
Let a be 10/8 - (-192)/256. Factor 24 + 2*f**2 + 455*f - 4*f**2 + 48 - 483*f - 2*f**a.
-4*(f - 2)*(f + 9)
Suppose 5*c - 3*i = 2, -5*i = -953*c + 952*c - 26. Let l(b) be the first derivative of -8/3*b**3 - 5 - b**c + 2*b**2 + 8*b. What is p in l(p) = 0?
-2, -1, 1
Let n(o) = -16*o - 77. Let s be n(-5). Factor -s*u - 117*u**2 + 228*u**2 - 114*u**2.
-3*u*(u + 1)
Suppose 105*u - 76 + 113 = 457. Let h(p) be the second derivative of 2/55*p**5 + 3/11*p**2 + 0 + 8/33*p**3 - 5/22*p**u - 3*p. Let h(r) = 0. Calculate r.
-1/4, 1, 3
Let g(v) be the third derivative of 3*v**5/100 + 241*v**4/10 - 322*v**3/5 + 73*v**2 + 33. Let g(h) = 0. Calculate h.
-322, 2/3
Let y(j) = -j**2 + 9*j + 18. Let c be y(11). Let u be 2*(-1)/(-1)*c. Let f(l) = -l**2 - l. Let h(w) = -16*w**2 - 2. Let t(k) = u*f(k) + h(k). Solve t(a) = 0.
1/2
Let b(o) be the first derivative of o**3/24 + 19*o**2/8 + 105*o/8 + 1024. Factor b(m).
(m + 3)*(m + 35)/8
Let r(v) be the second derivative of 130*v + 0 + 3/5*v**4 - 11/10*v**3 - 3/100*v**5 + 0*v**2. Determine d so that r(d) = 0.
0, 1, 11
Let c(d) = -2*d**3 - 2*d**2 + 2*d. Let l be c(-2). Let x be -3 + 3 + l + (-28)/8. Factor 0 - 1/8*h**3 - 3/8*h + x*h**2.
-h*(h - 3)*(h - 1)/8
Solve -95*n**3 + 11982*n**4 + 11990*n**4 - 23967*n**4 + 300*n**2 = 0.
0, 4, 15
Let a(s) = -s**2 - 10*s - 19. Let v be a(-10). Let b = 24 + v. Factor -5*k**2 + 8 + 1 + 1 - b*k.
-5*(k - 1)*(k + 2)
Suppose 38321*l - 51 = 38270*l. Factor -1/4*w**2 + 3/4*w + l.
-(w - 4)*(w + 1)/4
Let l(d) be the second derivative of d**5/70 + 13*d**4/21 + 71*d**3/21 + 46*d**2/7 + 4466*d. Factor l(r).
2*(r + 1)*(r + 2)*(r + 23)/7
Let a(d) be the first derivative of d**6/9 - 8*d**5/5 + 10*d**4/3 - 6805. Suppose a(z) = 0. What is z?
0, 2, 10
Let h(m) be the second derivative of -33*m**5/50 - 443*m**4/15 - 244*m**3/5 - 104*m**2/5 + m - 3185. Solve h(g) = 0 for g.
-26, -2/3, -2/11
Let g(n) be the first derivative of n**4/20 + n**3/3 - 6*n**2/5 - 36*n/5 + 2658. Determine w so that g(w) = 0.
-6, -2, 3
Let o(c) be the second derivative of 5/54*c**4 - 16/9*c**2 + 0 + 166*c + 38/27*c**3. Factor o(t).
2*(t + 8)*(5*t - 2)/9
Let a(v) be the third derivative of v**6/200 + 13*v**5/50 - 19*v**4/8 - 2166*v**3/5 - 2762*v**2. Factor a(i).
3*(i - 12)*(i + 19)**2/5
Let j = -4126 - -28888/7. Let -j - 29/7*b**2 - 72/7*b**3 + 37/7*b = 0. Calculate b.
-1, 2/9, 3/8
Let d be 9/(-12) - (-49959)/420. Let u = d + -117. Factor 1/5 + o**2 - u*o.
(o - 1)*(5*o - 1)/5
Let w(j) be the third derivative of 0 + 325*j**2 + 0*j + 1/270*j**5 + 11/27*j**4 + 43/27*j**3. Suppose w(z) = 0. What is z?
-43, -1
Let z(n) be the first derivative of -n**5/180 - 7*n**4/108 - 2*n**3/9 + 58*n + 213. Let w(s) be the first derivative of z(s). Determine l so that w(l) = 0.
-4, -3, 0
Let g(x) be the third derivative of 0 + 107*x**2 - 65/18*x**4 + 0*x + 4225/9*x**3 + 1/90*x**5. Factor g(d).
2*(d - 65)**2/3
Let r be (112/6 - (0 - -2))/(56979/1591029). Let r - 220/13*x + 2/13*x**2 = 0. Calculate x.
55
Let q(p) be the first derivative of -5*p**2 + 100 + 1/2*p**4 + 6*p + 2/3*p**3. Factor q(z).
2*(z - 1)**2*(z + 3)
Let j(q) = 2*q**3 + 9*q**2 - 547*q - 4365. Let f be j(-10). Let 2/9*i**f - 16/9*i**2 - 2/9*i**3 + 16/9*i**4 + 0 + 0*i = 0. What is i?
-8, -1, 0, 1
Let -2/5*d**4 - 22/5*d**3 - 56/5*d + 0 - 64/5*d**2 = 0. What is d?
-7, -2, 0
Let l(w) be the second derivative of -2*w**7/21 - 192*w**6/5 + 1752*w**5/5 - 3520*w**4/3 + 1568*w**3 + 446*w + 10. Factor l(k).
-4*k*(k - 2)**3*(k + 294)
Let j(x) be the first derivative of -2*x**3/21 + 2172*x**2/7 - 2358792*x/7 + 3621. Factor j(f).
-2*(f - 1086)**2/7
Let r(l) be the first derivative of -l**4/28 - 5*l**3/21 - 2*l**2/7 + 1607. Factor r(n).
-n*(n + 1)*(n + 4)/7
Let -2/15*x**4 - 14/15*x**3 - 8/15*x**2 + 0 + 8/5*x = 0. Calculate x.
-6, -2, 0, 1
Let q(y) be the first derivative of -98 + 0*y + 16/9*y**2 + 16/27*y**3 - 7/18*y**4 + 2/45*y**5. Suppose q(m) = 0. What is m?
-1, 0, 4
Let d(w) = 8*w**2 + 84*w - 90. Let y(g) = 4*g**2 + 29*g - 30. Let m(o) = 3*d(o) - 10*y(o). Factor m(s).
-2*(s + 3)*(8*s - 5)
Let l = 505611 + -505609. Factor -9*f**l + 0*f + 0 + 1/4*f**3.
f**2*(f - 36)/4
Let l(t) = 63*t**2 - 881*t - 11. Let a be l(14). Factor 1/7*f + 16/7*f**a - 8/7*f**2 + 0.
f*(4*f - 1)**2/7
Factor 47/2*d**3 + 0 - 191/4*d**2 + 1/4*d**4 + 24*d.
d*(d - 1)**2*(d + 96)/4
Let u = -4071 - -4071. Let a(i) be the first derivative of 0*i + 1/6*i**3 - 5 - 1/10*i**5 - 1/8*i**4 + 1/12*i**6 + u*i**2. Factor a(s).
s**2*(s - 1)**2*(s + 1)/2
Let c(b) be the second derivative of 3*b**5/20 + 437*b**4/4 + 47523*b**3/2 - 143883*b**2/2 - 1861*b. Suppose c(t) = 0. What is t?
-219, 1
Let f(a) be the second derivative of -94*a - 3/20*a**5 - 1/42*a**7 - 1/5*a**6 + 0*a**2 + 0*a**3 + 0 + 5/6*a**4. Factor f(v).
-v**2*(v - 1)*(v + 2)*(v + 5)
Let y(v) be the first derivative of 2/15*v**5 + 0*v**2 + 8/15*v**4 - 7/45*v**6 - 13 + 0*v + 8/45*v**3. Solve y(l) = 0 for l.
-1, -2/7, 0, 2
Let c(d) be the second derivative of 2*d**6/15 + d**5 + 8*d**4/3 + 8*d**3/3 - 2*d + 196. Factor c(p).
4*p*(p + 1)*(p + 2)**2
Let g(h) be the first derivative of -2*h**3/19 + 326*h**2/19 + 218*h/19 + 4904. Factor g(p).
-2*(p - 109)*(3*p + 1)/19
Let d = 22 - 20. Let r(a) = -83*a**2 + d*a**2 - 76*a + 40 - 122*a + 29*a. Let o(w) = 41*w**2 + 84*w - 20. Let f(z) = -9*o(z) - 4*r(z). Factor f(p).
-5*(p + 2)*(9*p - 2)
Let s(h) = 5*h**2 - 30*h + 46. Let v be (-1032)/(-559) - (-4)/26. Let b(f) = -110*f**2 + 660*f - 1015. Let o(j) = v*b(j) + 45*s(j). Factor o(p).
5*(p - 4)*(p - 2)
Let y(i) be the second derivative of i**6/50 + 9*i**5/25 - i**4/5 - 24*i**3/5 - 4*i - 897. Factor y(u).
3*u*(u - 2)*(u + 2)*(u + 12)/5
Let q(j) be the third derivative of -j**5/36 - 95*j**4/2 + 3425*j**3/18 - 3058*j**2. Let q(a) = 0. What is a?
-685, 1
Let p(b) be the first derivative of -20*b**3/3 + 256*b**2 + 208*b + 793. What is g in p(g) = 0?
-2/5, 26
Let d(c) = 4*c**4 - 78*c**3 - 78*c**2 + 170*c. Let r(a) = 5*a**4 - 76*a**3 - 77*a**2 + 169*a. Let i(g) = -7*d(g) + 6*r(g). Find l, given that i(l) = 0.
-44, -2, 0, 1
Let s = -315 + 321. Let u be (-4)/s - (6 - 618/90). Let u - 2/5*w**2 + 1/5*w = 0. What is w?
-1/2, 1
Let g(c) be the first derivative of 11*c**6/18 - 86*c**5/15 - 59*c**4/3 - 40*c**3/9 - 20. Suppose g(p) = 0. Calculate p.
-2, -2/11, 0, 10
Let b = 3364/7007 - 190/637. Factor 0 + 0*r - 8/11*r**3 + 0*r**2 + b*r**5 - 6/11*r**4.
2*r**3*(r - 4)*(r + 1)/11
Suppose 0 = 2*d - 8*b + 96, 9*d - 6*d + 5*b = 60. Factor -2/5*f**4 + d + 0*f**2 + 0*f - 2/5*f**5 + 4/5*f**3.
-2*f**3*(f - 1)*(f + 2)/5
Suppose -s = -4*s. Suppose s = 2*i + k - 4, -2*k = i + 4 - 3. Factor -5*w**2 + 3 + i*w**4 + 38*w**3 - 38*w**3 - w**2.
3*(w - 1)**2*(w + 1)**2
Let a(s) = -55*s + 120. Let w be a(-16). Factor -b**3 + w - b**4 - 1000.
-b**3*(b + 1)
Let -474*x**3 - 93*x**2 + 9*x**2 + 9*x**2 + 1360*x**5 - 1363*x**5 - 525*x**2 - 93*x**4 = 0. What is x?
-25, -4, -2, 0
Let z(t) = 20*t**3 - 6732*t**2 - 13476*t - 6748. Let c(a) = 33*a**3 - 11220*a**2 - 22461*a - 11247. Let r(f) = 8*c(f) - 13*z(f). Determine k so that r(k) = 0.
-1, 563
Let m(o) be the third derivative of o**7/42 + 15*o**6/4 + 783*o**5/4 + 9020*o**4/3 + 16810*o**3 - 202*o**2 + 2*o + 3. Factor m(b).
5*(b + 2)*(b + 6)*(b + 41)**2
Let q = 48/26471 - -211240/291181. Factor -2/11*g**2 - 8/11 + q*g.
-2*(g - 2)**2/11
Let u(z) be the first derivative of -z**7/105 + z**6/15 - z**5/10 + z**2/2 + 3*z + 7. Let j(q) be the second derivative of u(q). Factor j(f).
-2*f**2*(f - 3)*(f - 1)
Suppose 34 = 5*c + 3*g, -117*c + 114*c + g + 12 = 0. Let 215/2*p**2 - 75/2*p - 20*p**5 - 145*p**3 + c + 90*p**4 = 0. What is p?
1/2, 1, 2
Factor 12*o - 12*o + 10*o**2 + 10*o + 11*o.
o*(10*o + 21)
What is b in -8/3 - 88/3*b - 50/3*b**3 + 146/3*b**2 = 0?
-2/25, 1, 2
Let c be 106/4 + 4043/(-130) + 31. Solve c*b + 12 + 3/5*b**4 + 6*b**3 + 99/5*b**2 = 0.
-5, -2, -1
Let b(m) be the third derivative of 7/36*m**4 + 1/36*m**5 - m**2 - 1/1260*m**7 + 0 + 5/12*m**3 - 1/180*m**6 - 101*m. Factor b(u).
-(u - 3)*(u + 1)**2*(u + 5)/6
Let v = 2499 + -2496. Let h(a) be the third derivative of 1/105*a**7 + 0 + 1/3*a**4 - 8*