, 1, 2
Factor -1/3*f**5 + 0*f + 0 + 4/3*f**4 + 0*f**2 + 5/3*f**3.
-f**3*(f - 5)*(f + 1)/3
Factor 0 - 5/4*s**4 + 5*s**3 + 5/2*s - 25/4*s**2.
-5*s*(s - 2)*(s - 1)**2/4
Suppose 6*c - 52 = -7*c. Let b(m) be the second derivative of 13/24*m**3 - 3/4*m**2 + 0 + 5/48*m**c + 3*m. Suppose b(n) = 0. What is n?
-3, 2/5
Let g be -12*((-160)/(-6))/5. Let h = 454/7 + g. Suppose -2/7*q**2 - 2/7*q**4 + 4/7 - h*q + 6/7*q**3 = 0. Calculate q.
-1, 1, 2
Let a(z) = -10*z**2 + 4*z - 15. Let g(q) = -8*q**2 + 3*q - 14. Let m(k) = -5*a(k) + 6*g(k). Let i be m(-2). Find y such that 0 - 3*y + 9/2*y**2 - 3/2*y**i = 0.
0, 1, 2
Suppose -4*s + 5*y - 8 - 9 = 0, 3*s = -2*y + 16. Let x(k) be the first derivative of 0*k - 1/4*k**4 - 2 + 0*k**s + 1/3*k**3. Solve x(n) = 0.
0, 1
Factor 0*k + 0 + 2*k**4 + 5/9*k**3 - 2/9*k**2.
k**2*(2*k + 1)*(9*k - 2)/9
Let b be (21/(-6))/(-86 + 79). Factor b*d**2 + 0 + 1/2*d.
d*(d + 1)/2
Let r(w) be the second derivative of w**5/40 - w**4/8 + w**3/4 + 4*w**2 - 2*w. Let d(f) be the first derivative of r(f). Factor d(j).
3*(j - 1)**2/2
Let h(a) be the third derivative of -a**5/15 + 9*a**4/2 + 116*a**3/3 - 710*a**2. Determine f so that h(f) = 0.
-2, 29
Let q(x) be the first derivative of -1/3*x**4 + 4 + 0*x + 0*x**3 - 1/15*x**5 - 9/2*x**2. Let g(t) be the second derivative of q(t). Factor g(b).
-4*b*(b + 2)
Let p be 33 + (-2)/(1 + 0). Suppose 6*h - p = 23. Factor -3 - n**2 + 19*n**2 - 24*n**4 + 3*n**3 + h*n**3 + 9 - 21*n + 9*n**5.
3*(n - 1)**3*(n + 1)*(3*n - 2)
Let a(q) be the first derivative of -q**4/20 - q**3/5 - 3*q**2/10 - q/5 + 187. Solve a(u) = 0.
-1
Let n(r) be the second derivative of r**4/36 - 5*r**3/6 + 7*r**2/3 - 677*r. Factor n(a).
(a - 14)*(a - 1)/3
Suppose 4*k - 14 = -2*r, -13*r = -8*r + 5. Let o(x) be the third derivative of -1/90*x**5 + 1/36*x**k + 0*x - 5*x**2 + 0 + 2/9*x**3. Solve o(l) = 0.
-1, 2
Let c(d) = -3*d**3 + 10*d. Let b be c(0). Factor 2/17*w**2 - 2/17*w + b.
2*w*(w - 1)/17
Suppose 4*m = -t + 4, -t + 8 = -3*m + t. Let z(p) be the first derivative of -1/2*p**4 + p**2 + 0*p + m*p**3 + 6. Solve z(k) = 0.
-1, 0, 1
Let d(w) be the third derivative of w**6/180 - 19*w**5/90 + 11*w**4/4 - 9*w**3 + 478*w**2. What is v in d(v) = 0?
1, 9
Let x(v) be the first derivative of -1/6*v**3 - 1/4*v**2 - 8 + 1/2*v + 1/8*v**4. Solve x(f) = 0 for f.
-1, 1
Let d(g) be the first derivative of g**3/27 + g**2/2 + 543. Suppose d(l) = 0. Calculate l.
-9, 0
Suppose 0 = -17*v + 24 + 27. Let o be 4/v - 56/(-6). Solve 2/3*m**2 - 16/3*m + o = 0 for m.
4
Let s(h) be the third derivative of -h**9/45360 + h**7/7560 + 5*h**4/24 + 7*h**2. Let d(o) be the second derivative of s(o). Solve d(n) = 0 for n.
-1, 0, 1
Suppose -177 - 359 = -8*l. Let w = 202/3 - l. Factor w*i**4 + 4/3*i**2 - 4/3*i**3 + 0 + 0*i.
i**2*(i - 2)**2/3
Let s be (4/15)/(30/3625). Let b = 1522/45 - s. Factor 4/5*k**2 - b*k**3 - 18/5 + 24/5*k - 2/5*k**4.
-2*(k - 1)**2*(k + 3)**2/5
Let z(a) be the first derivative of -5*a**4/4 + 3*a**3 - 12*a**2/5 + 4*a/5 - 48. Factor z(w).
-(w - 1)*(5*w - 2)**2/5
Determine w so that -46*w**4 + 140*w**3 + 43 + 52*w - 144 + 99 - 144*w**2 = 0.
1/23, 1
Let d(r) be the second derivative of 0*r**2 - 5/6*r**3 + 17*r + 1/6*r**6 + 1/4*r**5 - 5/12*r**4 + 0. Solve d(j) = 0 for j.
-1, 0, 1
Let k = -234 - -236. Let v(l) be the first derivative of -1/21*l**3 + 0*l**k - 6 + 1/7*l. Factor v(g).
-(g - 1)*(g + 1)/7
Let z(g) be the first derivative of g**3/6 + 11*g**2/4 - 6*g + 74. What is x in z(x) = 0?
-12, 1
Let x be 114/(-171) - (-267)/36. Solve -9/4*i**3 + 1/2*i + 0 - x*i**4 + 27/4*i**5 + 7/4*i**2 = 0 for i.
-1/3, 0, 2/3, 1
Let c = 31 + -25. Let s be 1/((c - 21)/(-5)). Factor -1/3 + s*o**2 + 0*o.
(o - 1)*(o + 1)/3
Let y(i) be the second derivative of i**4/8 - 100*i**3 + 30000*i**2 + 2*i - 187. Factor y(c).
3*(c - 200)**2/2
Let n = -13 + 16. Solve -i**2 + 5*i - 5*i - 6*i**3 + 7*i**n = 0 for i.
0, 1
Determine u so that 129*u**2 - 25*u**4 - 953*u**2 - 290*u - 8*u**4 + 1130*u + 6*u**5 + 366*u**3 - 288 - 43*u**4 = 0.
2/3, 2, 3, 4
Let i(j) = -33*j + 9. Let s be i(1). Let p be 18/s*2/(-3). Factor -3/4*m - p + 1/2*m**2.
(m - 2)*(2*m + 1)/4
Suppose 7*n - 497 = 217. Factor i + 11*i + 118 - n + 2*i**2.
2*(i + 2)*(i + 4)
Suppose -69*l - 126*l = 12*l - 621. Solve 0*v**l + 2/9*v**4 - 2/3*v**2 + 0 - 4/9*v = 0 for v.
-1, 0, 2
Let j(l) be the first derivative of 2*l**5/35 + 3*l**4/14 - 12*l**3/7 + 4*l**2/7 + 48*l/7 - 400. Factor j(t).
2*(t - 2)**2*(t + 1)*(t + 6)/7
Let g(d) = 335*d**2 - 420*d - 35. Let v(x) = -28*x**2 + 35*x + 3. Let r(i) = -3*g(i) - 35*v(i). Factor r(m).
-5*m*(5*m - 7)
Factor -2/3*p**3 - 20/3*p**2 + 48 - 8*p.
-2*(p - 2)*(p + 6)**2/3
Let j = 140 + -279/2. Let q(z) be the second derivative of 0 + j*z**2 + 0*z**3 - 1/12*z**4 + z. Solve q(o) = 0.
-1, 1
Let h(d) = 10*d**4 + 1075*d**3 - 428*d**2 - 9*d. Let z(r) = 5*r**4 + 537*r**3 - 214*r**2 - 4*r. Let m(n) = -4*h(n) + 9*z(n). Factor m(a).
a**2*(a + 107)*(5*a - 2)
Let m(g) = g**4 - 2*g**3 + g + 1. Let t(p) = 30*p**4 + 66*p**3 + 63*p**2 + 9*p. Let w(u) = -6*m(u) + t(u). Let w(q) = 0. What is q?
-2, -1, -1/2, 1/4
Let y = 16 - 13. Factor -h**3 - 6*h**2 + 3 - 3*h + 7*h**3 + 3 - y*h**3.
3*(h - 2)*(h - 1)*(h + 1)
Let p(m) be the second derivative of m**7/350 + 3*m**6/200 - m**4/10 + 39*m**2/2 - 17*m. Let l(w) be the first derivative of p(w). Determine o so that l(o) = 0.
-2, 0, 1
Let u(v) be the third derivative of -1/42*v**4 + 0*v**5 - 1/21*v**3 + 0*v + 16*v**2 + 1/735*v**7 + 1/210*v**6 + 0. Find l, given that u(l) = 0.
-1, 1
Let u(w) be the third derivative of w**5/20 - 17*w**4/8 + 15*w**3 + 26*w**2 - 2. Factor u(n).
3*(n - 15)*(n - 2)
Let y be (-6)/26 - (-406)/182. Factor 2*n + y*n**2 + 0 - 3/2*n**3.
-n*(n - 2)*(3*n + 2)/2
Let b(o) be the third derivative of o**8/112 + o**7/14 + 9*o**6/40 + 7*o**5/20 + o**4/4 - 44*o**2. Factor b(c).
3*c*(c + 1)**3*(c + 2)
Factor -38/5*u**2 + 62/5*u + 102/5 + 2/5*u**3.
2*(u - 17)*(u - 3)*(u + 1)/5
Factor 8/5 + 2/5*l**2 + 2*l.
2*(l + 1)*(l + 4)/5
Let p(x) be the first derivative of -6*x + 27/2*x**2 + 29 - 4*x**3. Determine w so that p(w) = 0.
1/4, 2
Let u(x) be the first derivative of -6*x**6 + 156*x**5/5 - 58*x**4 + 48*x**3 - 16*x**2 + 87. Find j, given that u(j) = 0.
0, 2/3, 1, 2
Suppose 2*j - 5*s = -11, -2*j + 2*s = -s + 5. Suppose -4*k = -3*z - 0*z - 5, -k = -j*z. Factor -3/5*w**k + 3/5*w + 6/5.
-3*(w - 2)*(w + 1)/5
Let l be (-6)/30 + 32/10 - 3. Let s = 2395/9548 + -2/2387. Factor 1/4*f**2 + l - s*f.
f*(f - 1)/4
Let h(n) be the first derivative of n**4/24 + n**3/3 - 3*n**2 + 20*n/3 + 24. Solve h(m) = 0.
-10, 2
Let r be (18/(-10))/((-9)/60). Let s be (-4)/3*r/(-8). Factor i**2 + 0 - 2 - 32*i**3 - 17*i**s + 14*i.
-2*(i + 1)*(4*i - 1)**2
Let n(l) = -716*l**3 + 2476*l**2 - 1904*l + 176. Let x(k) = -110*k**3 + 381*k**2 - 293*k + 27. Let f(y) = 5*n(y) - 32*x(y). Factor f(z).
-4*(z - 2)*(z - 1)*(15*z - 2)
Let n = -93 - -95. Let u = -229/5 + 46. Factor -2/5*f**4 - u*f**5 + 2/5*f**n + 0*f**3 + 1/5*f + 0.
-f*(f - 1)*(f + 1)**3/5
Let s(a) be the first derivative of a**5/420 - a**4/42 - 2*a**3/7 - 13*a**2 + 8. Let m(y) be the second derivative of s(y). Factor m(x).
(x - 6)*(x + 2)/7
Let q = 1015 + -1013. Factor a**q - 1 - 11/2*a**3 + 11/2*a.
-(a - 1)*(a + 1)*(11*a - 2)/2
Let f(y) = -y**3 - 6*y**2 - y - 2. Let h be f(-6). What is t in -5*t**3 + 2*t**3 - 2*t**3 - 2*t**5 + t**5 + 4*t**h + 2*t**2 = 0?
0, 1, 2
Find p, given that -170*p + 64*p + 27 - p**2 + 80*p = 0.
-27, 1
Let i(u) be the third derivative of u**9/272160 + u**8/90720 - 19*u**5/60 - 19*u**2. Let j(b) be the third derivative of i(b). Factor j(g).
2*g**2*(g + 1)/9
Let n = 44 + -28. Factor 2*b**3 + n*b**2 + 0*b**3 + 216*b + 20*b**2 + 428 + 4.
2*(b + 6)**3
Let k(t) = t**4 + 10*t**3 - 12*t**2 - 10*t + 10. Let c = 77 - 76. Let x(q) = -q**3 + q**2 + q. Let i(r) = c*k(r) + x(r). Suppose i(p) = 0. Calculate p.
-10, -1, 1
Let c(x) be the first derivative of 1/5*x**5 + 0*x + 1/2*x**2 - 3/4*x**4 + 1/3*x**6 - 1/3*x**3 - 7. Solve c(y) = 0.
-1, 0, 1/2, 1
Let b = 16 - 13. Suppose 2*i - 20 = -2*c, 0 = -2*c - i + b*i. Factor q**2 + c*q**2 - 3*q**2 - 2*q**2 + q.
q*(q + 1)
Let 8/9*f + 2/3*f**4 + 2/9*f**3 - 16/9*f**2 + 0 = 0. Calculate f.
-2, 0, 2/3, 1
Let p be 8*((-18)/4 + 5). Find j such that 0 - 35*j**2 + 20 + 5*j**3 - 5*j**5 + 8186*j**4 - 8171*j**p = 0.
-1, 1, 2
