1
Let q(w) be the second derivative of w**9/7560 + w**8/8400 - w**7/2100 + 4*w**4/3 - 2*w. Let b(d) be the third derivative of q(d). Let b(z) = 0. What is z?
-1, 0, 3/5
Find d, given that -2/5 - 22326/5*d**2 + 453962/5*d**3 + 366/5*d = 0.
1/61
Suppose 60 = 5*x - 0. Suppose x = 2*p + 2*p. Suppose -l - 2*l - 1 - p*l**2 + 2*l**2 - 2*l**2 - l**3 = 0. What is l?
-1
Let q(f) be the second derivative of -5/3*f**3 + 3*f + 5/2*f**2 + 0 + 5/12*f**4. Find l such that q(l) = 0.
1
Let m(q) = -36*q**4 + 224*q**3 - 180*q**2 - 280*q + 272. Let n(g) = -4*g**4 + 25*g**3 - 20*g**2 - 31*g + 30. Let x(s) = -3*m(s) + 28*n(s). Factor x(z).
-4*(z - 6)*(z - 1)**2*(z + 1)
Suppose i - 57 = -77. Let n be 4/48*-3 + (-13)/i. Solve 2/5*l**5 + 0*l**2 + 0*l**4 - 4/5*l**3 + n*l + 0 = 0.
-1, 0, 1
Factor -9/2 - 2*v**2 + 21/4*v + 1/4*v**3.
(v - 3)**2*(v - 2)/4
Let y(p) be the first derivative of p**2 + 7 + 2*p - 2/3*p**3 - 1/2*p**4. Factor y(c).
-2*(c - 1)*(c + 1)**2
Let b(o) be the second derivative of -o**4/48 + 9*o**3/4 - 729*o**2/8 + 122*o. What is v in b(v) = 0?
27
Let b be (-6)/(((-2)/1)/776). Factor 0*w**3 - b - 8*w + 2328 + 2*w**3.
2*w*(w - 2)*(w + 2)
Find d, given that -5*d**2 - 17*d + d + 10*d - d**3 + 2*d = 0.
-4, -1, 0
Suppose 0 = -15*u + 10*u - 3*m + 6, -5*u = -2*m + 4. Determine c, given that u*c - 1/5 + 1/5*c**2 = 0.
-1, 1
Factor 10 + 16*z + 32/5*z**2.
2*(4*z + 5)**2/5
Suppose -37*m + 32*m = -25. Let s be (9/(-42))/(m/((-105)/6)). Factor -81*p - s*p**4 - 9*p**3 - 243/4 - 81/2*p**2.
-3*(p + 3)**4/4
Suppose 4*p = 5*n + 41, -3*n + 1 - 16 = 0. Suppose -10 = -0*b - 5*b - 3*c, 0 = 5*b - 2*c - 10. Factor 3*h**b + 0*h**4 - h**2 + 4*h**3 - 2*h**4 + p*h**4.
2*h**2*(h + 1)**2
Factor -5/3*g**2 - 15*g - 40/3.
-5*(g + 1)*(g + 8)/3
Let l(h) = -7*h**2 - 22*h - 17. Let o(z) be the third derivative of -31*z**5/12 - 485*z**4/24 - 125*z**3/2 - 4*z**2. Let y(x) = 45*l(x) - 2*o(x). Factor y(q).
-5*(q + 1)*(q + 3)
Let v(w) = -w + 9. Let j be v(4). Let g = j + -3. Determine t, given that -3/5*t**g + 0 - 3/5*t**3 - 1/5*t**4 - 1/5*t = 0.
-1, 0
Suppose -g - 5*u - 12 = 0, 3*g - u + 0*u = 12. Factor -12*p**2 - 15 + 14*p**2 + 5*p**4 - 20*p**g + 0*p**4 + 8*p**2 + 20*p.
5*(p - 3)*(p - 1)**2*(p + 1)
Let y(t) be the first derivative of t**7/420 + t**6/240 - t**5/120 - t**4/48 - 3*t**2 - 11. Let k(h) be the second derivative of y(h). Factor k(s).
s*(s - 1)*(s + 1)**2/2
Let q = 20 + -98/5. Let f = -6 + 8. What is u in 1/5*u**f + 1/5 - q*u = 0?
1
Factor -68/19*f - 578/19 - 2/19*f**2.
-2*(f + 17)**2/19
Let p(x) be the third derivative of -x**5/300 + 19*x**4/60 - 361*x**3/30 + 324*x**2. Find s, given that p(s) = 0.
19
Let x(f) = f**3 - 15*f**2 + 14*f. Let j = 37 + -23. Let p be x(j). Find s, given that p - 2/9*s + 4/9*s**2 = 0.
0, 1/2
Factor -10*w**4 - 9*w**3 + 7*w**4 + 0*w**4.
-3*w**3*(w + 3)
Let c = -39400174/135 + 1167415/4. Let d = -1/108 + c. Factor 2/5*h + 0*h**3 + 0 - 1/5*h**4 + d*h**2.
-h*(h - 2)*(h + 1)**2/5
Suppose -2*w - 5*v + 25 = -1, 5*w - 4*v + 1 = 0. Factor m**4 - 16*m**3 + m**5 + w*m**2 + 32*m**3 - 4*m**2 - 17*m**3.
m**2*(m - 1)*(m + 1)**2
Let 424*c**3 - 46*c**2 + 507*c - 32*c**2 - 421*c**3 = 0. Calculate c.
0, 13
Let p(s) be the third derivative of -3*s**5/80 + 23*s**4/48 - 5*s**3/24 + 98*s**2 - 3*s. Find o, given that p(o) = 0.
1/9, 5
Let j be (-10)/45 + (-8)/(-360)*25. Let -4/3 + 5/3*h - j*h**2 = 0. Calculate h.
1, 4
Let w = -2/595 + 1908778/5355. Let m = w + -356. Determine u so that -8/9*u**2 - 2*u - m = 0.
-2, -1/4
Let i(k) be the second derivative of -2/5*k**5 + 0*k**3 - 2/15*k**6 - 1/3*k**4 + 0 + 0*k**2 + 4*k. Determine w, given that i(w) = 0.
-1, 0
Let f be (-1552)/(-1746) + 4/(-18). Determine s so that 2/9*s + 2/9*s**4 - f*s**2 - 2/9*s**3 + 4/9 = 0.
-1, 1, 2
Find s, given that 5/2*s**2 - 3*s + 1/2*s**3 + 0 = 0.
-6, 0, 1
Let f be (1*-3 + (2 - 0))*1. Let b(r) = 2*r - 1. Let m(x) = x**2 + 28*x + 76. Let p(d) = f*m(d) + 5*b(d). Let p(g) = 0. What is g?
-9
Let c(f) be the second derivative of 0*f**4 - 1/720*f**6 + 0*f**2 - 1/480*f**5 + 3/2*f**3 + 0 - 12*f. Let g(n) be the second derivative of c(n). Factor g(o).
-o*(2*o + 1)/4
Let i(x) be the third derivative of 0*x**4 + 0*x + 0*x**3 - 8*x**2 - 2/105*x**7 + 0 + 1/10*x**6 - 2/15*x**5. Suppose i(k) = 0. What is k?
0, 1, 2
Let t(s) = -3*s**2 + 16*s + 36. Let h(j) = -4*j**2 + 17*j + 36. Let l be 4/(-6)*(-18 + 0)/3. Let a(f) = l*h(f) - 5*t(f). Determine r so that a(r) = 0.
-6
Suppose 0 = 47*r - 9*r + 10 - 86. Find f, given that 2*f**4 + 0*f - 18/5*f**r - 2/5*f**5 - 6/5*f**3 + 0 = 0.
-1, 0, 3
Suppose 5*q + 14 = 4*j + 3*q, 2*q - 18 = -4*j. Let h be (-28)/8 - -3 - (-2)/j. Let 0 + h*k + 0*k**2 + 3/2*k**3 = 0. Calculate k.
0
Let w(b) = b**3 - 3*b**2 + b + 2. Let j be w(3). Suppose -j*u + 15 = 0, -u = 4*m - 276 - 555. Factor m*k**3 - 82*k**3 + 1 - 2 + 8*k - 75*k**2 + 7*k.
(5*k - 1)**3
Let t(r) be the second derivative of 0 + 3/2*r**4 - 11/2*r**3 + 9*r**2 + 8*r - 3/20*r**5. Solve t(z) = 0 for z.
1, 2, 3
Suppose -2*w = -w - 2. Determine l, given that -l**3 - 16 + 6*l**w - l**4 - 3*l**2 + 5*l + 18 = 0.
-1, 2
Let t(z) be the third derivative of z**5/210 - 23*z**4/84 - z**2 - 292*z. Factor t(w).
2*w*(w - 23)/7
Let r be 0*(-3)/(-9) + 2. Find i such that 41*i**2 - 24*i - 26*i**r + 0*i**3 - 3*i**3 + 12 = 0.
1, 2
Determine s, given that -s**4 - 4*s + 4*s**5 - 5*s**4 - 2*s**4 - s**4 + s**4 + 8*s**2 = 0.
-1, 0, 1
Let v(i) be the first derivative of -i**3/12 + 9*i**2/4 - 18*i + 233. Factor v(u).
-(u - 12)*(u - 6)/4
Let t = 349 - 210. Suppose -5*x + c + t = -164, c = -5*x + 297. Factor -x*v**2 - 4*v**4 + 36*v**2 + 2*v**4 - 12*v**3 - 16*v.
-2*v*(v + 2)**3
Suppose -10 = -4*j + 5*a + 34, 0 = 5*j - 4*a - 46. Let g be (-2)/j + 20/6. Factor -2*w**2 + 3*w**2 + g*w**3 - 4*w**3 - w**4 + 0*w**2 + w**5.
w**2*(w - 1)**2*(w + 1)
Let a(p) be the second derivative of -p**5/120 + 29*p**4/72 - 22*p**3/3 + 60*p**2 - 667*p. Factor a(n).
-(n - 12)**2*(n - 5)/6
What is y in -2/3*y**2 + 44/3 + 14*y = 0?
-1, 22
Let u be (-10)/2*(-114)/1045. Let d = u + 4/33. Let 0 + d*a + 4/3*a**2 + 2/3*a**3 = 0. Calculate a.
-1, 0
Let p(l) be the third derivative of -l**8/30240 + l**7/756 - 5*l**6/216 + 17*l**5/60 - 4*l**2. Let f(u) be the third derivative of p(u). Factor f(s).
-2*(s - 5)**2/3
Factor -1331*c + 2*c**5 - 388*c**2 + 32*c**4 + 240 + 330*c**3 - 240 + 1356*c**2 - c**5.
c*(c - 1)*(c + 11)**3
Determine m, given that -3/2*m**4 + 0 + 63/2*m**2 - 33/2*m - 27/2*m**3 = 0.
-11, 0, 1
Suppose u + 300 = 4*x, 6*x - 2*x - 16 = 0. Let t = u - -284. Find i such that t - 1/7*i**2 + 5/7*i = 0.
0, 5
Let t = -2660 + 13303/5. Determine i, given that -3/5*i**3 + 0 + t*i**2 + 3/5*i - 3/5*i**4 = 0.
-1, 0, 1
Let c(m) be the first derivative of m**6/54 + m**5/9 + 7*m**4/36 + m**3/9 + 99. Factor c(f).
f**2*(f + 1)**2*(f + 3)/9
Factor 2/3*c**2 - 50/3*c + 92/3.
2*(c - 23)*(c - 2)/3
Factor 1/3*w**5 + 0 - w**3 - 1/3*w**4 + 1/3*w**2 + 2/3*w.
w*(w - 2)*(w - 1)*(w + 1)**2/3
Let x(c) be the third derivative of -c**5/30 - c**4/4 + 6*c**3 - 2*c**2 + 2*c. Solve x(h) = 0 for h.
-6, 3
Let j be (-246)/(-8) + 4/(-80)*-5. Suppose j = 5*o + 16. Factor 11/2*p**o + 2 + 21/2*p**2 + 8*p + p**4.
(p + 1)*(p + 2)**2*(2*p + 1)/2
Let t(c) be the second derivative of c**6/15 - c**4/6 - 82*c. Factor t(u).
2*u**2*(u - 1)*(u + 1)
Let g(l) be the second derivative of 3/140*l**5 + 1/70*l**6 + 0 - 1/28*l**4 - 1/14*l**3 + 0*l**2 - l. Factor g(p).
3*p*(p - 1)*(p + 1)**2/7
Let q(w) be the second derivative of 19*w**7/357 + 59*w**6/255 + 22*w**5/85 + 2*w**4/51 + 11*w. What is b in q(b) = 0?
-2, -1, -2/19, 0
Let v(r) be the second derivative of -r**4/84 + r**3/3 - 7*r**2/2 - 5*r + 7. Find a, given that v(a) = 0.
7
Let b be -3 - (1391/299 + -8). Factor -b*s + 0 - 80/23*s**2 - 234/23*s**3 - 162/23*s**4.
-2*s*(s + 1)*(9*s + 2)**2/23
Let j = -7195 - -7195. Factor 2/7*l + j + 6/7*l**3 + 6/7*l**2 + 2/7*l**4.
2*l*(l + 1)**3/7
Let x be ((-2700)/105 + 26)*14/6. Determine g, given that -96 - 16*g - x*g**2 = 0.
-12
Let b = -85 + 61. Let o = 28 + b. Factor 30*x**2 + 16*x**2 - 6*x - o*x**2 - 3*x**4 + 21*x**4 - 4 - 50*x**3.
2*(x - 1)**3*(9*x + 2)
Suppose 0 = 16*r + 8 - 77 + 5. Let 0 - 1/5*j**r - 1/5*j + 1/5*j**2 + 1/5*j**3 = 0. Calculate j.
-1, 0, 1
Let s be 10/4 - (-14)/(21/(-3)). Let w(l) be the first derivative of 2/3*l**3 + 0*l - 2*l**2 + s*l**4 - 11. 