**3
Let i(d) be the first derivative of 0*d + 3/10*d**2 - 13 - 1/5*d**3. Factor i(a).
-3*a*(a - 1)/5
Suppose 0 = -4*v - 0*v - 80. Let m = 38 + v. Factor 2*o**5 - 2*o**3 - 16*o**4 + m*o**4 + 0*o**2 - 2*o**2.
2*o**2*(o - 1)*(o + 1)**2
Let g(a) be the third derivative of -a**8/84 + 2*a**7/21 - 4*a**6/15 + 4*a**5/15 + 2*a**2 + 9. Let g(m) = 0. Calculate m.
0, 1, 2
Let g(o) = 2*o - 9. Let z be g(9). Let x = z + -5. Factor 3*w**3 + 6*w**3 - 9*w + 6 - 4*w**4 + w**x + 0*w**4 - 3*w**2.
-3*(w - 2)*(w - 1)**2*(w + 1)
Let v(a) be the second derivative of -2*a**6/285 - 7*a**5/190 - a**4/57 + a**3/19 + 13*a. What is t in v(t) = 0?
-3, -1, 0, 1/2
Let c(x) = -3*x**3 + 0*x**3 - 161 + 5*x - 5*x**2 + 157 + 4*x**3. Let p be c(4). Let 3/5*s + 3/5*s**3 + p + 6/5*s**2 = 0. What is s?
-1, 0
Let s(r) = 16*r**3 + 4 - 12 + 2*r**4 + 10*r**2 + 6*r - 12*r**3 - 4*r**4. Let l(n) = n**2 + n - 1. Let b(t) = 10*l(t) - s(t). Factor b(q).
2*(q - 1)**3*(q + 1)
Let t(i) be the first derivative of i**5/70 - i**4/14 - 15*i - 16. Let x(v) be the first derivative of t(v). Suppose x(l) = 0. What is l?
0, 3
Let x(m) be the third derivative of -m**6/10 + 4*m**5/15 - m**4/6 - 56*m**2 - 1. Find h such that x(h) = 0.
0, 1/3, 1
Let p(j) be the second derivative of -j**6/90 + j**5/12 + 7*j**4/18 + 29*j + 2. Factor p(v).
-v**2*(v - 7)*(v + 2)/3
Suppose 0 = -n + f + 2*f + 5, -15 = -3*n - f. Let t be (4 - n/(-5)) + -1. Suppose 2/7 - 4/7*z**2 + 0*z**3 + 0*z + 2/7*z**t = 0. Calculate z.
-1, 1
Let i(t) be the third derivative of -t**8/6720 + t**7/840 + t**6/80 - 7*t**5/20 - 20*t**2. Let s(z) be the third derivative of i(z). Factor s(d).
-3*(d - 3)*(d + 1)
Let c(w) be the first derivative of -3*w**5/35 + 45*w**4/28 + 598. Find r, given that c(r) = 0.
0, 15
Let w(i) = i - 2. Suppose -3*t + 4*o + 8 + 14 = 0, -2*o = 4*t. Let f be w(t). Determine g, given that 21/2*g**3 + 3*g + 27/2*g**2 + f = 0.
-1, -2/7, 0
Determine r so that -2/5*r**5 + 0*r**2 + 4/15*r**3 + 0 + 2/3*r**4 + 0*r = 0.
-1/3, 0, 2
Let d(y) be the second derivative of -3*y**6/35 - y**5/35 + 9*y**4/14 + 8*y**3/7 + 4*y**2/7 + 259*y - 2. What is i in d(i) = 0?
-1, -2/9, 2
Let x = -316/11 - -959/33. Suppose 0 + x*p**2 + 0*p - 1/3*p**4 + 1/3*p**5 - 1/3*p**3 = 0. What is p?
-1, 0, 1
Find n such that 0 + 4/9*n**2 + 92/3*n = 0.
-69, 0
Let z(j) be the third derivative of -j**7/8820 - j**6/840 - j**5/210 - 5*j**4/8 + 4*j**2. Let p(c) be the second derivative of z(c). Solve p(w) = 0.
-2, -1
Let c(j) be the first derivative of j**7/210 - j**6/90 - j**5/30 + j**4/6 + 10*j**3 + 17. Let h(f) be the third derivative of c(f). Find t such that h(t) = 0.
-1, 1
Let i(r) = 4*r**3 - 16*r**2 + 12*r. Let s(m) = 8*m**3 - 33*m**2 + 24*m + 1. Let q(u) = -9*i(u) + 4*s(u). What is c in q(c) = 0?
1
Let 5 - 25/4*f + 5/4*f**2 = 0. What is f?
1, 4
Let u(o) = o**4 - o**3 + o**2 - o. Let g(z) = -z**5 - 5*z**4 - 23*z**3 + 77*z**2 + 96*z - 144. Let p(l) = -g(l) + 6*u(l). Find a, given that p(a) = 0.
-8, -3, 1, 2
Let b = -22 - -48. Solve 6*m**3 + 10*m**5 - 4*m**4 - b*m**3 + 10*m - 3 + 0*m**5 + 8*m**2 - 1 = 0 for m.
-1, 2/5, 1
Let w be (12/(-8))/(3/(-6)). Suppose 0 = -5*q + 3*b + 3 + 3, -3*b + 3 = -2*q. Determine l, given that -1 - w*l**q + 1 = 0.
0
Let j(w) be the third derivative of 0*w**3 + 0*w**4 + 0*w - 1/105*w**7 + 0 - 1/180*w**6 + 0*w**5 - 1/252*w**8 - 6*w**2. Factor j(a).
-2*a**3*(a + 1)*(2*a + 1)/3
Let r = -275 + 531. Factor -r*y**2 + 55*y + 9*y - 3 - 1.
-4*(8*y - 1)**2
Let j(n) be the second derivative of 0*n**2 + 0*n**6 + 0*n**3 + 17*n + 0 + 1/70*n**5 + 0*n**4 - 1/147*n**7. Factor j(k).
-2*k**3*(k - 1)*(k + 1)/7
Let b be (14/(-10) - -1) + 11544/(-455). Let k = 186/7 + b. Solve 0*y**2 + 0 + k*y**4 + 2/5*y**3 + 0*y = 0 for y.
-1/2, 0
Suppose 1560*z = 1570*z. Let l(i) be the third derivative of 1/12*i**4 + z + 5*i**2 + 0*i**3 + 0*i + 0*i**5 - 1/60*i**6. Factor l(t).
-2*t*(t - 1)*(t + 1)
Let c(k) = -k**5 + k**3 + 2. Let v(b) = -2*b**5 - 26*b**4 + 90*b**3 - 130*b**2 + 92*b - 14. Let n(x) = -5*c(x) + v(x). Let n(w) = 0. What is w?
2/3, 1, 2, 3
Let s(y) be the first derivative of 50*y**2 - 5/2*y**4 + 35*y**3 - 7*y**5 + 20*y - 43. Suppose s(n) = 0. Calculate n.
-1, -2/7, 2
Let j(c) be the third derivative of 1/168*c**4 - 6*c**2 + 1/420*c**5 + 0*c**3 + 0*c + 0. Determine o so that j(o) = 0.
-1, 0
Suppose 4*a + 4 - 8 = 0. Let v be 119/17 + -2*a. Factor 0*b**v + b**3 - b**3 - 2*b**3 + 4*b**4 - 2*b**5.
-2*b**3*(b - 1)**2
Let h(x) be the first derivative of -2*x**3/39 - 5*x**2/13 - 12*x/13 + 112. Factor h(k).
-2*(k + 2)*(k + 3)/13
Let s(u) be the first derivative of 0*u**2 + 5 + 0*u + 1/6*u**4 - 2/45*u**5 - 4/27*u**3. Factor s(f).
-2*f**2*(f - 2)*(f - 1)/9
Let s(l) be the first derivative of l**4/96 - l**3/24 - 2*l + 16. Let r(c) be the first derivative of s(c). What is i in r(i) = 0?
0, 2
Let j(h) = 9*h**2 + 27. Let g(p) = 2*p**2. Let m(o) = 6*g(o) - j(o). Let m(f) = 0. What is f?
-3, 3
Let h = 108 + -44. Solve -6*z + 6*z**3 + h + 9*z**2 - 64 = 0 for z.
-2, 0, 1/2
Let v(b) be the first derivative of -b**5/5 + 4*b**4/3 - 10*b**3/3 + 4*b**2 - 3*b - 7. Let j(t) be the first derivative of v(t). Find l, given that j(l) = 0.
1, 2
Let k(m) be the third derivative of -m**7/780 - m**6/1170 - 5*m**3/3 + 10*m**2. Let d(z) be the first derivative of k(z). Factor d(c).
-2*c**2*(7*c + 2)/13
Let f = 23 + -16. Let x be (f - 38/6) + (-10)/42. Factor -9/7*n - 3/7*n**3 + x + 9/7*n**2.
-3*(n - 1)**3/7
Let m = 5/412 - -769/4532. Solve -2/11*c**2 + 2/11*c - 2/11*c**3 + m = 0 for c.
-1, 1
Let i be (-40)/(-12)*(-756)/(-245). Let o = -908/91 + i. Factor o*z + 2/13*z**4 + 8/13*z**3 + 0 + 10/13*z**2.
2*z*(z + 1)**2*(z + 2)/13
Let m(x) = x**3 + 9*x**2 - 11*x - 7. Let s be m(-10). Let 3*b - 7*b + 16*b**3 - 4 + 12*b**s - 24*b**3 + 4*b**2 = 0. Calculate b.
-1, 1
Let q(i) be the third derivative of i**8/168 + 2*i**7/7 + 14*i**6/15 - i**5/15 - 19*i**4/4 - 28*i**3/3 + 331*i**2. Factor q(p).
2*(p - 1)*(p + 1)**3*(p + 28)
Let n(x) = -7*x - 1. Let u be n(-2). Suppose -u = 5*o - 53. Factor k**2 + 7 - 1 + k - o.
(k - 1)*(k + 2)
Factor -21*n + 189*n + 178*n - 46*n - 60*n**2 - 82 + 4*n**3 - 418.
4*(n - 5)**3
Let c be 120 - -3 - (0 - (-3 + 3)). Factor -2*n**3 + c*n**2 - 3*n - 60*n**2 - 58*n**2.
-n*(n - 1)*(2*n - 3)
Let o(h) be the second derivative of h**5/80 - 3*h**4/32 + h**3/4 + 5*h**2/2 + 5*h. Let b(d) be the first derivative of o(d). Solve b(i) = 0 for i.
1, 2
Let y be (-408)/(-16) + 3/(-2). Let -28*l**3 - 46*l**4 - y*l**2 + 8 + 18*l**4 + 28*l + 44*l**4 = 0. What is l?
-1, -1/4, 1, 2
Suppose 4*z + 5*c - 1181 = -361, 824 = 4*z + 4*c. Determine w so that -216*w**2 - z*w**2 - 6 + 423*w**2 + 9*w = 0.
1, 2
Let v(j) be the second derivative of -j**5/5 + 22*j**4/3 + 50*j**3/3 - 92*j**2 + 4*j - 26. Factor v(b).
-4*(b - 23)*(b - 1)*(b + 2)
Suppose -3*u = -2308 - 956. Suppose 5*y = 6*y - u. Suppose 228*j**4 + 8 - 67*j + y*j**3 - 378*j**3 + 162*j**5 + 163*j + 402*j**2 + 330*j**4 = 0. What is j?
-1, -2/9
Determine g so that -39*g + 114*g + 5*g**2 + 143003 - 143003 = 0.
-15, 0
Let v(g) be the third derivative of -5*g**8/448 - g**7/168 + 7*g**6/48 + g**5/12 - 5*g**4/12 + 271*g**2. Solve v(k) = 0 for k.
-2, -1, 0, 2/3, 2
Let z be 129/12 - (-3)/12. Suppose -3*b = -z - 4. Solve 39*v + b*v**2 - 36*v - 2*v**2 = 0.
-1, 0
Suppose -2*j + 10 = 3*j. Factor -1/4*k**j + 1/2*k - 1/4.
-(k - 1)**2/4
Let o = 1431 + -1426. Find x such that 36/7*x**2 - 468/7*x**4 - 23/7*x**3 + 676/7*x**o + 0 + 4/7*x = 0.
-2/13, 0, 1/2
Let w = -7/302 + 33/27482. Let p = w - -827/364. Factor 1/2 + 1/4*h**4 + p*h**2 - 7/4*h - 5/4*h**3.
(h - 2)*(h - 1)**3/4
Let c(b) be the second derivative of -b - 4/17*b**2 - 1/255*b**6 - 13/102*b**4 - 3/85*b**5 + 0 - 4/17*b**3. Factor c(a).
-2*(a + 1)**2*(a + 2)**2/17
Let s be 8 + (-1 - (1 - -1)). Suppose 141 = 3*t + t - s*j, -3*t + 114 = -j. Solve 21*z**4 + 19*z**4 - t*z**4 + z**2 + 2*z**3 = 0.
-1, 0
Let t(q) = q**3 + 2*q**2 - 5*q - 2. Suppose 9 = -2*r - r. Let k be t(r). Factor 6*w**2 + 8 + 8*w**k - 11 - 6 + 1 + 32*w - 26*w**3.
2*(w - 2)**2*(w + 1)*(4*w - 1)
Let m(k) be the third derivative of k**5/15 + 17*k**4/6 + 21*k**2 - 2. Factor m(h).
4*h*(h + 17)
Let y(f) be the second derivative of f**4/18 + 19*f**3/9 - 20*f**2/3 - 262*f. Factor y(r).
2*(r - 1)*(r + 20)/3
Let c(o) = -o**5. Let a(f) = 3*f**5 - f**4 + 2*f**3. Let u be (-