*p**4 - 3/4*p**5 = 0.
-120, 0, 1
Solve 1089/2*a - 9/2*a**4 + 233*a**2 + 567/2 + 1/2*a**5 - 33*a**3 = 0 for a.
-7, -1, 9
Solve 108*r**3 + 1151 - 29*r**3 - 3023 + 163*r**3 + 3054*r - 5698*r**2 + 1458 = 0.
3/11, 23
Let t(g) be the second derivative of 0*g**2 + 11/20*g**6 + 55/4*g**4 - 25/2*g**3 + 0 - 1/56*g**7 - 423/80*g**5 - 30*g. Find s such that t(s) = 0.
0, 1, 10
Let y(i) be the second derivative of 0*i**2 + 1/40*i**5 + 3/4*i**3 - 4 - 1/4*i**4 + 8*i. Factor y(v).
v*(v - 3)**2/2
Solve 240/7 + 2/7*z**2 - 68/7*z = 0.
4, 30
Suppose 106*h - 32238 = -10614. Let y be 17/(h/80) - 4. Solve y*i**3 + 4/3*i + 2/3*i**4 + 0 + 10/3*i**2 = 0 for i.
-2, -1, 0
Let v(j) be the second derivative of j**5/20 + 71*j**4/12 + 549*j**3/2 + 12393*j**2/2 - 10*j - 4. Factor v(q).
(q + 17)*(q + 27)**2
Let g(t) = -6*t**3 + 63*t**2 - 1095*t + 3525. Let n(x) = -5*x**3 + 76*x**2 - 1094*x + 3526. Let w(a) = -2*g(a) + 3*n(a). Factor w(b).
-3*(b - 14)**2*(b - 6)
Suppose 0*h + 91 = l + 4*h, -4*l + 5*h = -385. Factor -6*n**3 - 36*n**2 + 22*n - 24*n**2 + 6 - 25*n**2 + l*n**2.
-2*(n - 3)*(n + 1)*(3*n + 1)
Let s(c) be the third derivative of -1/9*c**3 + 5/72*c**4 + 1/20*c**5 - 1/72*c**6 + 0*c - 1/90*c**7 + 2*c**2 + 25. Suppose s(m) = 0. What is m?
-1, 2/7, 1
Let s(l) be the first derivative of l**4/14 + 2*l**3/7 - 9*l**2/7 - 54*l/7 + 99. Factor s(n).
2*(n - 3)*(n + 3)**2/7
Let j = -24 - -21. Let f(h) = -h**2 - 4*h - 1. Let x be f(j). Factor 7*c**4 - x*c**4 + 15*c**3 + 15*c**2 + 0*c**4 + 5*c.
5*c*(c + 1)**3
Suppose -4*i - 2*i + 40*i = 0. Suppose 432*b - 424*b - 16 = i. Determine o so that 0 + 6*o**b - 4/3*o - 14/3*o**3 = 0.
0, 2/7, 1
Suppose 0 = -4*n - 996*i + 1017*i + 260, 46 = 5*n - 3*i. Solve 2/3*f**n - 2/3*f**5 - 4/3*f + 2*f**3 + 0 - 2/3*f**4 = 0 for f.
-2, -1, 0, 1
Suppose 4*f = -4*m + 68, -3*m - f - 133 + 158 = 0. Factor -4/11*x**m + 2/11 + 10/11*x**3 - 6/11*x**2 - 2/11*x.
-2*(x - 1)**3*(2*x + 1)/11
Let b(d) be the third derivative of 2*d**7/105 - 2*d**6/3 - 23*d**5/5 - 2*d**4/3 + 184*d**3/3 - 2329*d**2. Factor b(r).
4*(r - 23)*(r - 1)*(r + 2)**2
Let c(b) be the second derivative of 49/90*b**6 - 10/9*b**3 + 2/3*b**2 - b + 2 - 1/12*b**4 + 7/6*b**5. Factor c(d).
(d + 1)**2*(7*d - 2)**2/3
Let u(x) be the third derivative of -x**8/40320 - x**7/1120 + x**6/144 + x**5/60 + x**4/8 + 4*x**2 + 3. Let o(p) be the third derivative of u(p). Factor o(s).
-(s - 1)*(s + 10)/2
Let 36/5*b**4 + 588/5 - 2/5*b**5 + 96/5*b**2 - 188/5*b**3 + 182*b = 0. What is b?
-1, 6, 7
Let g(q) be the second derivative of q**5/12 - 35*q**4/18 - 115*q**3/6 - 45*q**2 + 93*q. Factor g(x).
5*(x - 18)*(x + 1)*(x + 3)/3
Let q(n) be the third derivative of -n**7/168 - 5*n**6/72 - n**5/3 - 5*n**4/6 + 11*n**3/6 + 33*n**2. Let m(z) be the first derivative of q(z). Factor m(g).
-5*(g + 1)*(g + 2)**2
Let d(n) be the second derivative of 9*n + 1/18*n**3 - 5 + 2/9*n**4 - 1/60*n**5 - 4/3*n**2. Factor d(b).
-(b - 8)*(b - 1)*(b + 1)/3
Suppose 0 = 6473*q - 6280*q. Find v such that 0*v + 1/2*v**3 + 25/2*v**2 + q = 0.
-25, 0
Suppose -19368 = -17*t + 39537. Let r be (-2)/11 + 1620/t. Factor -3/7*p + 1/7*p**2 + r.
(p - 2)*(p - 1)/7
Let n(m) = m**3 - 3*m**2 - 9*m - 21. Let z(i) = i**2 - 1. Suppose 118*o + 102 = 101*o. Let g(r) = o*z(r) - n(r). Factor g(w).
-(w - 3)*(w + 3)**2
Let u(z) be the third derivative of 0*z + 48*z**2 - 1/270*z**5 - 625/27*z**3 + 0 - 25/54*z**4. Suppose u(k) = 0. What is k?
-25
Let m be (63/(-90) - -1) + (2 - 69/30). Let h(i) be the third derivative of 0 + 1/44*i**4 + 0*i**3 + m*i - 1/660*i**6 - 11*i**2 + 1/165*i**5. Factor h(c).
-2*c*(c - 3)*(c + 1)/11
Let -334/21 - 2/21*v**3 - 110/7*v**2 + 222/7*v = 0. What is v?
-167, 1
Let m be (-103694)/(-102575) + -2 + ((-312)/25)/(-6). Factor -2/11*d**2 + m*d - 10/11.
-2*(d - 5)*(d - 1)/11
Let w(q) be the second derivative of q**8/112 + q**7/35 - 3*q**6/40 + 65*q**2/2 + 3*q + 16. Let x(m) be the first derivative of w(m). Factor x(z).
3*z**3*(z - 1)*(z + 3)
Let m(n) = -140*n + 1823. Let k be m(13). Let f(g) be the first derivative of -2 + 9/4*g**2 - 2*g + 1/8*g**4 - g**k. Determine v, given that f(v) = 0.
1, 4
Let f(j) be the second derivative of j**4/4 + j**3/6 - 2*j**2 - 21*j - 5. Factor f(h).
(h - 1)*(3*h + 4)
Let a(m) be the second derivative of 116*m + 0*m**4 + 1/5*m**6 + 0 + 3/8*m**5 + 0*m**3 + 0*m**2 - 1/28*m**7. Solve a(y) = 0 for y.
-1, 0, 5
Let g = 67262 + -67259. Factor 128/5*x - 8*x**g - 4/5*x**4 + 512/5 - 96/5*x**2.
-4*(x - 2)*(x + 4)**3/5
Let w = 242 - 139. Let h = w + -100. Factor -4*v**3 - 5*v**2 - 8*v**4 - 6*v**h + 3*v**4.
-5*v**2*(v + 1)**2
Let p be -5 - (22/10 + -5)/(56/980). Let p*y + 40/3*y**2 + 4/3*y**3 + 48 = 0. Calculate y.
-4, -3
Let a(z) be the third derivative of 6/5*z**5 + 1/84*z**8 - 4/15*z**6 - 4/105*z**7 - 3/2*z**4 + 0 + 0*z**3 - 2*z**2 + 0*z. Solve a(y) = 0.
-3, 0, 1, 3
Suppose -116*t + 256 + 92 = 0. Let k(j) be the first derivative of -225/2*j**2 + 15*j**3 - t + 375*j - 3/4*j**4. Factor k(u).
-3*(u - 5)**3
Factor -265 - 9*q + 44*q + 11*q**2 - 6*q**2 + 325.
5*(q + 3)*(q + 4)
Let y(u) be the second derivative of 2*u**7/35 + 3*u**6/8 + 3*u**5/5 - u**4/2 + 19*u**2/2 - 23*u - 2. Let x(l) be the first derivative of y(l). Solve x(n) = 0.
-2, 0, 1/4
Let m be 3/((-12)/142) - 5/(-10). Let y be (-16)/(-28) - (-10)/m*-194. Factor 3 - 13 + 76*j**2 - y*j + 26 - 50*j**3 + 16*j**4 - 2*j**5.
-2*(j - 2)**3*(j - 1)**2
Let l(c) be the second derivative of 3*c**5/40 + 21*c**4 - c**3/4 - 126*c**2 - c + 1862. Factor l(a).
3*(a - 1)*(a + 1)*(a + 168)/2
Let b(o) = -147*o**2 + 290*o + 332. Let k(f) = -112*f**2 + 289*f + 333. Let r(j) = 3*b(j) - 4*k(j). Factor r(z).
(z - 42)*(7*z + 8)
Let h(o) be the second derivative of o**5/20 + 179*o**4/36 - 10*o**3/3 - 6839*o. Factor h(j).
j*(j + 60)*(3*j - 1)/3
Let s(t) be the first derivative of 4*t**3/3 + 1664*t**2 + 692224*t + 8529. Determine y, given that s(y) = 0.
-416
Let q(x) = x**2 - 2*x + 2. Suppose 5*u - 3*p - 102 = 0, -2*u + 8 = -2*p - 32. Let d(c) = 8*c**2 - 91*c - 64. Let o(v) = u*q(v) - 3*d(v). Factor o(m).
-3*(m - 78)*(m + 1)
Let r be 3/(-9) + (-520)/60. Let l be (-14)/(-3) - (-2)/(-3). Let h(a) = -8*a**2 + 12*a. Let o(v) = -17*v**2 + 24*v. Let p(g) = l*o(g) + r*h(g). Factor p(n).
4*n*(n - 3)
Let p(f) be the second derivative of f**7/42 + 2*f**6/15 - f**5/5 - 4*f**4/3 + 2515*f. Let p(d) = 0. Calculate d.
-4, -2, 0, 2
Let c(h) = 3*h**2 + 3*h + 3. Let x be (0 - 1) + (7 + -7)/(-2). Let i be c(x). Factor 6*y**3 + 8*y**3 + 0*y**3 + y + i*y + 18*y**2.
2*y*(y + 1)*(7*y + 2)
Let j(x) be the third derivative of x**7/700 - 2*x**6/225 - 11*x**5/225 - 4*x**4/45 + 2*x**3 + 67*x**2. Let k(h) be the first derivative of j(h). Factor k(n).
2*(n - 4)*(3*n + 2)**2/15
Let k(z) be the first derivative of -z**3/9 - 29*z**2 - 173*z/3 - 309. Factor k(u).
-(u + 1)*(u + 173)/3
Let t = 300169 - 300169. Factor 2/5*i + i**2 + t + 2/5*i**3.
i*(i + 2)*(2*i + 1)/5
Factor 3/5*f**2 - 57/5*f - 546/5.
3*(f - 26)*(f + 7)/5
Solve 1551*p**3 - 29307*p - 60843*p - 3*p**4 + 38108*p - 199689*p**2 - 79167*p - 70034*p = 0.
-1, 0, 259
Let m(q) = -q**5 - 3*q**4 - q**3 + 1. Let p(v) = 1921*v**5 + 803*v**4 + 111*v**3 + 5*v**2 - 1. Let h(b) = m(b) + p(b). Factor h(i).
5*i**2*(6*i + 1)*(8*i + 1)**2
Suppose -466*u**2 + 2/7*u**5 - 66/7*u**4 + 3120/7*u + 750/7*u**3 + 7200/7 = 0. What is u?
-1, 5, 12
Let a(w) be the third derivative of -w**7/3780 + 7*w**6/1620 - w**5/45 - 13*w**3/3 + w**2 + 1. Let k(x) be the first derivative of a(x). What is s in k(s) = 0?
0, 3, 4
Suppose 3*b + 108 - 27 = 3*i, 0 = 2*b + 5*i + 82. Let m = 33 + b. Factor -1/4*f**m + 0*f + 0.
-f**2/4
Let r be 5/(-20) + 105790/280. Let j = -377 + r. Factor 20/7*h + 8/7 + 16/7*h**2 + j*h**3.
4*(h + 1)**2*(h + 2)/7
Suppose 0 = 3*b + 3*b. Suppose b = -0*p - p. Factor 0*t**5 - 6*t**2 + p*t**5 + 6*t**4 + t**5 - 3*t + 2*t**5.
3*t*(t - 1)*(t + 1)**3
Let x be (-3)/((-15)/55) + (-1330)/152. Let o = 7 + -3. Factor 0 - x*t**2 + 5/4*t**o + 0*t - 1/4*t**5 - 3/4*t**3.
-t**2*(t - 3)**2*(t + 1)/4
Let r = 106 + -101. Let a(z) = -3*z**2 - 22*z + 20. Let o(c) = 5*c**2 + 33*c - 30. Let l(p) = r*o(p) + 8*a(p). Factor l(u).
(u - 10)*(u - 1)
Let n(g) be the first derivative of -g**4 + 16*g**3/3 + 218*g**2 + 416*g + 175. Factor n(b).
-4*(b - 13)*(b + 1)*(b + 8)
Let x(h) be the second derivative of -76/5*h**5 - 148*h + 0 + 1