0
Let j(s) be the third derivative of -1/12*s**4 - 1/2*s**3 + 0 + 1/15*s**5 - s**2 + 0*s. Let u(z) = -3*z**2 + 2*z + 2. Let x(i) = -2*j(i) - 3*u(i). Factor x(m).
m*(m - 2)
Let y(b) be the second derivative of -5/6*b**4 + 0 - 3*b + 1/4*b**5 + 5/6*b**3 + 0*b**2. Factor y(w).
5*w*(w - 1)**2
Suppose 5*i**2 - 14*i**3 + 35*i**2 + 9*i**3 - 60*i = 0. What is i?
0, 2, 6
Suppose -4*n = 0, 2*f = -f + 2*n. Let z(x) be the third derivative of 1/12*x**3 + 1/24*x**5 - 3/32*x**4 + 0*x - 5*x**2 + f. Determine m so that z(m) = 0.
2/5, 1/2
Let a = 0 + 0. Let y be 6/3 - (a - 0). Suppose p**2 + y*p**2 - 4*p**2 - 2*p = 0. What is p?
-2, 0
Let b be -1*(-100)/55 - 8/(-44). Let n(j) be the third derivative of 1/8*j**4 + 0*j**3 + 0*j - 1/80*j**6 + 1/40*j**5 + 2*j**b + 0. Factor n(m).
-3*m*(m - 2)*(m + 1)/2
Let u be (20/(-15) + 2)*-18. Let o be (-6)/u - (-7)/(-22). Determine t, given that 4/11*t - o*t**2 - 2/11 = 0.
1
Let v(h) = h + 4. Let k be v(2). Solve 22 - 42 + k*d + 8*d**2 + 18 = 0 for d.
-1, 1/4
Let k(u) = -6*u + 3. Let y(w) be the third derivative of -1/6*w**3 - 6*w**2 + 0 + 0*w + 1/24*w**4 - 1/60*w**5. Let f(a) = -k(a) + 3*y(a). Factor f(q).
-3*(q - 2)*(q - 1)
Let g(q) = q**2 - q + 1. Let f(d) = -3*d**3 - 6*d**2 + 6*d. Let h be ((-10)/20)/((-1)/(-2)). Let r(t) = h*f(t) - 3*g(t). Factor r(b).
3*(b - 1)*(b + 1)**2
Factor 0*a + 0 + 0*a**2 + 2/9*a**3 + 2/9*a**4.
2*a**3*(a + 1)/9
Let r(m) be the first derivative of m**7/1365 + m**6/260 + m**5/130 + m**4/156 + 7*m**2 - 3. Let t(s) be the second derivative of r(s). Factor t(w).
2*w*(w + 1)**3/13
Factor 21094 - 7049 + 3*g**2 + 530*g + 2*g**2.
5*(g + 53)**2
Let v(m) be the first derivative of -4 + 1/30*m**5 + 1/6*m**2 + 0*m - 1/12*m**4 - 1/18*m**3. Factor v(n).
n*(n - 2)*(n - 1)*(n + 1)/6
Let w = -6/317 + 437/6340. Let q(t) be the second derivative of -2/3*t**2 + 4/9*t**3 + 0 + 11/36*t**4 + 4*t + w*t**5. Find d such that q(d) = 0.
-2, 1/3
Let m(i) = -3*i**3 + 5*i**2 - 7*i - 5. Let n(v) = -4*v**3 + 6*v**2 - 8*v - 6. Let a(h) = 6*m(h) - 5*n(h). Factor a(x).
2*x*(x - 1)*(x + 1)
Let a = -67/2 + 339/10. Let d = 496 + -494. Factor a*f + 1/5 + 1/5*f**d.
(f + 1)**2/5
Let g be (-1 + 1)/((-20)/(-4) - 6). Let h(d) be the second derivative of g - 3/14*d**3 - 3/7*d**2 - 1/28*d**4 + 3*d. Factor h(x).
-3*(x + 1)*(x + 2)/7
Suppose 0 + 2/11*d**2 - 32/11*d = 0. Calculate d.
0, 16
Let l(h) be the third derivative of -1/20*h**5 + 0*h + 1/2*h**3 + 1/24*h**4 + 0 - 1/120*h**6 - 5*h**2. Solve l(a) = 0.
-3, -1, 1
Let j(i) be the first derivative of -i**2/2 - 10*i - 62. Let h be j(-10). Factor 3/5*s**4 + 9/5*s - 3/5*s**2 - 9/5*s**3 + h.
3*s*(s - 3)*(s - 1)*(s + 1)/5
Let p be ((-10)/50*0)/(-8). Factor 2/13*r**2 - 2/13*r + p.
2*r*(r - 1)/13
Factor 0 + 0*c**3 - 2/3*c**4 + 0*c**2 - 3/2*c**5 + 0*c.
-c**4*(9*c + 4)/6
Let p = -78 - -82. Solve -6/11*h**3 + 0*h**2 + 0*h - 6/11*h**p + 0 = 0 for h.
-1, 0
Factor -8/3 + 1/3*x**4 + 14/3*x - 4/3*x**3 - x**2.
(x - 4)*(x - 1)**2*(x + 2)/3
Let u(a) be the third derivative of a**6/60 - 49*a**5/15 + 193*a**4/12 - 32*a**3 - 395*a**2. Factor u(f).
2*(f - 96)*(f - 1)**2
Let p(b) be the third derivative of b**5/150 - 3*b**4/20 - 2*b**3/3 - 3*b**2 - 11*b. Find k such that p(k) = 0.
-1, 10
Let b(o) = 4*o**2 + 41*o - 107. Let d(s) = 36*s**2 + 368*s - 964. Let n(a) = -28*b(a) + 3*d(a). Factor n(c).
-4*(c - 2)*(c + 13)
Suppose -4*k - 5*u - 2 = 0, 0 = 5*k - 0*k - 3*u - 16. Let a(c) = 10*c - 240. Let z be a(24). Factor 1/6*r**k + 0*r + z.
r**2/6
Let x = -14065 - -70337/5. Let -x*s + 28/5*s**2 - 4*s**3 + 0 + 4/5*s**4 = 0. Calculate s.
0, 1, 3
Suppose -3 - 5 = -4*r. Let o(k) be the first derivative of -4*k**2 - 2 + 2*k**r + 3*k - k**2 + k**3. Suppose o(t) = 0. Calculate t.
1
Suppose -3*w + 2 = -w. Let v = w + -4. Let z(j) = -3*j**2 + 3*j. Let a(m) = -m + 1. Let k(x) = v*a(x) + z(x). Suppose k(n) = 0. What is n?
1
Suppose -7*f = -21*f + 686. Let m = -146/3 + f. Solve 0 + 0*v**3 + 1/2*v**2 - 1/6*v**4 + m*v = 0.
-1, 0, 2
Suppose 36/7*u**2 + 30/7*u + 18/7*u**3 + 3/7*u**4 + 9/7 = 0. Calculate u.
-3, -1
Let c = -243 - -249. Let b be ((-1)/c)/(1/(-6))*2. Determine k, given that 0*k - 2/3*k**4 + 0 - 4/3*k**3 - 2/3*k**b = 0.
-1, 0
Let c(f) = 8*f**3 + 41*f**2 - 82*f + 45. Let u(m) = -58*m**3 - 288*m**2 + 574*m - 316. Let y(z) = 44*c(z) + 6*u(z). Factor y(r).
4*(r - 1)**2*(r + 21)
Find s, given that 0*s - 116*s**3 + 111*s**3 + 5*s = 0.
-1, 0, 1
Suppose -5*t + 4*u = 650, 0 = -5*t + 2*t - 5*u - 390. Let k be t/(-210) - (-2)/(-7). Factor k + q**2 - q - 1/3*q**3.
-(q - 1)**3/3
Let g(t) be the third derivative of 169/8*t**3 + 1/80*t**5 - 13/16*t**4 + 0*t - 24*t**2 + 1. Find a, given that g(a) = 0.
13
Let -13 - 8 + 5 - 6*t + t + t + 2*t**2 = 0. What is t?
-2, 4
Let z = -208 - -152. Let d be z/30*(-342)/76. Factor -d*v**3 - 24/5*v - 9/5*v**4 - 12*v**2 + 0.
-3*v*(v + 2)**2*(3*v + 2)/5
Let v(f) be the third derivative of 12*f**2 - 13/84*f**4 + 1/735*f**7 + 0 + 4/21*f**3 + 1/14*f**5 - 1/60*f**6 + 0*f. Factor v(i).
2*(i - 4)*(i - 1)**3/7
Let -1077*v**2 + 6480*v - 5184 - 158*v**2 - 65*v**2 - 104*v**2 + 111*v**3 - 3*v**4 = 0. What is v?
1, 12
Suppose -954 = -229*g + 38*g - 190. Suppose -8/3*t**g - 10/3*t**3 + 0*t - 4/3*t**2 - 2/3*t**5 + 0 = 0. What is t?
-2, -1, 0
Let t be 37521/20295 + (-2)/41. Factor -t*a + 6/5 + 3/5*a**2.
3*(a - 2)*(a - 1)/5
Let x = -46188/35 + 6604/5. Determine c, given that -1/7*c**4 + 2/7*c**3 - x*c + 3/7*c**2 + 4/7 = 0.
-2, 1, 2
Let a(y) be the first derivative of -94*y**5/15 + 8*y**4 - 2*y**3/9 - 659. Determine l so that a(l) = 0.
0, 1/47, 1
Let y(r) = r**3 + r**2 - 1. Let j be y(-2). Let x be (0 - 5)*(j + 4). Factor 0*u**5 - 10*u**4 - 2*u**x - 14*u**2 + u - 4*u - u - 18*u**3.
-2*u*(u + 1)**3*(u + 2)
Let u(i) = 2*i**2 - 16*i - 357. Let k be u(18). Solve 1/3*t**2 + 4/3*t**k - 1/3 - 4/3*t = 0 for t.
-1, -1/4, 1
Factor 10*s**2 + 134/7*s + 2/7*s**3 + 66/7.
2*(s + 1)**2*(s + 33)/7
Let f(i) be the second derivative of -i**3 + 1/12*i**4 + 20*i + 5/2*i**2 + 0. Factor f(l).
(l - 5)*(l - 1)
Let i be (-4)/18 - (-10)/45. Suppose -5*c = -5*o - 15, i = c + 3*o - 5 + 2. Factor 1/2*u**3 + c*u**2 + 0 + 9/2*u.
u*(u + 3)**2/2
Let i be 4 + -8 + 4 - -3. Let x = -15 - -22. Factor -21*w**4 - 5*w**3 - 6*w**2 - 6*w**3 - 9*w**i - x*w**3.
-3*w**2*(w + 1)*(7*w + 2)
Let d(u) be the first derivative of 3*u**5/5 + 5*u**4/4 + 7*u**3/9 + u**2/6 + 71. Suppose d(g) = 0. What is g?
-1, -1/3, 0
Let y(w) be the first derivative of 0*w - 1/3*w**3 - 12 + w**2. Solve y(c) = 0 for c.
0, 2
Let t(y) be the second derivative of y**7/210 - y**6/30 + y**5/15 + y**3/2 + 7*y**2/2 + 6*y - 3. Let l(d) be the second derivative of t(d). Factor l(b).
4*b*(b - 2)*(b - 1)
Suppose -3 - 1 = -2*w. Suppose 4*a + a = -20, w*a = 4*j - 24. Determine k, given that -6*k + 2*k**3 - k**4 - 6 + 2 + 3*k**j - 6*k**2 - 4*k = 0.
-1, 2
Let q(m) be the first derivative of -m**5/40 - 5*m**4/32 + m**3/4 + 186. Factor q(d).
-d**2*(d - 1)*(d + 6)/8
Suppose k = -39*k + 7*k. Let c(r) be the first derivative of -4 + k*r**2 - 1/16*r**4 + 3/20*r**5 + 0*r - 1/6*r**3. Factor c(z).
z**2*(z - 1)*(3*z + 2)/4
Let r(c) be the second derivative of c**8/6720 + 11*c**7/6300 - 17*c**6/3600 - c**5/60 + 3*c**4/4 + 5*c. Let s(y) be the third derivative of r(y). Factor s(o).
(o - 1)*(o + 5)*(5*o + 2)/5
Let m = 6 - 4. Let h(r) be the third derivative of 0*r - 1/60*r**4 + 2/45*r**3 - 4*r**m + 1/450*r**5 + 0. Factor h(b).
2*(b - 2)*(b - 1)/15
Let u be (27/(-189))/((-1)/28). Let 148/5*c**2 - 242/15*c**3 + 16/15 - 112/3*c**u - 152/15*c + 98/5*c**5 = 0. What is c?
-1, 2/7, 1/3, 2
Let w(s) be the third derivative of s**7/315 - s**6/20 + 5*s**5/18 - 3*s**4/4 + 10*s**3/9 + 13*s**2 - 2. Factor w(v).
2*(v - 5)*(v - 2)*(v - 1)**2/3
Suppose 5*x + 86 = 3*d, -54 = 2*x + x - d. Let v = x + 22. Let 0*t - 8*t - 4 - t**4 + 2*t**4 + 3*t**4 + 8*t**v = 0. What is t?
-1, 1
Let m = -189 - -191. Let w(g) be the second derivative of g + 0 - 1/35*g**5 + 0*g**4 + 2/21*g**3 - 1/105*g**6 + 1/7*g**m. Factor w(p).
-2*(p - 1)*(p + 1)**3/7
Let l(q) = 2*q**3 + 19*q**2 - 61*q - 9. Let a be l(-12). Let m(i) be the first derivative of -1/2*i**a + 1/4*i**2 + 0*i - 6. Factor m(k).
-k*(3*k - 1)/2
Factor 16/3 + 56*i + 147*i**2.
(21*i + 4)**2/3
Let a(w) = 3*w**2 + 11*w - 2. Let y be a(-4). Let j(s) be the second derivative of -s**y + 4*s + 1/6*s**4 + 0 + 0*s**