*(t - 2)*(t - 1)**2
Let p(i) be the second derivative of -i**7/280 - i**6/80 + i**5/20 + i**4/4 + 11*i**2 + 7*i. Let m(g) be the first derivative of p(g). Factor m(w).
-3*w*(w - 2)*(w + 2)**2/4
Let o(j) be the third derivative of -j**8/392 + 8*j**7/735 - j**5/21 + j**4/28 + 2*j**3/21 - 75*j**2. Find f, given that o(f) = 0.
-1, -1/3, 1, 2
Solve -2/5*k**3 - 8/5 + 0*k + 2/5*k**5 - 6/5*k**4 + 14/5*k**2 = 0 for k.
-1, 1, 2
Suppose 2*w - 4*l = 4*w + 4, -1 = -2*w + l. Let a be w/(8 + -4) + 0. Factor a + 1/4*d**2 + 1/4*d.
d*(d + 1)/4
Suppose 3*u = -2*f - f + 87, 2*f = -u + 54. Suppose 3*m + 33 = -5*y + 8, -5*y - f = -2*m. Solve -5*t**3 - 4*t + 0*t + 3*t + 2 + m*t - 8*t**2 = 0.
-1, 2/5
Let h(t) be the third derivative of t**10/60480 + t**9/10080 + t**8/4480 + t**7/5040 + t**4/4 + 8*t**2. Let x(s) be the second derivative of h(s). Factor x(w).
w**2*(w + 1)**3/2
Let o be (1 - 51/63)*(-14751)/(-894). Find h, given that 0 - 8/7*h**5 - 8/7*h + 32/7*h**2 + 6/7*h**3 - o*h**4 = 0.
-2, 0, 1/4, 1
Let s be ((-286)/(-96) + -3)*1*-2. Let i(b) be the first derivative of 2 + s*b**4 + 0*b - 1/6*b**2 - 1/18*b**3. Factor i(x).
x*(x - 2)*(x + 1)/6
Let n = -7 + 9. Suppose n*p = -0*p + 4. Factor 4/7 + 8/7*f**p + 10/7*f + 2/7*f**3.
2*(f + 1)**2*(f + 2)/7
Let t = -2674 + 2679. Suppose -5/2*x**2 - 5/2*x**4 + t*x**3 + 0 + 0*x = 0. What is x?
0, 1
Let 297 + 2*j**4 - 100*j - 141*j + 12*j**2 + 215 + 24*j**3 - 143*j - 4*j**2 = 0. What is j?
-8, 2
Let v(z) be the second derivative of z**6/90 - 7*z**5/120 + z**4/8 - z**3/6 + 3*z. Let o(f) be the second derivative of v(f). Determine i so that o(i) = 0.
3/4, 1
Let 109/6*x + 1/3*x**2 + 9 = 0. Calculate x.
-54, -1/2
Let o(m) be the second derivative of 11*m + 0 - 8*m**2 - 1/5*m**5 + 0*m**3 + m**4. Suppose o(n) = 0. Calculate n.
-1, 2
Let h be ((-3)/54)/(1/(3/(-2))). Let v(r) be the first derivative of 1/2*r**2 + 0*r**3 - h*r**4 - 6 + 2/3*r. Find i, given that v(i) = 0.
-1, 2
Let s be 2212/(-588) + (2 - -1). Let p = 10/7 + s. Suppose 0*h**2 - 4/3*h + p - 2/3*h**4 + 4/3*h**3 = 0. What is h?
-1, 1
Let t(p) = p + 10. Let b be t(-7). Suppose 0 = 2*v + b*v - 4*d - 3, d - 18 = -5*v. Factor 6 - g**2 - 10*g + 13*g - 3*g**v - 5*g**2.
-3*(g - 1)*(g + 1)*(g + 2)
Let x = 24 - 22. Factor 3*t + t**2 - 18*t - 3*t**2 - 3*t**x.
-5*t*(t + 3)
Find i, given that -1/4*i**5 + 5/4*i - i**3 + 1/2*i**2 + 1/2 - i**4 = 0.
-2, -1, 1
Factor 0 + 7/2*s - 1/2*s**3 - 3*s**2.
-s*(s - 1)*(s + 7)/2
Let r(s) be the second derivative of -s**8/3360 + s**7/630 + s**6/360 - s**5/30 + 25*s**4/12 + 24*s. Let g(o) be the third derivative of r(o). Factor g(i).
-2*(i - 2)*(i - 1)*(i + 1)
Find w such that 10*w**2 + 750 - 150*w - 2/9*w**3 = 0.
15
Find f such that 1/4*f**2 + 21/4*f + 5 = 0.
-20, -1
Suppose -5*i - 2*s = -79, -3*i = -0*s - s - 43. Determine d, given that 10*d**2 + 5*d**5 + 15*d**3 + 8*d**4 - i*d**2 - 12*d**4 - 11*d**4 = 0.
0, 1
Factor 3*m**3 + 213*m - 2264 - 2082 + 4112 - 54*m**2.
3*(m - 13)*(m - 3)*(m - 2)
Let k be (14/(-252)*21)/((-28)/16). Factor -k*q + 2/3*q**2 + 0.
2*q*(q - 1)/3
Let m = 4079/54 + -1999/27. Factor -3/2*c**4 + 3/2*c + 0 + 3/2*c**2 - m*c**3.
-3*c*(c - 1)*(c + 1)**2/2
Let q be (-1*146)/(11 + -13). Let w = -71 + q. Factor 10/11*k**3 + 4/11*k - 14/11*k**w + 0.
2*k*(k - 1)*(5*k - 2)/11
Suppose 4*l + 632 = 4*q, -2*q = -4*q + 8. Let g = -150 - l. Factor -t**2 + 0 + 1/2*t - 1/2*t**3 + t**g.
t*(t - 1)*(t + 1)*(2*t - 1)/2
Let b(y) = -4*y**4 + 16*y**3 + 6*y**2 - 4*y - 2. Let s(p) = 3*p**4 - 15*p**3 - 6*p**2 + 5*p + 3. Let o(n) = 5*b(n) + 6*s(n). Factor o(q).
-2*(q - 1)*(q + 1)**2*(q + 4)
Let b(i) be the second derivative of i**6/15 - 13*i**5/15 - 2*i**4/3 + 26*i**3/9 + 3*i**2 - 103*i - 2. Let b(c) = 0. What is c?
-1, -1/3, 1, 9
Factor -8/3*r - 2 - 2/3*r**2.
-2*(r + 1)*(r + 3)/3
Let g(a) = -a**2 - 1. Let k(t) = 27*t**2 - 24*t + 9. Suppose -3*u + 12 = -3*s, 0 = 3*u - 2*u - 5*s - 24. Let n(q) = u*k(q) - 6*g(q). Factor n(b).
-3*(b - 1)*(7*b - 1)
Let a(t) be the first derivative of 0*t**3 + 5 + 0*t**2 + 0*t**4 + 1/110*t**5 - 3*t. Let b(v) be the first derivative of a(v). Suppose b(m) = 0. What is m?
0
Let y(h) = 4*h**2 - 5*h + 4. Let r be y(1). Factor -3*k**r + 2*k**2 + 11*k**2 + 12*k - 4*k**2.
-3*k*(k - 4)*(k + 1)
Factor 388*b**4 + 382*b**4 + 12*b**3 + 3*b**2 - 18*b - 767*b**4.
3*b*(b - 1)*(b + 2)*(b + 3)
Let n(i) = i - 4. Let u be n(8). Suppose 2*f - 13 = -l, f = -0*f + 2*l - 1. Factor 3*z**5 + 3*z**3 + 4*z**2 + 3*z**u - 7*z**2 - 3*z**5 - 3*z**f.
-3*z**2*(z - 1)**2*(z + 1)
Let r be (-1 + 2)*(-20)/(-4). Factor 5*s**4 - 133*s - 10*s**3 + r*s**5 + 133*s.
5*s**3*(s - 1)*(s + 2)
Let -7*w**3 + 7945*w - 177*w**2 + 27*w**3 - 2445*w - 293*w**2 - 10000 - 430*w**2 + 4*w**4 = 0. What is w?
-20, 5
Find k such that 2/3*k**2 + 86/3 - 88/3*k = 0.
1, 43
Let d(g) be the second derivative of -g**9/6048 - g**8/3360 + g**7/840 - g**3/3 - 12*g. Let i(y) be the second derivative of d(y). Find c such that i(c) = 0.
-2, 0, 1
Let x(m) be the second derivative of m**5/50 - 19*m**4/30 - 41*m**3/15 - 21*m**2/5 + 407*m. Solve x(a) = 0 for a.
-1, 21
Let s(x) be the third derivative of -x**6/40 - 3*x**5/20 - 144*x**2. What is o in s(o) = 0?
-3, 0
Factor 0*j - 2/7*j**4 - 18/7*j**2 + 0 - 12/7*j**3.
-2*j**2*(j + 3)**2/7
Let z(h) = 30*h**2 - 24*h + 4. Let q be (-6)/(1 - 25/15). Let g(p) = -120*p**2 + 95*p - 16. Let b(d) = q*z(d) + 2*g(d). Factor b(n).
2*(3*n - 2)*(5*n - 1)
Let c = -1901/6 - -317. Let f(v) be the second derivative of -1/4*v**2 + 0 - 1/24*v**4 + c*v**3 - 5*v. Factor f(r).
-(r - 1)**2/2
Let n(o) be the third derivative of o**5/240 + o**4/96 - 4*o**2. Factor n(s).
s*(s + 1)/4
Suppose 5*t = 100 + 20. Solve t*c**3 - 15*c**4 - 3*c**3 - 48*c - 24*c**2 + 12*c**4 = 0 for c.
-1, 0, 4
Factor 0 - 6*f**3 + 3/4*f**5 + 3/4*f**4 + 0*f - 9*f**2.
3*f**2*(f - 3)*(f + 2)**2/4
Factor -1 - 9/2*y**2 - 5/2*y**3 - 7/2*y - 1/2*y**4.
-(y + 1)**3*(y + 2)/2
Let z(q) = -126*q**2 - 945*q - 222. Let k(b) = -25*b**2 - 189*b - 44. Let r(j) = 24*k(j) - 5*z(j). Factor r(w).
3*(w + 6)*(10*w + 3)
Let v(m) be the second derivative of m**5/5 + 2*m**4/3 - 10*m**3 - 72*m**2 - 92*m. Determine l so that v(l) = 0.
-3, 4
Let z(k) = -10*k - 28. Let g be z(-3). Factor 4*x**g + 3*x**3 + 9*x - 11*x + 3*x**3.
2*x*(x + 1)*(3*x - 1)
Let u(g) = -3*g**2 + 20*g - 38. Let n(a) = a**2 - 10*a + 20. Let f(x) = 5*n(x) + 2*u(x). Factor f(p).
-(p - 2)*(p + 12)
Let a(b) be the second derivative of -b**6/75 - b**5/25 - b**4/30 - 70*b. Factor a(i).
-2*i**2*(i + 1)**2/5
Let 2/13*y**4 - 2/13*y**2 + 0 + 12/13*y**3 - 12/13*y = 0. What is y?
-6, -1, 0, 1
Suppose 0 = 118*d + 22*d. What is c in d + 1/4*c**4 + 0*c - c**2 + 0*c**3 = 0?
-2, 0, 2
Determine m, given that -5*m**3 - 378*m**4 + 180*m - 147*m**5 + 14 - 15*m**3 + 6 + 4 - 13*m**3 + 354*m**2 = 0.
-2, -1, -2/7, 1
Let m(s) be the first derivative of s**3/24 + 5*s**2/8 + 9*s/8 - 168. Find t, given that m(t) = 0.
-9, -1
Suppose j = -5, 0*j + j - 110 = 5*u. Let y be u/(-12) - (-80)/(-64). Factor -y*f**2 - 2 + 8/3*f.
-2*(f - 3)*(f - 1)/3
Let j = -49/5 + 157/15. Factor -j*p**2 - 4/3*p + 0.
-2*p*(p + 2)/3
Factor 3/7*r**4 + 12/7*r**2 + 0*r + 0 + 15/7*r**3.
3*r**2*(r + 1)*(r + 4)/7
Let q(h) = -h**3 - h**2 + 5*h + 2. Let s be q(-3). Suppose -31 = 2*f - 5*f - s*p, 2*f + 21 = 5*p. Factor 0 - 4/3*a + a**3 + 1/3*a**4 + 0*a**f.
a*(a - 1)*(a + 2)**2/3
Let o(k) be the third derivative of k**5/75 + 4*k**4/15 - 6*k**3/5 + 37*k**2 - 2*k. Factor o(i).
4*(i - 1)*(i + 9)/5
Suppose 124 = 4*g - 2*x, 5*g - 4*g - 5*x = 13. Let h be (308/g)/((-4)/(-6)). Let 3*i**3 - 9 - 3*i - h + 20 + 3*i**2 = 0. What is i?
-1, 1
Let l(m) be the second derivative of 7*m**6/60 + 11*m**5/10 + 47*m**4/24 + 5*m**3/6 - m - 29. Suppose l(t) = 0. What is t?
-5, -1, -2/7, 0
Suppose -3/2 + 1/4*t + 1/4*t**3 + t**2 = 0. Calculate t.
-3, -2, 1
Let j(u) be the first derivative of 127896*u**3 - 876*u**2 + 2*u + 374. Factor j(s).
2*(438*s - 1)**2
Let y(r) be the third derivative of -r**5/210 - 8*r**4/21 - 31*r**3/21 + r**2 - 146*r. Factor y(h).
-2*(h + 1)*(h + 31)/7
Let w be ((-9)/7 + 2/7)*1. Let i(v) = -6*v - 20. Let p(c) = c**2. Let y(n) = w*i(n) - 2*p(n). Factor y(t).
-2*(t - 5)*(t + 2)
Let h(v) be the first derivative of -v**7/315 - 4*v**6/225 + 8*v**4/45 + 16*v**3/45 - 6*v - 8. Let g(s) be the first derivative of h(s). Factor g(f).
-2*f*(f - 2)*(f + 2