t**3 + 2*t**2 - 10*t - 1. Let g(l) = -l**4 + l**3 - l**2 + 3*l + 1. Let s(m) = 5*g(m) + x(m). Factor s(b).
-(b - 1)*(b + 1)**2*(b + 4)
Let 21*x + 1/2*x**2 + 41/2 = 0. What is x?
-41, -1
Suppose -4/7*q + 2/7*q**2 - 6/7 = 0. What is q?
-1, 3
Let m = -4/69 + 31/138. Solve 0 + 1/6*h**3 - 1/6*h**2 - 1/6*h + m*h**4 = 0.
-1, 0, 1
Let b be -3 + 46/6 - 2/3. Suppose -2*c - 2 = -3*q - 0, -b*q + 16 = 0. Determine p so that 21/2*p**2 - 12*p**4 + 21/2*p + 3/2 + 24*p**c - 69/2*p**3 = 0.
-1, -1/4, 1
Let b(z) be the first derivative of -z**3/12 + 85*z**2/8 - 21*z + 477. Find d such that b(d) = 0.
1, 84
Let l = 4027 + -4027. Factor 3/8*r**4 + 9/8*r**3 + 0 + l*r + 3/4*r**2.
3*r**2*(r + 1)*(r + 2)/8
Let g(o) be the third derivative of o**5/30 - 13*o**4/3 + 676*o**3/3 + 174*o**2. Factor g(l).
2*(l - 26)**2
Let b(t) = -99*t + 297. Let h be b(3). Let l = -1 + 1. Factor l*z**2 + 1/3*z**4 + 1/3*z**5 + 0*z**3 + h*z + 0.
z**4*(z + 1)/3
Let n(x) be the first derivative of -x**5/30 + 7*x**4/24 - 5*x**3/6 + 13*x**2/12 - 2*x/3 + 234. Factor n(h).
-(h - 4)*(h - 1)**3/6
Suppose 7 = -6*d + 43. Suppose -d*z - 5*i - 5 = -z, 5*z = 2*i + 16. Solve 2/7*a**4 + 0*a + 2/7*a**3 - 2/7*a**z - 2/7*a**5 + 0 = 0 for a.
-1, 0, 1
Determine b so that -62/7*b + 2/7*b**2 + 0 = 0.
0, 31
Let s be 7 + 35/(-12) + -4. Let j(y) be the second derivative of 0*y**2 + 0*y**5 - 1/8*y**4 + 1/15*y**6 - 4*y + 0 + s*y**3. Factor j(w).
w*(w + 1)*(2*w - 1)**2/2
Let y(o) be the third derivative of o**7/945 + 13*o**6/540 - 7*o**5/135 - 118*o**2. Factor y(n).
2*n**2*(n - 1)*(n + 14)/9
Let p be 2/(60/(-86)) - -3. Let z(i) be the first derivative of 14/45*i**3 + 0*i + 1/9*i**6 - p*i**2 - 1/10*i**4 - 1 - 14/75*i**5. Let z(l) = 0. What is l?
-1, 0, 2/5, 1
Suppose -42/11*x**5 - 16/11*x**2 - 24/11*x**3 + 100/11*x**4 + 0 + 0*x = 0. What is x?
-2/7, 0, 2/3, 2
Let s(h) be the third derivative of 2*h**7/315 + 37*h**6/180 + 13*h**5/5 + 15*h**4 + 24*h**3 - 13*h**2 + 4. Determine d, given that s(d) = 0.
-6, -1/2
Let z(b) be the second derivative of -25*b**7/21 + 41*b**6/7 + 221*b**5/35 - 202*b**4/21 - 8*b**3/7 + 32*b**2/7 - 106*b + 3. Determine q so that z(q) = 0.
-1, -2/7, 2/5, 4
Let r(w) be the third derivative of 1/24*w**4 - 1/120*w**6 + 0 + 0*w + 9*w**2 - 1/60*w**5 + 0*w**3 + 1/210*w**7. Determine f so that r(f) = 0.
-1, 0, 1
Let g(u) be the second derivative of -u**8/2240 - u**7/420 + 7*u**6/240 - u**5/10 - 31*u**4/12 + 11*u. Let d(f) be the third derivative of g(f). Factor d(m).
-3*(m - 1)**2*(m + 4)
Let -2*d**4 - 3600*d + 3*d**4 + 132*d**3 - 6*d**4 - 2592 - 928*d**2 + d**4 + 56*d**2 = 0. Calculate d.
-2, -1, 18
Suppose 37*v - 59 - 13 = 39. Suppose 2/5*q**5 + 4/5*q**4 + 2/5*q**v + 0*q + 0 + 0*q**2 = 0. Calculate q.
-1, 0
Let u(j) be the third derivative of j**8/336 + j**7/105 + j**6/120 + 109*j**2. Find s such that u(s) = 0.
-1, 0
Let d = -3079 - -6175/2. Find h such that -289/8*h**2 - d*h - 1/2 = 0.
-2/17
Let d(o) be the first derivative of 9*o**4 - 11*o**3 + 3*o**2 - 256. Let d(x) = 0. What is x?
0, 1/4, 2/3
Let b(r) = -5 + 44*r**2 - 3*r**3 + 7*r - 29*r**2 - 22*r**2. Let h(y) = -8*y**3 - 20*y**2 + 20*y - 14. Let g(k) = 11*b(k) - 4*h(k). Factor g(f).
-(f - 1)**3
Let a(f) be the second derivative of 0 + 1/2*f**2 + 1/3*f**3 + 1/12*f**4 + 13*f. Factor a(y).
(y + 1)**2
Suppose -3*j + 3*d + 12 = 0, -5*j + 3*d = 2 - 18. Suppose -2*x**3 - 2*x**3 - 7*x**j + x**3 - x**4 + 5*x**2 = 0. Calculate x.
-2, -1, 0
Let z = 8056/12075 - 2/4025. Solve 16/3*y**2 - 7/3*y**3 + z - 11/3*y = 0.
2/7, 1
Let a(o) = 24*o**4 - 86*o**3 - 20*o**2 + 82*o - 16. Let d(i) = -16*i**4 + 57*i**3 + 13*i**2 - 55*i + 10. Let m(b) = -5*a(b) - 8*d(b). Let m(q) = 0. Calculate q.
-1, 0, 5/4, 3
Let b(v) = v**3 - 2*v**2 - v + 4. Let s(a) = -a**3 - a**2 - 12*a - 8. Let u(m) = 2*b(m) + s(m). Factor u(z).
z*(z - 7)*(z + 2)
Let z(s) be the third derivative of s**8/1344 - 11*s**7/1260 + 7*s**6/180 - s**5/15 + s**4/8 - 15*s**2. Let h(g) be the second derivative of z(g). Factor h(j).
(j - 2)**2*(5*j - 2)
Let z(d) be the first derivative of -2/17*d**3 + 0*d - 3 - 5/17*d**4 - 6/85*d**5 + 0*d**2. Suppose z(m) = 0. What is m?
-3, -1/3, 0
Let t = 7 + 21. Let m = t - 28. Determine s, given that 1/2*s**2 + 1/6*s**4 + 1/2*s**3 + m + 1/6*s = 0.
-1, 0
Let x(g) be the second derivative of 5*g**4/12 + 20*g**3/3 - 165*g**2/2 + 20*g. Factor x(h).
5*(h - 3)*(h + 11)
Let z = -429 + 431. Factor -1 + 1/3*k**z + 2/3*k.
(k - 1)*(k + 3)/3
Factor -6*m**4 + 8*m**4 + 6*m + m**3 - 2*m**2 - 8*m**2 + m**3.
2*m*(m - 1)**2*(m + 3)
Let b(y) be the first derivative of 1/14*y**4 - 2/35*y**5 - 10 + 0*y**2 + 0*y - 1/21*y**6 + 2/21*y**3. Factor b(x).
-2*x**2*(x - 1)*(x + 1)**2/7
Let o(d) be the second derivative of 1/12*d**4 - 11*d + 1/2*d**2 + 0 - 1/3*d**3. Factor o(u).
(u - 1)**2
Suppose 134*k + 2 = 137*k - 4. Factor -1/3*y**k + 1/3*y**4 + 0 - 4/3*y + 4/3*y**3.
y*(y - 1)*(y + 1)*(y + 4)/3
Let q = 0 - -2. Suppose -m + 9 = q*a, 5*m + 8 = 2*a - 7. Factor 0*r**2 - 3/5*r + 0*r**4 + 6/5*r**3 - 3/5*r**a + 0.
-3*r*(r - 1)**2*(r + 1)**2/5
Let n = -157/42 - -629/84. Factor -n*q - 5/2 + 5/2*q**2.
5*(q - 2)*(2*q + 1)/4
Let w(r) be the first derivative of 25*r**5 - 3225*r**4/4 - 2660*r**3 + 3950*r**2 - 1680*r + 832. Find x such that w(x) = 0.
-3, 2/5, 28
Let p(f) = f**3 - f**2 - f - 3. Let r(l) = -8*l**3 - 96*l**2 + 114*l + 30. Let m(t) = -10*p(t) - r(t). What is v in m(v) = 0?
0, 1, 52
Let d(g) = 3*g**2 - 15 - 22*g**2 + 7*g**2 + 50*g - 23*g**2. Let p(z) = 5*z**2 - 7*z + 2. Let u(q) = 2*d(q) + 15*p(q). Solve u(h) = 0 for h.
0, 1
Suppose 0 = 2*g, -4*d + 2*d = 5*g - 12. Let s be d/9*3 + -2. Factor -2/9*j**2 + 0 + s*j - 2/9*j**3.
-2*j**2*(j + 1)/9
Let p be 11/((-9)/(-6) - 3/6). Suppose 10*n - p*n = -22*n. Find v such that -4/3*v**3 + n*v**4 + 0 + 0*v**2 + 2/3*v + 2/3*v**5 = 0.
-1, 0, 1
Let a(d) be the first derivative of -2*d**6/15 - 13*d**5/25 + 13*d**4/20 + 52*d**3/15 + 6*d**2/5 - 899. Suppose a(l) = 0. Calculate l.
-3, -2, -1/4, 0, 2
Let n(d) be the third derivative of d**6/20 + 9*d**5/20 - 17*d**4/8 + 3*d**3 - 2*d**2 - 8. Let n(i) = 0. What is i?
-6, 1/2, 1
Let v(r) be the first derivative of -r**3/3 + r + 145. Solve v(a) = 0.
-1, 1
Let g = -1103 - -1105. Let p be 1/3 + 10/6. What is o in 8 - 2*o**p - g*o + o - 5*o = 0?
-4, 1
Let u(q) = -q**2 + q + 1. Let h(f) = 15*f**2 - 10*f**3 + 2 + 7 + 8*f**2 - 13*f - 4*f**2. Let t(p) = -h(p) + 5*u(p). Factor t(r).
2*(r - 1)**2*(5*r - 2)
Suppose -48*t = 14*t. Let v(k) be the second derivative of -2/21*k**7 + t + 4*k**2 + 4/5*k**5 - 2/3*k**4 + 0*k**6 - 2*k**3 + 8*k. Factor v(d).
-4*(d - 1)**3*(d + 1)*(d + 2)
Let z(t) be the third derivative of t**5/150 - 7*t**4/15 + 32*t**3/5 - 164*t**2 + 2*t. Factor z(q).
2*(q - 24)*(q - 4)/5
Let a = -4 + 6. Let s be (525/196)/5 - (-3)/((-105)/10). Find c, given that 0 - s*c**4 + 0*c - 1/2*c**3 - 1/4*c**a = 0.
-1, 0
Let n(m) = -m - 1. Let w(g) = -5*g**3 + 10*g + 10. Let v(r) = -r**3 + 5*r**2 - 10. Let h be v(5). Let a(i) = h*n(i) - w(i). Factor a(k).
5*k**3
Solve -2/9*y**5 - 4/9*y**4 + 4/3*y**3 - 10/9*y - 4/3 + 16/9*y**2 = 0.
-3, -1, 1, 2
Let t be (-240)/81 - -3 - 2560/(-864). Solve -9*l**2 + 9*l - 1/3*l**4 + 3*l**t + 0 = 0.
0, 3
Find x, given that -4/3 - 10/9*x + 2/9*x**2 = 0.
-1, 6
Let s(y) = -y**3 + 3*y**2 - y + 7. Let d be s(3). Let a be 5 + (-5 - d) - (-4 - 0). Solve -2/5*x**3 - 6/5*x - 8/5*x**2 + a = 0 for x.
-3, -1, 0
Suppose 5*p = 13*p - 16. Factor 2/3 + 1/3*q - 2/3*q**p - 1/3*q**3.
-(q - 1)*(q + 1)*(q + 2)/3
Suppose 4 = -m + 3*m. Find l such that -6*l**2 - 21*l - 12 + 0*l**3 + l**3 + m*l**3 = 0.
-1, 4
Factor -b**5 + 2*b**4 - b**5 - 67*b**2 + b**5 + 4*b**3 + 59*b**2.
-b**2*(b - 2)**2*(b + 2)
Let n be (-18)/(-4) - (-150)/(-100). Find x, given that 1/4*x**n + x + 0 + x**2 = 0.
-2, 0
Let b(v) be the second derivative of v**6/40 - 3*v**5/20 + 3*v**4/8 - v**3/2 - 8*v**2 + 3*v. Let q(m) be the first derivative of b(m). Factor q(o).
3*(o - 1)**3
Suppose -5*s = -20, -2 = -2*v - s + 8. Let q(m) be the second derivative of -1/8*m**4 - 2*m + 0 + m**v - 3*m**2. Factor q(h).
-3*(h - 2)**2/2
Let y(b) be the third derivative of -b**8/6720 - b**7/560 - b**6/120 - b**5/12 + 11*b**2. Let u(n) be the third derivative of y(n). Factor u(g).
-3*(g + 1)*(g + 2)
Let n be -8 - 5/2*8/(-10). Let d be (-50)/45*n/5. Suppose 0 + 2/3*c**3 + 2/3*c + d*c**2 = 0. Calcu