f = 0.
-3, -1
Factor -31/8*x - 1 - 13/4*x**3 - 11/2*x**2 + 1/8*x**5 - 1/2*x**4.
(x - 8)*(x + 1)**4/8
Let p be (-57)/(-252) + (-8)/56. Let o(q) be the third derivative of 0 - 7*q**2 + p*q**4 + 0*q**5 + 0*q**3 + 0*q - 1/60*q**6. Find y, given that o(y) = 0.
-1, 0, 1
Let l be -1*5 - (-21)/3. Suppose -l*k + 2*b + 8 = 0, -2*b + 0*b = -3*k + 12. What is r in -1/2 + 5/2*r - 7*r**3 + 9/2*r**5 - r**2 + 3/2*r**k = 0?
-1, 1/3, 1
Let 0 + 378*q - 2*q**3 + 8 - 5*q**2 + q**3 - 380*q = 0. Calculate q.
-4, -2, 1
Let q(n) be the third derivative of 0*n - 5*n**2 + 0 + 1/180*n**6 - 1/12*n**4 + 0*n**5 - 1/2*n**3. Let w(g) be the first derivative of q(g). Factor w(c).
2*(c - 1)*(c + 1)
Let 0 + 25/3*g**3 + 0*g - 31/3*g**4 + 10/3*g**5 - 2*g**2 = 0. Calculate g.
0, 1/2, 3/5, 2
Let g(z) be the third derivative of 0 + 0*z - 1/6*z**4 - 4/3*z**3 + 27*z**2 - 1/120*z**5. Factor g(n).
-(n + 4)**2/2
Let s(d) = -d**2 - 11*d - 30. Let r be s(-6). Let q(b) be the third derivative of -4*b**2 + 1/100*b**5 + r + 0*b + 1/40*b**4 - 1/5*b**3. Factor q(w).
3*(w - 1)*(w + 2)/5
Let n = 13388 + -13388. Suppose 0*l**2 + 0*l - 5/4*l**4 + n - 1/4*l**5 + 0*l**3 = 0. Calculate l.
-5, 0
Suppose 2*p = 3*f + 15, 3*p + 7*f = 4*f. Factor 4*l - 9*l + 6*l**2 + 6*l + 2*l + 3*l**p.
3*l*(l + 1)**2
Let s(r) be the second derivative of -5/12*r**4 - 3/2*r**2 + 8*r + 0 + 1/20*r**5 + 7/6*r**3. Let s(m) = 0. What is m?
1, 3
Let t = -13730 + 27461/2. Factor 1/4 + 0*o**3 + 1/4*o**4 + 0*o - t*o**2.
(o - 1)**2*(o + 1)**2/4
Factor 20*n**2 + 28*n - 26 + 74 - 18*n**2.
2*(n + 2)*(n + 12)
Let t(z) = 4*z**2 + 12*z + 9. Let c(d) = d**2 + 3*d + 2. Let w = -11 - -29. Let g(h) = w*c(h) - 4*t(h). What is b in g(b) = 0?
-3, 0
Let q(g) be the first derivative of 3*g + 1 + 5/3*g**3 - 1/4*g**4 - 7/2*g**2. Factor q(v).
-(v - 3)*(v - 1)**2
Let l(y) be the second derivative of 0 + 8*y - 15/16*y**2 + 7/24*y**3 + 1/96*y**4. Determine w, given that l(w) = 0.
-15, 1
Let b(p) be the third derivative of 0 - 1/540*p**6 + 0*p**4 + 1/270*p**5 + 0*p + 0*p**3 - 15*p**2. What is x in b(x) = 0?
0, 1
Suppose -3*k + 3*o - 21 = 0, -2*k + 3*k - 1 = -3*o. Let f(j) = -j**3 - 5*j**2 - 2*j - 5. Let c be f(k). Factor -3*b - b**3 - 2*b**2 + 4*b + c*b**2 - 3*b**4.
-b*(b - 1)*(b + 1)*(3*b + 1)
Let b(j) be the third derivative of 3*j**2 - 2/15*j**4 - 1/300*j**6 + 0*j + 4/15*j**3 + 1/30*j**5 + 0. Factor b(u).
-2*(u - 2)**2*(u - 1)/5
Determine g so that 10 + 5/4*g**2 - 15/2*g = 0.
2, 4
Let p(c) be the second derivative of -c**7/168 - c**6/72 + c**5/12 + 17*c**3/6 + 16*c. Let x(a) be the second derivative of p(a). Solve x(k) = 0 for k.
-2, 0, 1
Let x(w) = -3*w**2 + 17*w. Let s be x(4). Suppose s*d - 22*d + 4 = 0. Solve 1/3*q**3 + 2/3*q + q**d + 0 = 0.
-2, -1, 0
Let o(t) be the second derivative of t**3/2 - 12*t**2 + 33*t. Let z be o(9). Factor -2/5*g + 2/5*g**z - 2/5 + 2/5*g**2.
2*(g - 1)*(g + 1)**2/5
Let 13*s + 1/3*s**3 - 7*s**2 - 19/3 = 0. Calculate s.
1, 19
Let b(j) = 2*j**2 + 32*j - 4. Let m(x) = x**2 + 32*x - 6. Let u(g) = 3*b(g) - 2*m(g). Factor u(c).
4*c*(c + 8)
Let n be (-38)/(-6) + -5*(-11)/(-165). Let k(u) be the second derivative of 2*u + u**3 - 1/21*u**7 - 1/5*u**n + u**2 + 1/3*u**4 + 0 - 1/5*u**5. Factor k(x).
-2*(x - 1)*(x + 1)**4
Let h(k) be the second derivative of -k**5 + k**4 + 8*k**3 + 8*k**2 + 5*k + 2. Factor h(d).
-4*(d - 2)*(d + 1)*(5*d + 2)
Let a(u) be the second derivative of -u**4/21 + 64*u**3/7 - 4608*u**2/7 + 79*u. Solve a(n) = 0.
48
Let x(g) = -3*g - 1. Let m = 3 - 5. Let s be x(m). Factor 2*z - s*z - 6*z**2 - z**3 - 2*z**3.
-3*z*(z + 1)**2
Suppose 3*p = 2*r, -5*r = 11*p - 16*p. Factor p*q**2 + 2/21*q + 0 - 2/21*q**3.
-2*q*(q - 1)*(q + 1)/21
Let u(s) be the first derivative of -3*s**5/5 - 45*s**4/4 - 13*s**3 + 45*s**2/2 + 42*s - 46. Factor u(a).
-3*(a - 1)*(a + 1)**2*(a + 14)
Let l(c) be the third derivative of -c**5/140 - 11*c**4/28 - 57*c**3/14 - 138*c**2 - 1. Factor l(y).
-3*(y + 3)*(y + 19)/7
Let u = -29 - -48. Suppose -2*k = 3*h - u, 4*h + 5*k + 1 = 17. Factor -h*w + 3/2 + 15/2*w**2.
3*(w - 1)*(5*w - 1)/2
Let c(p) be the second derivative of 0 + 25*p - 6*p**2 + 0*p**3 + 1/4*p**4. Find w such that c(w) = 0.
-2, 2
Factor -2/5*d**2 + 36/5 - 14/5*d.
-2*(d - 2)*(d + 9)/5
Let q be 27/81*3/50. Let b(p) be the second derivative of 0*p**3 + 0*p**2 + 11*p + 0 + q*p**5 + 1/30*p**4. Solve b(w) = 0.
-1, 0
Let t be 3/4 - (-10)/8. Factor 0 - 4/11*f + 18/11*f**t - 8/11*f**3.
-2*f*(f - 2)*(4*f - 1)/11
Determine z so that -14/5 + 8/3*z + 2/15*z**2 = 0.
-21, 1
Let n be 1 + 3/(-5) - 304/(-190). Factor -1/2*d - 1/2*d**3 - d**n + 0.
-d*(d + 1)**2/2
Let x = -144 + 146. Let p(j) be the first derivative of -4 + 4/7*j + 5/21*j**3 + 4/7*j**x + 1/28*j**4. Suppose p(w) = 0. Calculate w.
-2, -1
Let s(f) be the first derivative of -f**5/10 - f**4/3 + 12*f + 9. Let y(m) be the first derivative of s(m). Suppose y(a) = 0. Calculate a.
-2, 0
Let l(s) be the second derivative of 0*s**3 + 1/3*s**4 - 1/30*s**5 + 0*s**2 + 0 - 1/45*s**6 - 20*s. Determine x so that l(x) = 0.
-3, 0, 2
What is q in 9/10*q - 1/2*q**2 + 0 = 0?
0, 9/5
Let b(i) = i**2 + 28*i + 75. Let y be b(-25). Factor -2/5*a**4 - 6/5*a**3 + y - 6/5*a**2 - 2/5*a.
-2*a*(a + 1)**3/5
Suppose 0 = -30*x + 25*x + 10. Let z = -7 + 9. Determine g so that -4*g**2 - 3*g**2 + 2*g**x - 2*g - g**z = 0.
-1/3, 0
Suppose -3 = -v - k, 8 + 4 = 5*v + 2*k. Suppose -5*u = -0*u - 20. Let -1 - 4*j + 4*j**2 + u*j**2 - 11*j**v = 0. What is j?
-1, -1/3
Let -2/5*m**2 - 16 + 26/5*m = 0. What is m?
5, 8
Let u be -2 + 2 + (-1)/(-10)*6. Let k(s) = -s + 7. Let d be k(5). Suppose 0*p + 0*p**3 - u*p**4 + 0*p**d + 0 = 0. What is p?
0
Let m(u) be the third derivative of -1/540*u**6 - 1/270*u**5 - 12*u**2 + 0*u + 1/27*u**3 + 0 + 1/108*u**4. Let m(i) = 0. What is i?
-1, 1
Solve -302/7*j - 300/7 - 2/7*j**2 = 0.
-150, -1
Let a(j) = j**2 - 5*j. Let l(p) = p. Let m(t) = -t**3 + 16*t**2 - 15*t - 1. Let f be m(15). Let v(x) = f*a(x) - 6*l(x). Find w such that v(w) = 0.
-1, 0
Let d(a) = 0 + 5 + 4*a - 35 + 16*a**2 - 2*a**3 + 26*a**3. Let h(g) = 5*g**3 + 3*g**2 + g - 6. Let f(w) = -3*d(w) + 14*h(w). Let f(n) = 0. Calculate n.
-3, -1, 1
Let k be 9/(-18)*(-1 + 1/3). Determine g so that 1/6*g**2 - 1/2 - k*g = 0.
-1, 3
Let z = 11/1306 - -5191/3918. What is a in 26/9*a**3 + 8/9*a + 2/9*a**5 - z*a**4 + 0 - 8/3*a**2 = 0?
0, 1, 2
Factor 32/3*d**2 + 2/3*d**3 - 2/3*d - 32/3.
2*(d - 1)*(d + 1)*(d + 16)/3
Let m(g) = -2*g**2 + 75*g + 161. Let z(y) = 15*y**2 - 600*y - 1285. Let a(w) = -25*m(w) - 3*z(w). Suppose a(f) = 0. Calculate f.
-2, 17
Let r(k) be the first derivative of 25*k**6/51 - 18*k**5/17 - k**4/34 + 82*k**3/51 - 24*k**2/17 + 8*k/17 - 284. Solve r(j) = 0.
-1, 2/5, 1
Solve -20*o**2 + 27*o**3 - o**2 + 20*o**5 + 15*o**5 + 6*o - 32*o**5 - 15*o**4 = 0.
0, 1, 2
Let x(p) = -p**5 - p**3 + p**2 + p. Let a(s) = 20*s**4 + 30*s**3 - 2*s**2 - 32*s - 16. Let f(d) = -a(d) + 2*x(d). Determine g so that f(g) = 0.
-8, -1, 1
Let q(z) be the third derivative of 8/21*z**7 - 5/6*z**3 + 5/3*z**4 + 0 + 0*z + z**2 - 5/4*z**5 - 1/3*z**6. Factor q(p).
5*(p - 1)*(p + 1)*(4*p - 1)**2
What is f in -32*f**2 - 39*f**2 - 42*f**2 + 108*f**2 - 2205 - 210*f = 0?
-21
Solve 3/8*k**4 + 0 - 435/8*k**2 - 219/8*k - 213/8*k**3 = 0.
-1, 0, 73
Let d be (-5)/1*4/(-10). Let o(w) be the third derivative of -1/330*w**5 + 0*w + 0 + 0*w**3 - 1/132*w**4 - 10*w**d. What is c in o(c) = 0?
-1, 0
Let s = 1/1975 + 17773/3950. Let p be 4/6*(7 - 1). Solve -4*u**2 - s*u**5 - 3*u**p + 0 + 10*u**3 + 0*u = 0.
-2, 0, 2/3
Factor -10*a**3 - 23*a**3 - 19*a**3 - 100 - 140*a + 57*a**3 - 35*a**2.
5*(a - 10)*(a + 1)*(a + 2)
Find n such that 18 - 7*n**4 + 6*n**5 + 0*n - 17*n**4 - 2*n**5 - 7*n**5 + 39*n + 6*n**2 - 36*n**3 = 0.
-6, -1, 1
Let z(p) = p**2 - 7*p + 3. Let k(v) = v - 1. Let c(m) = -3*k(m) - z(m). Factor c(y).
-y*(y - 4)
Factor 8*c - 12*c**2 + 16/3 + 10/3*c**3.
2*(c - 2)**2*(5*c + 2)/3
Let s(z) be the second derivative of -7/12*z**2 + 10 - 2*z - 1/6*z**3 + 1/72*z**4. Factor s(x).
(x - 7)*(x + 1)/6
Factor 59*a + 0 + 1/2*a**2.
a*(a + 118)/2
Let x(q) be the third derivative of 13*q**2 + 0*q**4 - 7/360*q**6 + 1/210*q**7 + 0 + 0*q**3 + 1/90*q**5 + 0*q. Let x(g) = 0. Calculate g.
0, 1/3, 2
Let v = 1590 + -1586. Let j(q) be the second derivative of 4/3*q**3 + 2/3*q**6 + 12/5*q**5 + 3*q**4 + 0 + v*q + 0*q**2. Find d s