, 1/3
Let l(t) be the second derivative of 0*t**2 + 3/35*t**6 + 1/21*t**4 + 9*t + 9/70*t**5 + 0*t**3 + 0. What is y in l(y) = 0?
-2/3, -1/3, 0
Suppose -2 = u, 6*z + u = z + 8. Factor -4/3*x**z + 2/9*x**3 + 8/3*x - 16/9.
2*(x - 2)**3/9
Suppose 0 = 4*y - 4, 5*y - 14 = -0*l - 3*l. Suppose -g - 3*j = -6*j + 13, -5*g = -5*j + 15. Let 15/4*p**g + 7/4*p - 10*p**4 - 1/2 - 17/2*p**l = 0. What is p?
-1, -1/2, 1/4, 2/5
Let o = -4 + 11/2. Suppose -3/2*c**4 + 3*c**2 - 3*c**3 + 3/2*c - 3/2 + o*c**5 = 0. What is c?
-1, 1
Let i(h) be the second derivative of -h**7/21 + 2*h**6/15 + 3*h**5/10 - h. Suppose i(z) = 0. Calculate z.
-1, 0, 3
Let f = 2/25 - -1/50. Let h(r) be the first derivative of 0*r - 2/15*r**3 + 1/20*r**4 + 3 + f*r**2. Factor h(s).
s*(s - 1)**2/5
Let q(t) = t**2 + 10*t + 4. Let o be q(-10). Factor -x**3 - x**o + x**2 + x**2 - 2*x**2.
-x**3*(x + 1)
Let g(y) = -y**2 + 1. Let k(m) = -5*m**4 - 7*m**3 + m**2 + 7*m + 4. Let i = -20 + 21. Let o be 2/7 - (-16)/(-7). Let p(w) = i*k(w) + o*g(w). Factor p(q).
-(q - 1)*(q + 1)**2*(5*q + 2)
Let v(a) be the first derivative of -a**7/420 + 2*a**6/135 - 7*a**5/180 + a**4/18 - a**3 + 3. Let m(k) be the third derivative of v(k). What is p in m(p) = 0?
2/3, 1
Let v(h) = -h**4 + h**3 - h**2 - h. Let s(k) = -4*k**4 - k**3 - 5*k**2 + k + 3. Let o(d) = s(d) - 3*v(d). Factor o(a).
-(a - 1)*(a + 1)**2*(a + 3)
Let a(x) be the third derivative of 3*x**8/280 + x**7/50 - 2*x**6/75 - 19*x**5/300 + x**4/30 + 2*x**3/15 - 3*x**2. Determine f, given that a(f) = 0.
-1, -1/2, 2/3
Suppose -3*g + 2*g = -3. Let s(n) = -n**3 - 6*n**2 + 7*n + 2. Let x be s(-7). Suppose 2*l**4 + 3*l**2 + 2*l**5 - 4*l**4 - x*l**g - l**2 = 0. What is l?
-1, 0, 1
Let n(p) be the first derivative of -7*p**4/6 - 3*p**3 - 2*p**2 - p - 2. Let a(j) be the first derivative of n(j). Determine f, given that a(f) = 0.
-1, -2/7
Let f(d) be the second derivative of d**6/6 - 3*d**5/4 + 5*d**4/12 + 5*d**3/2 - 5*d**2 + 7*d + 5. Factor f(c).
5*(c - 2)*(c - 1)**2*(c + 1)
Let g(j) = 5*j**2 + 7*j + 9. Let c = 1 + 1. Let o(p) = -3*p - 3 - c*p**2 - 1 + 0. Let w(n) = -6*g(n) - 14*o(n). Suppose w(i) = 0. Calculate i.
-1, 1
Let n be (-21)/(-28) + (-3)/9. Let l(j) be the third derivative of n*j**4 - 1/12*j**6 - 2*j**2 - 2/3*j**3 + 0 + 0*j + 1/15*j**5. Find d, given that l(d) = 0.
-1, 2/5, 1
Suppose -3 = -4*m + 9. Solve 19*d + 24*d**2 + 6 - 2 - 3*d + 16*d**m + 4*d**4 = 0.
-1
Let z be (1/(-3))/((-12)/16). Let b = 304/1395 - -2/465. Determine n, given that b + z*n + 2/9*n**2 = 0.
-1
Factor 4/5 + 4/5*g**2 + 8/5*g.
4*(g + 1)**2/5
Let r = 6 + -3. Suppose 3*v = r + 3. Determine d so that d - 4*d**v + 0*d + 5*d**2 + 0*d = 0.
-1, 0
Let h = 10 - 8. Factor -3*i**2 + 3*i**4 - 2*i - h*i + 3*i**3 + 0*i + i.
3*i*(i - 1)*(i + 1)**2
Let g(a) be the first derivative of a**6/27 + 4*a**5/45 + a**4/18 + 7. Factor g(i).
2*i**3*(i + 1)**2/9
Let u(x) = -x - 6. Let t be u(-5). Let b be (1/1 + t)/2. Determine h, given that -2*h + 4*h**2 + 2*h**3 + 4*h + b*h**3 + 0*h**2 = 0.
-1, 0
Suppose 0 = -5*m + 13 + 17. Let b(l) be the third derivative of 4*l**2 + 0*l**3 + 1/180*l**m - 1/90*l**5 + 0 + 0*l + 0*l**4. Factor b(d).
2*d**2*(d - 1)/3
Let h be (96/(-10))/(-1*30/20). Factor 28/5*v**3 - h + 16*v - 72/5*v**2 - 4/5*v**4.
-4*(v - 2)**3*(v - 1)/5
Determine t so that 21/2*t**4 + 0 + 3*t**2 + 27/2*t**3 + 0*t = 0.
-1, -2/7, 0
Factor -o**2 - 10*o - 2*o**3 - 3*o**2 - o**2 + 7*o**3.
5*o*(o - 2)*(o + 1)
Suppose b**3 - b**3 + 3*b**3 - 8*b**3 = 0. Calculate b.
0
Suppose -4*p - 6 = -14. What is b in 1/3*b**3 + 1/3*b - 2/3*b**p + 0 = 0?
0, 1
Let s(a) = -80*a**2 + 35. Let k(h) = 9*h**2 - 4. Let c(x) = 35*k(x) + 4*s(x). Let c(y) = 0. What is y?
0
Let q(b) = b**2 + 8*b + 2. Let c be q(-8). Suppose -2 - c*s**3 - 2 + s**3 - s**3 + 6*s = 0. What is s?
-2, 1
Suppose -y + 4*y - 6 = 0. Let z = y - 2. Factor -1/3*s**2 + 0*s + z.
-s**2/3
Let v(j) = 3*j**2 + j. Let y be v(-1). Factor u + 0*u + u**3 + 9*u**2 - 11*u**y.
u*(u - 1)**2
Let g(o) = -o**3 - o**2 - o + 1. Let b(x) = 10*x**2 + 10*x + 10. Let i(k) = b(k) - 5*g(k). Factor i(t).
5*(t + 1)**3
Let z be (2 - (-1 + 0))*1. Let x(d) = d**2 - 2*d - 3. Let w be x(z). Factor w*n + 2/3*n**2 - 2/3.
2*(n - 1)*(n + 1)/3
Let v(u) = 0 - 4*u - 9 + 5*u. Let i be v(11). Determine t, given that 0*t**2 - 2*t**3 + t**4 + 0*t**2 - 3*t**4 + 2*t**2 + i*t = 0.
-1, 0, 1
Suppose 0 = -3*n + 2 - 44. Let z be (8/10)/(n/(-5)). Let 0 - z*f - 2/7*f**2 = 0. What is f?
-1, 0
Suppose 2*v + 28 = 3*o, -3*o = 2*v + 23 + 29. Let b be (-5)/6*v/25. Factor -2/3 + b*i**2 + 0*i.
2*(i - 1)*(i + 1)/3
Let v(n) = -2*n + 0*n - 3 + 3*n - 3*n. Let j be v(-3). Factor s**j + 2*s**3 - 3*s + s**5 - 4*s**5 + 3*s**3.
-3*s*(s - 1)**2*(s + 1)**2
Let f(c) be the third derivative of 5*c**2 + 0 - 1/150*c**5 + 0*c**4 + 0*c**3 + 0*c. Factor f(z).
-2*z**2/5
Let a(w) = 8*w**2 - 2*w - 10. Let r(l) = -l**2 + 1. Let m(j) = a(j) + 6*r(j). Factor m(q).
2*(q - 2)*(q + 1)
Factor -2/7*q**2 + 2/7*q**3 - 2/7*q + 2/7*q**4 + 0.
2*q*(q - 1)*(q + 1)**2/7
Suppose -d + 5*j = 7*j + 8, -2*d + 5*j = -20. Factor d*f + 2/5*f**2 + 0.
2*f**2/5
Factor 1/5*p**2 + 0 + 1/5*p**3 + 0*p.
p**2*(p + 1)/5
Let j(g) be the first derivative of -1/16*g**4 + 1/6*g**3 + 1/8*g**2 - 1/2*g + 1. Find r, given that j(r) = 0.
-1, 1, 2
Let c = -144 + 152. Let f(g) be the third derivative of g**2 + 0*g**4 + 0*g**5 + 0 + 0*g**3 + 0*g + 0*g**7 - 1/120*g**6 + 1/336*g**c. Factor f(l).
l**3*(l - 1)*(l + 1)
Let -33/8*c**2 + 105/8*c - 75/8 + 3/8*c**3 = 0. Calculate c.
1, 5
Let l(s) = -6*s**4 + 99*s**3 - 126*s**2 + 84*s - 21. Let v(x) = x**4 - 14*x**3 + 18*x**2 - 12*x + 3. Let i(y) = -2*l(y) - 15*v(y). Factor i(k).
-3*(k - 1)**4
Factor -4*l - 4*l**3 - 6*l**2 - 7 - l**4 - 6 + 12.
-(l + 1)**4
Let v(t) = 48*t**3 + 39*t**2 - 105*t - 45. Let r(p) = -12*p**3 - 10*p**2 + 26*p + 11. Let i(z) = -21*r(z) - 5*v(z). Factor i(m).
3*(m - 1)*(m + 2)*(4*m + 1)
Let k(w) be the second derivative of w**5/60 + w**2/2 - 2*w. Let m(c) be the first derivative of k(c). Find f, given that m(f) = 0.
0
Let a be (-1)/(1 + 2)*-49. Suppose 10*f + 12 = 14*f. Determine g, given that 42*g**f - 4/3 - a*g**4 - 109/3*g**2 + 12*g = 0.
2/7, 1
Let p = -2 + -2. Let k be 1/p + (-25)/(-4). Factor 3*m - 5*m + k*m**2 - m**3 - 4 - 2*m**4 + 3*m**3 + 0*m.
-2*(m - 2)*(m - 1)*(m + 1)**2
Let x(p) be the second derivative of p**5/60 + p**4/18 + p**3/18 + 7*p. Solve x(g) = 0 for g.
-1, 0
Let f = 3 - 1. Suppose -50 = -3*h - 2*h. Factor 5*d - 11*d + 4 - 8*d + h*d**f.
2*(d - 1)*(5*d - 2)
Factor -5*b**4 - 10 + 0*b**4 - 6 + 8*b**2 + 4*b**4.
-(b - 2)**2*(b + 2)**2
Let g = 4 + -1. Let r(p) = 3*p - 7. Let u be r(g). Find q such that -2/9*q**u - 2/9 + 4/9*q = 0.
1
Let g(m) be the third derivative of 0 + 0*m**5 - 1/504*m**8 - 1/36*m**4 - 3*m**2 + 0*m**3 + 0*m + 1/90*m**6 + 0*m**7. Determine l so that g(l) = 0.
-1, 0, 1
Let o(n) be the first derivative of -4 + 0*n**2 - 1/10*n**4 + 2/15*n**3 + 3*n. Let k(u) be the first derivative of o(u). Factor k(b).
-2*b*(3*b - 2)/5
Let z = -7021/9 - -781. Let l = z + -2/9. Solve 0*q - l + 2/3*q**2 = 0 for q.
-1, 1
Let m be ((-4)/16)/((-1)/28). Suppose -2*b + 5*b**4 - 4*b**2 + 7*b**2 - m*b**2 - b**4 + 2*b**5 = 0. Calculate b.
-1, 0, 1
Let h(c) be the first derivative of c**4/12 + c**3/3 + c**2/3 - 21. Solve h(q) = 0 for q.
-2, -1, 0
Let f(i) be the first derivative of i**4 + 28*i**3/3 + 12*i**2 + 5. Find q such that f(q) = 0.
-6, -1, 0
Factor -5/3*m**2 - 1/3*m**3 - 1 - 7/3*m.
-(m + 1)**2*(m + 3)/3
Let -d**4 - 99 + 0*d**4 + 2*d**5 + 2*d**2 + 98 - 4*d**3 + 2*d = 0. Calculate d.
-1, 1/2, 1
Let c = 4 + -4. Suppose 5 = 2*x + u, 0 = -c*u + 4*u + 12. Factor -1/2*v**2 + 0 + 1/2*v - 1/2*v**3 + 1/2*v**x.
v*(v - 1)**2*(v + 1)/2
Let r(s) = -3*s**3 + s**2 + 7*s - 5. Let x(f) = 2*f**3 - 6*f + 4. Let d be (-8)/10*(-20)/4. Let a(h) = d*r(h) + 5*x(h). Factor a(j).
-2*j*(j - 1)**2
Factor -g**2 + 2*g**3 - 3*g**4 + g**2 - 3*g + 2*g**2 + 1 + g**5.
(g - 1)**4*(g + 1)
Let o = -5983/15 + 399. Factor 0 + 2/15*f**2 + o*f.
2*f*(f + 1)/15
Let z(k) be the third derivative of k**7/105 + k**6/30 - 11*k**2. Determine s so that z(s) = 0.
-2, 0
Let x(q) be the first derivative of -q**4/4 - 5*q**3/3 - q**2 + 5*q - 1. Let f(m) = -4*m**2 - 2*m + 4. Let p(u) = -3*f(u) + 2*x(u). Factor p(y).
-2*(y - 1)**2*(y + 1)
Let w(g) be the third derivative of 2*g**7/105 - 