**6/140 - 2*c**5/35 - 3*c**4/56 + c**3/7 - 5*c**2. Factor b(s).
3*(s - 1)**4*(5*s + 2)/7
Let n(a) be the second derivative of -1/48*a**4 + 2*a + 1/12*a**3 - 1/8*a**2 + 0. Find h such that n(h) = 0.
1
Suppose h - 4*h = -15. Let -u**h + 6*u**5 + 0*u**5 - 3*u**5 = 0. Calculate u.
0
Find d such that 176*d**4 - 85*d**5 + 309*d**5 + 0*d**2 + 46*d**3 + 4*d**2 = 0.
-2/7, -1/4, 0
Suppose 2*p + 14 = -3*v + 4, -4*v = -3*p - 15. Let w(c) be the first derivative of v*c**3 - 2 + 2*c**2 - c**4 + 2*c - 2/5*c**5. Determine u so that w(u) = 0.
-1, 1
Let v(f) = f**4 - f. Let t(w) = -3*w**4 - 3*w**2 + 2*w. Let i(u) = 2*u**3 + 4*u**2 + u - 2. Let p be i(-2). Let y(r) = p*v(r) - t(r). Factor y(m).
-m*(m - 2)*(m + 1)**2
Let u(o) = -o**4 + o**3 - o**2 - o + 1. Let m = -11 - -10. Let j(p) = 4*p**4 + 14*p**3 + 3*p**2 - 5*p + 1. Let a(r) = m*u(r) + j(r). Factor a(s).
s*(s + 1)*(s + 2)*(5*s - 2)
Suppose 5*l**2 - 20*l**3 + 5*l**4 - 2*l**4 + 20*l**5 - 8*l**4 = 0. What is l?
-1, 0, 1/4, 1
Let h(j) be the second derivative of -2/15*j**6 + 0 + 0*j**2 + 0*j**4 + j + 0*j**3 + 1/10*j**5 + 1/21*j**7. Let h(l) = 0. What is l?
0, 1
Suppose 4*x - 3*x = 5. Let i(n) = n**3 - 6*n**2 + 8*n - 7. Let t be i(5). Solve -6*a**4 - 2*a**3 + 0*a**3 - 2*a**2 + t*a**3 + 2*a**x = 0 for a.
0, 1
Let k(a) be the second derivative of -a**4/60 - a**3/6 - 2*a**2/5 + 16*a. Determine p, given that k(p) = 0.
-4, -1
Let u(d) be the third derivative of -1/60*d**5 + 0 - d**2 + 1/24*d**4 + 1/210*d**7 + 0*d**3 + 0*d - 1/120*d**6. Factor u(z).
z*(z - 1)**2*(z + 1)
Let a be 9 - (0 - -3)/3. Let o(f) = f - 3. Let n be o(a). Factor -3*s**4 - s**2 - 2*s + 3*s**3 + 2*s + s**n.
s**2*(s - 1)**3
Let y = 2/657 - -5242/4599. Factor -y*p - 8/7 - 2/7*p**2.
-2*(p + 2)**2/7
Let b(d) be the first derivative of 7*d**3 + 2*d + d**5 + 17/4*d**4 - 2 + 11/2*d**2. What is f in b(f) = 0?
-1, -2/5
Let y(f) = -f**3 - f**2 + 2*f + 2. Let o = -34 + 32. Let v be y(o). What is c in -2/5 - 6/5*c**v + 6/5*c + 2/5*c**3 = 0?
1
Let q(m) be the first derivative of -3/2*m**2 - 9/2*m**4 - 2 - 1/2*m**6 - 4*m**3 - 12/5*m**5 + 0*m. What is b in q(b) = 0?
-1, 0
Let j be (-2)/(-8) - (68/80 + -1). Factor -2/5*w**3 + 0*w**2 + j*w + 0.
-2*w*(w - 1)*(w + 1)/5
Let b = -3 + 9. Let 10 + 6*u - b + u**2 + u**2 = 0. What is u?
-2, -1
Let h be (3/((-27)/6))/((-21)/126). Let s(o) be the third derivative of 0*o - o**2 + 1/120*o**6 - 1/3*o**3 + 5/24*o**h - 1/15*o**5 + 0. Factor s(i).
(i - 2)*(i - 1)**2
Let g(k) = -2*k**2 + 8 + 3*k**2 + 0*k**2 + 7. Let h(y) = -y**2 + y - 14. Let d(w) = 5*g(w) + 6*h(w). Factor d(i).
-(i - 3)**2
Let c(z) = -5*z**2 + 16*z + 15. Let q(o) = -30*o**2 + 95*o + 90. Let b(f) = 35*c(f) - 6*q(f). Solve b(y) = 0 for y.
-1, 3
Let g(r) be the second derivative of -9*r**5/20 + r**4/4 + 4*r**3/3 - 2*r**2 - 6*r. Factor g(h).
-(h + 1)*(3*h - 2)**2
Let o(x) = x**3 + 9*x**2 + 18*x + 10. Let l(g) = 2*g**3 + 26*g**2 + 54*g + 30. Let n(w) = 3*l(w) - 8*o(w). Let n(u) = 0. What is u?
-1, 5
Let r = -8/167 + 199/668. Find t such that 0 + 1/4*t**3 + r*t**2 + 0*t = 0.
-1, 0
Let z(o) be the first derivative of -5 + 0*o**2 - 2/5*o + 2/15*o**3. Determine v so that z(v) = 0.
-1, 1
Factor 2/3*x**2 - 4*x + 10/3.
2*(x - 5)*(x - 1)/3
Let 3*w**4 - 24 - w**4 + 24 + 2*w**3 - 4*w**2 = 0. What is w?
-2, 0, 1
Let j(r) = -r**3 + 6*r**2 - 10*r + 8. Let u be j(4). Factor 3/7*v**3 - 3/7*v**5 + 3/7*v**4 - 3/7*v**2 + 0*v + u.
-3*v**2*(v - 1)**2*(v + 1)/7
Let b = -246 - -246. Factor 0*w - 2/9 + b*w**3 + 4/9*w**2 - 2/9*w**4.
-2*(w - 1)**2*(w + 1)**2/9
Let a be (-13)/(-208)*4/1. Factor 1/4*w**3 - 1/4*w + 1/4*w**4 - a*w**2 + 0.
w*(w - 1)*(w + 1)**2/4
Suppose 0*u = -9*u. Determine o so that -1/4*o**2 + u - 1/4*o = 0.
-1, 0
Let u(h) be the first derivative of -h**6/2 + 3*h**5/5 + 3*h**4/4 - h**3 - 13. Factor u(t).
-3*t**2*(t - 1)**2*(t + 1)
Let h be 20/(-24)*(-5)/125. Let d(o) be the third derivative of -1/12*o**4 + 0 - 3*o**2 + 0*o**3 + h*o**5 + 0*o. Factor d(l).
2*l*(l - 1)
Let o(p) be the second derivative of -p**4/16 + 7*p. Find y, given that o(y) = 0.
0
Let f(a) be the second derivative of 4*a - 1/3*a**3 + 0*a**2 + 21/10*a**5 - 5/12*a**4 + 0. Find z, given that f(z) = 0.
-1/6, 0, 2/7
Let d = -122/15 - -25/3. Factor 0 + d*w + 2/5*w**2 + 1/5*w**3.
w*(w + 1)**2/5
Factor -14*w**3 - 46*w**2 + 16*w + 4*w**4 + 17*w**3 + 23*w**3.
2*w*(w - 1)*(w + 8)*(2*w - 1)
Let r(d) be the third derivative of 1/30*d**6 + 0*d + 1/3*d**3 - 1/35*d**7 - 1/4*d**4 + 4*d**2 + 1/15*d**5 + 0 + 1/168*d**8. Let r(v) = 0. What is v?
-1, 1
Suppose 3/2*r + 3/4*r**2 + 9/4*r**5 - 3/4*r**4 - 15/4*r**3 + 0 = 0. What is r?
-1, -2/3, 0, 1
Let n(r) be the second derivative of r**5/20 + 3*r**2/2 - 2*r. Let f be n(0). Determine t so that -2*t**2 + t + 4*t**2 - f*t**2 = 0.
0, 1
Let i(c) be the second derivative of -c**7/7560 - c**6/1080 - c**5/360 - c**4/12 - 2*c. Let p(x) be the third derivative of i(x). Factor p(t).
-(t + 1)**2/3
Let m = -3/44 - -25/44. Find k such that -3/4*k**3 + 1/4*k**5 + 1/4*k**4 - 1/4*k**2 + m*k + 0 = 0.
-2, -1, 0, 1
Suppose -22 - 14 = -3*r. Let n = r + -82/7. Factor 2/7*p**4 + 4/7*p**3 - 2/7*p - 4/7*p**2 - n*p**5 + 2/7.
-2*(p - 1)**3*(p + 1)**2/7
Let h(s) = 10*s**2 - 85*s + 65. Let r(u) = 5*u**2 - 43*u + 32. Let t(a) = -3*h(a) + 5*r(a). Factor t(w).
-5*(w - 7)*(w - 1)
Let y be 2/20 + 4/10. Suppose 0 = j - 2*j - i + 2, 14 = 4*j - 2*i. Find r such that -r**j - 1/2 - y*r**4 + 1/2*r + r**2 + 1/2*r**5 = 0.
-1, 1
Let f be 3/15 - (-104)/(-20). Let o = f - -5. Suppose 2/3*p**2 + o + 2/3*p**4 + 4/3*p**3 + 0*p = 0. Calculate p.
-1, 0
Let q(z) be the third derivative of z**5/20 + 3*z**4/8 + z**3 + z**2 - 10. Let q(b) = 0. Calculate b.
-2, -1
Let y(n) be the third derivative of -3*n**2 + 1/12*n**6 + 0*n + 0*n**4 + 0*n**3 + 2/15*n**5 + 1/105*n**7 + 0. Factor y(l).
2*l**2*(l + 1)*(l + 4)
Let g = -2 - -1. Let v(d) = 1. Let z(c) = 2*c**2 - 6*c - 2. Let b(a) = g*z(a) - 2*v(a). Factor b(o).
-2*o*(o - 3)
Let n = -8882/3 - -2898. Let c = -62 - n. Factor -4/3*o - 2*o**2 + c.
-2*(o + 1)*(3*o - 1)/3
Let l(b) be the first derivative of -b**3 + 3*b**2/2 + 12. Let l(r) = 0. Calculate r.
0, 1
Let k(j) be the third derivative of 0 + 1/60*j**6 + 0*j**3 + 0*j**4 + 0*j**5 + 0*j + 2*j**2. Factor k(t).
2*t**3
Let w(b) = -b**3 + b**2. Let a(j) = -3*j**4 - 29*j**3 - 67*j**2 - 96*j - 48. Let m(h) = -a(h) + 5*w(h). Determine d, given that m(d) = 0.
-2
Factor 0 + 0*f + 14/3*f**3 - 4/3*f**2.
2*f**2*(7*f - 2)/3
Let q(p) be the first derivative of -p**6/360 + p**4/24 - p**3/3 - 1. Let d(o) be the third derivative of q(o). Factor d(r).
-(r - 1)*(r + 1)
Let j(b) = -4*b - 7. Let m be j(-4). Find a such that m*a**2 - 9*a**2 - 24*a + 4*a**2 + 36 = 0.
3
Let o(y) be the first derivative of -2*y**5/55 + 4*y**3/33 - 2*y/11 + 12. Determine d so that o(d) = 0.
-1, 1
Let p be (3/(-10))/((-252)/70). Let s(m) be the first derivative of -2 + 0*m + 1/4*m**2 - p*m**3. Factor s(z).
-z*(z - 2)/4
Let c be (-42)/(-45) + (-4)/(-20)*2. Factor c*p - 2/3*p**2 - 2/3.
-2*(p - 1)**2/3
Let r(d) = -5*d**2 - 2*d + 3. Let m(n) = 6*n**2 + 3*n - 3. Let t be (36/(-24))/((-2)/4). Suppose -7 - 3 = -5*h. Let v(i) = h*m(i) + t*r(i). Factor v(u).
-3*(u - 1)*(u + 1)
Let m be 10/45 - 50/(-18). Determine a, given that a**5 + 2*a**4 - a**4 + a**2 - 2*a**4 + 3*a**m - 2*a - 2*a**5 = 0.
-2, -1, 0, 1
Let p(y) = -y**2 - y + 2. Suppose 8*k - 3*k = -10. Let f be p(k). Factor 2*w**2 - 2*w**4 - 2*w**3 + f*w**4 + 2*w**3.
-2*w**2*(w - 1)*(w + 1)
Let j(k) = -k**3 + 2*k**2 + k + 2. Suppose -3*h = -4*h + 3*o + 9, 3*o = -12. Let d(m) = m**3 - 3*m**2 - m - 3. Let i(x) = h*j(x) - 2*d(x). Factor i(t).
t*(t - 1)*(t + 1)
Let y = -178 - -713/4. Find n, given that -1/4*n**2 + 0 + y*n = 0.
0, 1
Find g such that -22*g**3 - 28*g**3 - 16*g**4 - 89*g**2 - 56*g - g**2 + 14*g**2 - 2*g**5 - 16 = 0.
-2, -1
Let i(p) = -6*p**2 - p**2 - 2*p + 10*p**2 - 1. Let x(r) = r - 1. Let m(o) = -i(o) - 5*x(o). Factor m(n).
-3*(n - 1)*(n + 2)
Let j(m) be the third derivative of 1/3*m**3 + 1/4*m**4 - 2*m**2 + 0*m + 1/10*m**5 + 0 + 1/60*m**6. Suppose j(t) = 0. What is t?
-1
Let t(b) be the second derivative of -b**5/90 + b**4/18 - 3*b. Factor t(n).
-2*n**2*(n - 3)/9
Let x(l) = -4*l - 3*l**2 + 5*l**2 + 2 - 3 - 3*l**3 + 4*l**3. Let f be x(-3). Suppose -2*m**2 - m - m**4 + 4*m**2 - 3*m**3 + f*m**4 + m**2 = 0. What is m?
0, 1
Let y(u