etermine c so that 4*c**3 - 2*c**4 + 2*c**2 + 0*c**3 + k*c**5 - 6*c**3 = 0.
-1, 0, 1
Find a such that -a**3 - 67*a - 2 + 0*a**3 + 70*a = 0.
-2, 1
Let p(k) = -k**2 + 9*k - 18. Let t be p(3). Find b, given that -6/5*b**2 + 0*b + 3/5*b**3 + t = 0.
0, 2
Factor 2/3*v**3 - 4*v + 0 + 10/3*v**2.
2*v*(v - 1)*(v + 6)/3
Let u = -1 + 1. Let s(v) be the third derivative of -4*v**2 + u*v**3 + 1/60*v**4 - 1/150*v**5 + 0 + 0*v. Find c, given that s(c) = 0.
0, 1
Let i be 2/8 + 1/(-4). Let a(f) be the second derivative of -5/48*f**4 - 1/4*f**2 + i - 7/24*f**3 + f. Factor a(s).
-(s + 1)*(5*s + 2)/4
Let h be ((-28)/(-12))/7 + (-2)/24. Let o be -2*-1*(-1)/(-4). Factor -o*i + 1/4 + h*i**2.
(i - 1)**2/4
Let c(x) be the third derivative of 0*x + 0*x**3 + 3/80*x**5 + 0 + 1/40*x**6 - 2*x**2 + 1/168*x**7 + 1/48*x**4. Suppose c(q) = 0. Calculate q.
-1, -2/5, 0
Factor -5*p**2 + 0 + 43*p**3 - 41*p**3 - 2 + 4*p + 1.
(p - 1)**2*(2*p - 1)
Factor -40 - 49*x**2 - 260*x - 210*x**2 + 245*x**3 - 91*x**2.
5*(x - 2)*(7*x + 2)**2
Let z(m) be the second derivative of m**4/6 - m**3/6 - m**2/2 - 5*m + 1. Factor z(u).
(u - 1)*(2*u + 1)
Let q be 18/4 + 1/(-2). Let o be (-18)/(-4)*8/q. Solve 4*c + 6*c - 3*c**3 + 5*c - 2*c**4 - c**4 + o*c**2 + 6 = 0 for c.
-1, 2
Let b(s) be the second derivative of s + 0*s**3 + 1/48*s**4 + 0*s**2 + 0 - 1/80*s**5. Factor b(g).
-g**2*(g - 1)/4
Suppose 2*b + 2*c + 4 = 20, 4*b - 2*c - 2 = 0. Let n(f) be the third derivative of -1/27*f**b - 1/54*f**4 + 0 - 3*f**2 + 0*f - 1/270*f**5. Factor n(r).
-2*(r + 1)**2/9
Let x(b) be the first derivative of 1/4*b**3 + 0*b - 1 + 1/8*b**2. Factor x(p).
p*(3*p + 1)/4
Let i(h) be the second derivative of -h**6/6 - 4*h**5 - 65*h**4/2 - 280*h**3/3 - 245*h**2/2 + 2*h + 25. Find n, given that i(n) = 0.
-7, -1
Factor -3/7*y**3 + 3/7*y**4 + 0 + 3/7*y - 3/7*y**2.
3*y*(y - 1)**2*(y + 1)/7
Factor 2/9*t**2 + 0 + 0*t.
2*t**2/9
Let h = -1599/7 - -229. Determine p so that -2/7 - h*p + 0*p**2 + 2/7*p**4 + 4/7*p**3 = 0.
-1, 1
Factor 4/9*p**2 - 4/9 + 10/9*p - 10/9*p**3.
-2*(p - 1)*(p + 1)*(5*p - 2)/9
Let a(k) be the second derivative of 0*k**2 + 3*k - 1/110*k**5 + 1/66*k**4 - 1/165*k**6 + 0 + 1/33*k**3. Factor a(m).
-2*m*(m - 1)*(m + 1)**2/11
Factor 8*a**2 - 9*a**3 + 26*a**4 - 23*a**4 - 2*a**2.
3*a**2*(a - 2)*(a - 1)
Let m = -6 + 4. Let k = 7 + m. Factor -2*o - 51*o**4 - 22*o - 3 - 2*o**k - 84*o**3 - 10*o**5 - 66*o**2.
-3*(o + 1)**4*(4*o + 1)
Let c be (-2)/(-10) + 124/(-20). Let u be (c/(-15))/((-12)/(-15)). Factor -u*g + 0 + 1/2*g**2.
g*(g - 1)/2
Let r = 255 - 250. Let -3/2*i**2 + 9/4*i**4 + 9/4*i - 3/4 - 3/2*i**3 - 3/4*i**r = 0. What is i?
-1, 1
Let k = 149/3 + -49. Let d(s) = s**2 + 13*s + 15. Let p be d(-12). Factor 2/3*q + 2/3*q**2 - k*q**p - 2/3*q**4 + 0.
-2*q*(q - 1)*(q + 1)**2/3
Let x = -476/9 + 2398/45. Suppose -x*u**4 - 4/5*u + 0*u**3 + 0 + 6/5*u**2 = 0. What is u?
-2, 0, 1
Let q be -8*3*(-16)/(-90). Let o = q + 794/165. Find g such that 2/11*g**2 + 4/11 - o*g = 0.
1, 2
Let k be 6/14 + 116/7. Suppose -z = -2*h + 8, 2*h - k = -z - 1. Suppose -1 + 5 + h*r + 0*r + 2*r**2 = 0. Calculate r.
-2, -1
Let t be 24/4*(-4)/(-6). Factor j**2 - 4*j**2 + t*j**2 - j**4.
-j**2*(j - 1)*(j + 1)
Let i = -6 - -8. Let a be 3/(-9)*0/i. Factor 0 + 1/3*c**2 + a*c + 1/3*c**3.
c**2*(c + 1)/3
Let j(s) be the third derivative of s**7/70 - s**6/40 - 3*s**5/20 + s**4/8 + s**3 + 8*s**2. Factor j(i).
3*(i - 2)*(i - 1)*(i + 1)**2
Let f(d) be the third derivative of d**6/300 + 2*d**5/75 - 11*d**4/60 + 2*d**3/5 + 7*d**2. Solve f(g) = 0.
-6, 1
Let a(w) be the first derivative of -9/5*w**5 + 3*w + 1/2*w**6 - 2 + 3/2*w**4 - 9/2*w**2 + 2*w**3. Factor a(y).
3*(y - 1)**4*(y + 1)
Let i(g) be the first derivative of -4/7*g + 2/21*g**3 + 3 + 1/7*g**2. Factor i(s).
2*(s - 1)*(s + 2)/7
Let d = 10 - 4. Suppose -b + 3*b = d. Factor 0*j**3 + 2*j**b - j**3 + 3*j**2 + j - j**2.
j*(j + 1)**2
Let i(o) be the third derivative of o**5/60 + o**4/8 + 2*o**2. Let l(v) = -5*v**2 - 13*v. Let s(f) = -9*i(f) - 2*l(f). What is w in s(w) = 0?
0, 1
Let b = 25/18 - 8/9. Determine z, given that -7/4*z**4 + b*z + 0 - 3/4*z**2 - 3*z**3 = 0.
-1, 0, 2/7
Let z = -9 + 10. Let k = z + 2. Factor -2*j**2 + 3*j**k - j + 4*j**5 + 3*j**3 - 5*j**5 + 1 - 4*j**3 + j**4.
-(j - 1)**3*(j + 1)**2
Let j(m) be the second derivative of -m**5/10 - 2*m**4/3 - 4*m**3/3 + m. Factor j(w).
-2*w*(w + 2)**2
Let n = -21 + 10. Let t(y) = y**2 + 12*y + 11. Let b be t(n). Factor b + 5/3*f**3 - f**2 - 2/3*f.
f*(f - 1)*(5*f + 2)/3
Let r(b) be the second derivative of -5*b**6/6 + 3*b**5 + 5*b**4/12 - 10*b**3 + 10*b**2 - 9*b. Let r(y) = 0. Calculate y.
-1, 2/5, 1, 2
Let r be (-38)/14*1 + (-60)/(-20). Solve -8/7*t - r*t**2 - 8/7 = 0 for t.
-2
Let o(p) = 13*p - 3. Let k be o(3). Let f = -21 + k. Factor 66*r**4 + 39*r - 1 + 1 + f*r**5 + 6 + 114*r**3 + 96*r**2.
3*(r + 1)**4*(5*r + 2)
Let c be (-5223)/1269 + 36/9. Let r = 5/47 - c. Factor -r*b + 0 + 2/9*b**3 + 2/9*b**4 - 2/9*b**2.
2*b*(b - 1)*(b + 1)**2/9
Factor -2/3 - 10/9*l**2 + 14/9*l + 2/9*l**3.
2*(l - 3)*(l - 1)**2/9
Let j(t) be the first derivative of -5*t**3 - 6*t**2 + 3*t - 5. Factor j(q).
-3*(q + 1)*(5*q - 1)
Let y(n) be the second derivative of -7*n**6/60 - 2*n**5/5 - 11*n**4/24 - n**3/6 - 4*n. Determine q so that y(q) = 0.
-1, -2/7, 0
Let m(d) = -2*d + 1. Let y be m(-3). Let k(g) = -6*g**3 - 22*g**2 - 5*g - 10. Let j(n) = 4*n**3 + 15*n**2 + 3*n + 7. Let q(s) = y*j(s) + 5*k(s). Factor q(o).
-(o + 1)**2*(2*o + 1)
Let v(p) be the first derivative of 2*p**5/35 - p**4/7 + 2*p**3/21 + 12. Find d, given that v(d) = 0.
0, 1
Let u = -5 - 1. Let i(s) = s - 1. Let c(n) = -2*n**2 + 10*n - 6. Let m = 34 - 33. Let f(b) = m*c(b) + u*i(b). Factor f(j).
-2*j*(j - 2)
Suppose 4*g = -5*d + 26, 2*d = 2*g - 7*g + 7. Factor 4*f**2 + f**4 - 2*f + f**4 - d*f**3 + 2*f**2.
2*f*(f - 1)**3
Let c(i) = -5*i**2 - 7*i - 8. Let g(b) be the first derivative of 4*b**3/3 + 3*b**2 + 7*b - 2. Let x(w) = -5*c(w) - 6*g(w). What is r in x(r) = 0?
-1, 2
Let s(g) be the second derivative of 5*g**7/252 + 3*g**6/20 + g**5/3 - g**4/9 - 4*g**3/3 - 4*g**2/3 + 8*g. Let s(q) = 0. Calculate q.
-2, -2/5, 1
Let a(i) be the third derivative of i**7/1260 - i**6/90 + i**5/15 - 2*i**4/9 + 4*i**3/9 - 27*i**2. Find u, given that a(u) = 0.
2
Let c(k) be the third derivative of 2*k**2 + 0*k + 0*k**3 + 0 - 1/210*k**5 - 1/84*k**4. Determine l, given that c(l) = 0.
-1, 0
Factor -4/7*q - 6/7 + 2/7*q**2.
2*(q - 3)*(q + 1)/7
Let w be 14/8*(-10)/(-35). Let s(g) be the first derivative of -w*g**3 - 5/8*g**2 + 1/8*g**6 - 1/4*g + 1/8*g**4 + 7/20*g**5 - 1. Factor s(y).
(y - 1)*(y + 1)**3*(3*y + 1)/4
Let f be (-6 - -4) + 0 + 6. Suppose 6*t**f + t**3 + 2*t**5 + 2*t**2 + 5*t**3 + 0*t**3 = 0. What is t?
-1, 0
Let a(u) be the first derivative of u**4/14 + 2*u**3/7 - u**2/7 - 6*u/7 + 27. Factor a(l).
2*(l - 1)*(l + 1)*(l + 3)/7
Suppose -5*t + 2*v = 7*v - 10, 3*v = t - 6. Suppose 11*m**5 + 16*m**t + 8*m**2 - 8*m**4 - 36*m**3 + 9*m**5 = 0. What is m?
-1, 0, 2/5, 1
Suppose 4*t + t = 2*v - 1, -3*v - 4*t = -13. Suppose -2*r = -v*r + 2. Factor -2*j**2 - 2*j + 2 + 4*j + r.
-2*(j - 2)*(j + 1)
Let v(n) = -2 - 1 - 4 + 3*n - 4*n. Let p be v(-10). Let 0*z + 0*z**p + 0 - 6/5*z**4 - 4/5*z**5 + 2/5*z**2 = 0. Calculate z.
-1, 0, 1/2
Let b(n) = 3*n**2 + 1. Suppose 0 = -3*q + 7*q - 4. Let z be b(q). Factor -2 + a - 4*a - 5*a**2 - z*a.
-(a + 1)*(5*a + 2)
Let w(o) be the third derivative of -o**7/10 - o**6/20 + 7*o**5/20 + o**4/4 + 33*o**2. Suppose w(g) = 0. What is g?
-1, -2/7, 0, 1
Let y = 169/5 - 33. Solve -4/5 + y*m - 1/5*m**2 = 0.
2
Let b(d) be the second derivative of -d**5/110 + d**3/33 + 2*d. Suppose b(w) = 0. Calculate w.
-1, 0, 1
Let g(w) be the second derivative of 1/2*w**2 - 1/15*w**3 + 1/150*w**5 - 1/300*w**6 + 1/60*w**4 + w + 0. Let h(n) be the first derivative of g(n). Factor h(z).
-2*(z - 1)**2*(z + 1)/5
Let x(d) = -d**2 + 9*d + 2. Let y be x(9). Factor -3 + 5*a**y - a**2 + 7 - 8*a.
4*(a - 1)**2
Let y(l) be the first derivative of -2/9*l**3 + 2 + 0*l + 1/3*l**2. Factor y(x).
-2*x*(x - 1)/3
Let f = 7 - 9. Let n be -5 + 6 - f/(-2). Factor n + 1/4*t**2 - 1/2*t.
t*(t - 2)/4
Let a(r) be the second derivative of r**8/504 + 2*r**7/315 - r**5/45 - r**4/36 + 3*r**2/2 - r. Let s(f) be the first derivative of a(f). Factor s(y).
2*y*(y - 1)*(y + 1)**3/3
Let w = -1208/3