et x(o) be the first derivative of o**3/12 - 7*o**2/8 + 3*o/2 - 54. Determine k, given that x(k) = 0.
1, 6
Determine f so that -12*f**2 - 116*f + f**3 + 5*f**3 + 128*f - 2*f**3 - 4 = 0.
1
Let t(i) be the first derivative of 5 + 0*i - 3/4*i**4 - 2*i**3 + 0*i**2. Find u such that t(u) = 0.
-2, 0
Suppose -s - 2*s = 5*g - 19, -5*g - 2*s = -16. Let b = -5/3 + g. What is z in -1/3 - b*z**3 + 1/3*z + 1/3*z**2 = 0?
-1, 1
Suppose -1/6*q + 1/6*q**3 + 1/3 - 1/3*q**2 = 0. What is q?
-1, 1, 2
Let z be 11/(55/30) - 4. Let r(v) be the first derivative of -2 + 0*v + 2/27*v**3 - 1/9*v**z. Solve r(n) = 0 for n.
0, 1
Let r = -61/9 - -91/9. Factor 2*n**2 + 4/3 + r*n.
2*(n + 1)*(3*n + 2)/3
Let j(z) be the third derivative of -z**7/105 + z**6/60 + z**5/10 - 5*z**4/12 + 2*z**3/3 - 27*z**2. Let j(k) = 0. Calculate k.
-2, 1
Let y(i) be the first derivative of -2/15*i**3 - 2/25*i**5 - 6 + 0*i - 1/5*i**4 + 0*i**2. Find h, given that y(h) = 0.
-1, 0
Let b(v) be the second derivative of -5*v**4/12 + 5*v**3/3 - 5*v**2/2 - 11*v. Factor b(i).
-5*(i - 1)**2
Let b(z) be the second derivative of -z**5/4 + 5*z**4/6 + 5*z**3/6 - 5*z**2 + 30*z. Factor b(l).
-5*(l - 2)*(l - 1)*(l + 1)
Let m = 894 + -894. Suppose 1/4*b + b**2 + m = 0. What is b?
-1/4, 0
Suppose -44*f**2 + 6*f + 47*f**2 - 3*f**3 + 0*f**3 = 0. What is f?
-1, 0, 2
Let a = 25 - 49/2. Determine z, given that 1/2*z - z**2 + 0 + a*z**3 = 0.
0, 1
Solve -1/10*l**3 + 1/10*l**2 + 0*l + 0 = 0 for l.
0, 1
Let j(p) be the third derivative of -1/240*p**6 + 1/24*p**3 + 0*p + 0 + 0*p**4 - 3*p**2 - 1/80*p**5. Factor j(v).
-(v + 1)**2*(2*v - 1)/4
Let s = 22 - 10. Let n be ((-12)/9)/((-8)/s). Factor -1/3*q**5 + 0*q**n + 0*q**4 + 0*q**3 + 0 + 0*q.
-q**5/3
Let j(k) = -4*k**5 - 6*k**4 + 2*k**2 + 6. Let c(x) = -12*x**5 - 18*x**4 + 6*x**2 + 17. Let b(v) = -6*c(v) + 17*j(v). What is r in b(r) = 0?
-1, 0, 1/2
Let j(o) be the first derivative of o**5/40 + o**4/32 - 10. Factor j(x).
x**3*(x + 1)/8
Determine u so that 4/17*u - 14/17*u**3 + 10/17*u**2 + 0 = 0.
-2/7, 0, 1
Let b(f) be the third derivative of -f**5/210 - 2*f**4/21 - 16*f**3/21 - 11*f**2. Factor b(s).
-2*(s + 4)**2/7
Let g(r) = r**3 - r + 1. Let h(c) = 6*c**3 + 5*c**2 + 2*c + 8. Let b(t) = 15*g(t) - 3*h(t). Factor b(m).
-3*(m + 1)**2*(m + 3)
Find c, given that -15/4*c**3 + 3/4*c**5 + 3/4*c**4 + 9/4*c**2 + 0*c + 0 = 0.
-3, 0, 1
Let p = 46 - 187/4. Let z = -1/12 - p. Factor -z*n**2 + 0*n + 0.
-2*n**2/3
Let h(n) be the second derivative of n**6/20 - n**4/4 + 3*n**2/4 + 10*n. Let h(f) = 0. Calculate f.
-1, 1
Let x(k) be the third derivative of k**5/4 + 25*k**4/24 - 5*k**3/3 + 6*k**2. Let x(l) = 0. Calculate l.
-2, 1/3
Let k(u) = -10*u**2 + 3*u + 6. Let x = -10 + 0. Let s = 5 + x. Let q(l) = -7*l**2 + 2*l + 4. Let d(w) = s*k(w) + 7*q(w). Factor d(p).
(p - 2)*(p + 1)
Suppose -7*v = -9*v - 6. Let n be 0/((v - -2)*1). Determine l, given that n - l**2 - 3/2*l**5 + 0*l + l**4 + 3/2*l**3 = 0.
-1, 0, 2/3, 1
Let p(u) be the third derivative of 0*u**4 + 0 + 1/60*u**5 - 1/210*u**7 + 0*u**6 + 0*u + 0*u**3 - 3*u**2. Suppose p(s) = 0. Calculate s.
-1, 0, 1
Let i be 0 + 1 + 9/(-9). Determine g, given that 3/2*g**4 + 0*g**2 + i - 1/2*g**3 + 0*g = 0.
0, 1/3
Suppose 2*m - 6*m + 5*c - 20 = 0, -12 = -3*c. What is s in 0 - 2/9*s**2 + m*s = 0?
0
Factor -4/5*u**2 + 32/5 + 8/5*u.
-4*(u - 4)*(u + 2)/5
Let x(u) = -7*u**5 - 2*u**4 - 4*u**3 - 8*u**2 + 11*u + 4. Let g(d) = -d**5 - d**4 - d**2 + d + 1. Let l(h) = -6*g(h) + x(h). Factor l(v).
-(v - 2)*(v - 1)**3*(v + 1)
Suppose -6*p + 7 + 11 = 0. Let g be ((-4)/(-45))/(6/15). Determine f, given that 0*f**4 - g*f**5 - 2/9*f + 0*f**2 + 0 + 4/9*f**p = 0.
-1, 0, 1
Let y be ((-2)/(-6))/(24/(-252)) + 4. Find s, given that -y*s**3 + 1 - 5/2*s + 2*s**2 = 0.
1, 2
Let t be 1 - 2 - 7/(-3). Suppose 2*l + 18 = 13*j - 8*j, -5*j - 5*l = 10. Let -1/3*z**4 + 4/3*z - 2*z**j - 1/3 + t*z**3 = 0. Calculate z.
1
Let g(c) = 2*c**3 + 5*c**2 - 3. Let a(v) = v**3 + 4*v**2 - 2. Let k(d) = 3*a(d) - 2*g(d). Suppose k(n) = 0. What is n?
0, 2
Let u(b) be the third derivative of -b**8/1176 + b**6/420 - 7*b**2. Factor u(t).
-2*t**3*(t - 1)*(t + 1)/7
Let 0*x + 2*x**3 - 14/9*x**4 + 0 - 4/9*x**2 = 0. Calculate x.
0, 2/7, 1
Let n(b) = -b**5 - b**4. Let c(v) = -8*v**5 - 24*v**4 - 58*v**3 - 78*v**2 - 36*v. Let f(p) = 2*c(p) - 12*n(p). Determine k, given that f(k) = 0.
-3, -2, -1, 0
Let n(r) = 12*r**4 - 21*r**3 - 45*r**2 + 12. Let d(a) = -3*a**4 + 5*a**3 + 11*a**2 - 3. Let w be (42/4)/(3/6). Let k(f) = w*d(f) + 5*n(f). Factor k(h).
-3*(h - 1)**2*(h + 1)**2
Let a(b) = 4*b + 1. Let x(d) = d + 1. Let i(y) = -a(y) - 3*x(y). Let v be i(-4). Determine l so that -1 - 2 + v*l - 18*l**2 - 5 = 0.
2/3
Let c(h) = h**3 + 4*h**2 - 6*h - 2. Let l be c(-5). Let y(o) be the first derivative of 0*o - 1 + 1/4*o**4 + 2/3*o**l + 1/2*o**2. Find m such that y(m) = 0.
-1, 0
Suppose -4*o + 26 = 2*r, 2 = -6*o + 4*o + 4*r. Factor 0*a**4 + a**4 - a**2 + a**3 - 4*a**o + 3*a**5.
-a**2*(a - 1)**2*(a + 1)
Let g(d) be the first derivative of 2*d**7/105 - 3*d**5/100 + d**4/60 - 2*d - 3. Let r(m) be the first derivative of g(m). Let r(o) = 0. Calculate o.
-1, 0, 1/2
Factor 199*z**4 - 60*z - 63*z**3 + 16 - 193*z**4 + 78*z**2 + 23*z**3.
2*(z - 4)*(z - 1)**2*(3*z - 2)
Let s = 3 - -1. Suppose 1 + 4*p + 13*p**3 - 1 - 16*p**3 + p**s = 0. Calculate p.
-1, 0, 2
Suppose -3*j = 2*d - 25, 7*d = 5*j + 2*d. Let z(x) be the third derivative of 2/3*x**3 + 0*x - 1/3*x**4 - 1/12*x**j + 0 + x**2. Solve z(g) = 0 for g.
-2, 2/5
Factor -158*d**5 + d**3 + 0*d**3 + 157*d**5 + d**4 - d**2.
-d**2*(d - 1)**2*(d + 1)
Let h be (-1 + 3)/(4 + -3). Let l(z) = 6*z**3 + 14*z + 6 + h - 4*z. Let m(r) = -r**3 - r - 1. Let v(p) = -l(p) - 8*m(p). What is t in v(t) = 0?
-1, 0, 1
Let h(p) be the second derivative of p**5/15 + 9*p**2/2 + 4*p. Let k(i) be the first derivative of h(i). Factor k(c).
4*c**2
Let x(v) = -5*v**3 - v**2 - 2*v - 1. Let n be x(-1). Let y = -2 + n. Find z, given that z**5 + 2*z**4 - 5*z**4 + 0*z**2 - z**2 + 3*z**y = 0.
0, 1
Let t(h) be the third derivative of -1/672*h**8 + 0*h**4 + 0*h**5 + 0 + 0*h**3 + 0*h**6 + 1/420*h**7 + h**2 + 0*h. Find o, given that t(o) = 0.
0, 1
Let d(a) = -a**3 + 4*a**2 + 5*a. Let s be d(5). Suppose x = -s*x. Factor x + 2/3*h**2 + 2/3*h.
2*h*(h + 1)/3
Let i(m) be the first derivative of m**8/1344 + m**7/280 + m**6/160 + m**5/240 + m**2/2 - 1. Let c(k) be the second derivative of i(k). What is z in c(z) = 0?
-1, 0
Let p be -1*(-1413)/117 - 9. Let 36/13*o**2 - p*o**3 - 14/13*o + 2/13 + 16/13*o**4 = 0. What is o?
1/2, 1
Factor -3 - 3/8*f**3 + 3/4*f**2 + 3/2*f.
-3*(f - 2)**2*(f + 2)/8
Let g(x) = 3*x**3 + 5*x**2 + 4*x + 2. Let i(j) = -j - 1. Let v(f) = 3*g(f) + 6*i(f). Factor v(r).
3*r*(r + 1)*(3*r + 2)
Let v(u) be the first derivative of -u**8/1344 + u**7/420 - u**6/480 - u**2 - 2. Let q(n) be the second derivative of v(n). Factor q(x).
-x**3*(x - 1)**2/4
Let a = 59 + -59. Solve 0*p + a - 2/5*p**2 - 2/5*p**3 = 0 for p.
-1, 0
Let t be 6/(-21) + 459/63. Let r(d) be the second derivative of 0*d**6 + 2*d + 0*d**3 + 0*d**4 + 0*d**2 + 0 - 1/30*d**5 + 1/63*d**t. Factor r(o).
2*o**3*(o - 1)*(o + 1)/3
Let c(a) be the second derivative of -a**8/112 - a**7/35 + a**5/10 + a**4/8 - 2*a**2 - 4*a. Let z(n) be the first derivative of c(n). Find f such that z(f) = 0.
-1, 0, 1
Let h be ((0 - 1) + 0)*-61. Let i = h + -243/4. Factor 0 + 0*g**2 + 1/4*g**4 + 0*g + 0*g**3 - i*g**5.
-g**4*(g - 1)/4
Let u be 2/(2 - (-5)/(-3)). Suppose t + 2*t - 12 = 0. Factor -4*j - u*j + 18*j**3 - 5*j**2 - 7*j**2 + t.
2*(j - 1)*(3*j - 1)*(3*j + 2)
Let g be ((-6)/8)/(-1) - -2. Let y = g - 5/4. Solve -s - 1/2*s**3 - y*s**2 + 0 = 0 for s.
-2, -1, 0
Let l(m) be the first derivative of m**6/33 - 2*m**5/55 - m**4/22 + 2*m**3/33 + 1. Factor l(j).
2*j**2*(j - 1)**2*(j + 1)/11
Suppose 5*a - 142 = 2*w + 5, 0 = 3*a - 3*w - 90. Let l = 31 - a. Determine d, given that 0 - 2/3*d + 2/3*d**l = 0.
0, 1
Let k(h) be the third derivative of 0 + 0*h - 8/3*h**4 - 5/24*h**6 - 19/12*h**5 - 2*h**3 + 2*h**2. Find y, given that k(y) = 0.
-3, -2/5
Let i(n) = n**2 - 4*n + 1. Let x(h) = h**3 - h**2 + h + 1. Let f = -3 + 2. Let g(j) = f*x(j) - i(j). Suppose g(m) = 0. Calculate m.
-2, 1
Suppose 2*a + 41 = 5*k, 28 = 5*k + 3*a + 2. Let j = k - 4. Suppose -2/5*n + 0 + 4/5*n**4 - 4/5*n**2 + 2/5*n**j = 0. Wha