j + 2*j**2 - h*j - 2*j**3 = 0.
-1/3, 0, 1
Let a = 38 - 36. Let r be (-5)/a*16/(-50). What is k in r*k**2 + 2*k + 4/5 = 0?
-2, -1/2
Let m(c) be the first derivative of 0*c**2 + 0*c - 1/30*c**5 + 1/12*c**4 + 3 - 1/18*c**3. Factor m(v).
-v**2*(v - 1)**2/6
Let z(a) be the first derivative of -a**5/140 - a**4/7 - 8*a**3/7 + 3*a**2/2 - 3. Let m(d) be the second derivative of z(d). Find k, given that m(k) = 0.
-4
Let g(z) be the second derivative of z**7/1120 + z**6/240 - z**5/160 - z**4/16 + z**3 - z. Let j(h) be the second derivative of g(h). Factor j(y).
3*(y - 1)*(y + 1)*(y + 2)/4
Find p, given that 46*p**3 - 3*p**4 - 100*p**2 - p**4 - 86*p**3 = 0.
-5, 0
Let h(x) be the second derivative of x**4/12 - x**3/3 + 5*x**2/2 + x. Let k(f) = -f**2 + 2*f - 6. Let s = -9 + 13. Let u(n) = s*k(n) + 5*h(n). Factor u(v).
(v - 1)**2
Determine p so that p**4 + 15*p**3 - 1/2*p + 14*p**2 - 3 - 5/2*p**5 = 0.
-1, 2/5, 3
Suppose -19*i**2 - 1/2*i**5 - 4*i**4 - 25/2*i**3 - 14*i - 4 = 0. What is i?
-2, -1
Let a = 48/35 - 2557/1890. Let v(u) be the second derivative of 0*u**3 + u + 1/9*u**2 + 0 - a*u**4. Find j such that v(j) = 0.
-1, 1
Let v(a) be the first derivative of 0*a**3 - 3/5*a**5 + 9 + 3*a - 3*a**2 + 3/2*a**4. Factor v(n).
-3*(n - 1)**3*(n + 1)
Suppose -f + 5*b = 6 - 0, 14 = 4*f - b. Suppose 0 = 3*h + 5*g - 4, -f*h + 4*g = h - 19. Factor -2*t**5 - 3*t + 3*t + 2*t**h - 2*t**2 + 2*t**4.
-2*t**2*(t - 1)**2*(t + 1)
Factor 5/4 + 33/8*z - 7/8*z**2.
-(z - 5)*(7*z + 2)/8
Let k(i) be the first derivative of -3*i**4/16 - i**3/4 - 1. Factor k(j).
-3*j**2*(j + 1)/4
Let r(m) be the third derivative of -m**8/1008 + m**7/315 - m**5/90 + m**4/72 + 3*m**2. Factor r(o).
-o*(o - 1)**3*(o + 1)/3
Factor 9*h + 6*h - 5*h**3 + 45 - 55.
-5*(h - 1)**2*(h + 2)
Let t = 8 - 8. Suppose t*z = -3*z. Suppose 4/3*x**3 + z + 0*x**2 - 2/3*x + 0*x**4 - 2/3*x**5 = 0. What is x?
-1, 0, 1
Let a(f) = -f**2 + f + 1. Let r(b) = -4*b + 8. Let d(l) = 4*a(l) - r(l). Determine i, given that d(i) = 0.
1
Let q(v) be the second derivative of 0 + 5/24*v**4 + 0*v**2 - 1/6*v**3 + 1/60*v**6 - 2*v - 1/10*v**5. Factor q(m).
m*(m - 2)*(m - 1)**2/2
Let h(r) = -20*r**4 + 25*r**3 - 10*r**2 - 25*r - 20. Let w(p) = p**4 - p**3 + p + 1. Let c(m) = h(m) + 25*w(m). Find t such that c(t) = 0.
-1, 1
Let z(f) be the second derivative of f**7/14 - f**6/5 + f**4/2 - f**3/2 - 7*f. Factor z(j).
3*j*(j - 1)**3*(j + 1)
Let g be 3/(-5) + 5/(-900)*-109. Let h(c) be the third derivative of 0 + 1/630*c**7 + 0*c + 0*c**5 - g*c**6 + c**2 + 1/36*c**4 - 1/18*c**3. Factor h(y).
(y - 1)**3*(y + 1)/3
Factor -6*k**4 + 9*k**4 - 3*k**2 - 3*k + k**3 + 2*k**3.
3*k*(k - 1)*(k + 1)**2
Factor 0 - 2/5*v - 2/5*v**4 - 6/5*v**3 - 6/5*v**2.
-2*v*(v + 1)**3/5
Let i(a) = -2*a - 1. Suppose -6*j + j - 10 = 0. Let l be i(j). Solve t**2 - 2*t**l + 3*t**3 - 2*t**2 = 0.
0, 1
Factor 0*u + 8/3*u**2 + 0 + 1/3*u**5 + 2*u**4 + 4*u**3.
u**2*(u + 2)**3/3
Let h(g) be the first derivative of 1/2*g**2 - 3 + 0*g + 0*g**3 - 1/4*g**4. Factor h(q).
-q*(q - 1)*(q + 1)
Let m(t) be the second derivative of 0 + 0*t**2 - 6*t + 3/20*t**5 - 1/14*t**7 + 0*t**6 + 0*t**4 + 0*t**3. Factor m(u).
-3*u**3*(u - 1)*(u + 1)
Let m(q) be the first derivative of -1/6*q**2 + 2 + q - 1/36*q**4 + 1/9*q**3. Let w(u) be the first derivative of m(u). Factor w(k).
-(k - 1)**2/3
Let l(y) be the third derivative of -1/180*y**5 + 0*y + 0*y**4 + 0*y**3 + 2*y**2 + 0. Suppose l(x) = 0. Calculate x.
0
Factor -27/2 - 3/2*m**2 + 9*m.
-3*(m - 3)**2/2
Let p(u) = 32*u**3 - 175*u**2 + 231*u + 81. Let j(d) = -8*d**3 + 44*d**2 - 58*d - 20. Let z(v) = -9*j(v) - 2*p(v). Suppose z(l) = 0. What is l?
-1/4, 3
Let p(q) be the third derivative of 1/70*q**7 + 3/40*q**6 + 3*q**2 - 1/112*q**8 + 0 + 0*q + 0*q**3 - 1/20*q**5 - 1/4*q**4. Determine z so that p(z) = 0.
-1, 0, 1, 2
Find w, given that -8/7 - 2/7*w**3 + 2/7*w + 8/7*w**2 = 0.
-1, 1, 4
Suppose -36 = -6*m - 24. Solve 0*z**4 - 2/11*z**3 + 2/11*z**5 + 0 + 0*z**m + 0*z = 0.
-1, 0, 1
Let s(j) be the first derivative of -2/27*j**3 + 5 - 4/9*j + 1/3*j**2. What is i in s(i) = 0?
1, 2
Let r be 0 + (-3 - -5 - -3). Suppose d + r = 3*x, -7*d = -3*d - 2*x. Factor 0*h**3 + h - 2*h**3 + h**4 + h - d + 0*h**4.
(h - 1)**3*(h + 1)
Let q = 25 + -17. Let a be (q/(-10))/((-1)/5). Factor -4/7*r**2 + 2/7*r + 4/7*r**a + 0*r**3 + 0 - 2/7*r**5.
-2*r*(r - 1)**3*(r + 1)/7
Let u = 44 + -171/4. Let l(w) be the first derivative of -2 + 1/2*w**2 + u*w**4 - 8/3*w**3 + 2*w. Let l(c) = 0. What is c?
-2/5, 1
Let x(g) be the first derivative of g**3 + 0*g**2 - 4 + 3/2*g**4 + 0*g + 3/5*g**5. Suppose x(m) = 0. What is m?
-1, 0
Let b(k) = k**3 - 9*k**2 + 7*k + 8. Let u be b(8). Factor -2/3*a**2 + u + 1/3*a + 1/3*a**3.
a*(a - 1)**2/3
Let x(k) be the first derivative of 0*k**5 + 0*k - 2 + 0*k**3 + 0*k**2 + 1/10*k**4 - 1/15*k**6. Determine i, given that x(i) = 0.
-1, 0, 1
Determine p, given that 0 + 3/5*p**2 - 24/5*p = 0.
0, 8
Let b = -2/22963 + -1676033/3054079. Let j = -5/19 - b. Factor 0*v**2 + 0 - j*v + 2/7*v**3.
2*v*(v - 1)*(v + 1)/7
Suppose 0*f - 4*j - 26 = -3*f, -2*j = 10. Let x(o) be the first derivative of 17/18*o**4 - 32/27*o**3 - 2 + 0*o + 4/9*o**f - 2/9*o**5. What is h in x(h) = 0?
0, 2/5, 1, 2
Let p(m) be the second derivative of -2/135*m**6 + 1/189*m**7 + 0*m**5 + 1/27*m**4 - 5*m + 0*m**2 + 0 - 1/27*m**3. Let p(x) = 0. What is x?
-1, 0, 1
Let s be 1/(2*5/10). Let o(j) be the first derivative of -1/5*j**4 + 2/5*j**2 + 0*j**3 - 2/25*j**5 + 2/5*j + s. What is a in o(a) = 0?
-1, 1
Let u be ((-8)/20)/((-6)/5). Suppose u + 1/3*h**2 - 2/3*h = 0. What is h?
1
Suppose 5*a - 4 = 2*i, 3*a - 21*i - 18 = -25*i. Factor -8/5 - 2/5*y**a + 8/5*y.
-2*(y - 2)**2/5
Suppose 4 - 28 = -4*t. Let r(l) be the first derivative of l**2 - 2*l - 1 - 2/5*l**5 + 4/3*l**3 + 1/3*l**t - l**4. Suppose r(g) = 0. Calculate g.
-1, 1
Let x = -12 - 28. Let v = -4 - x. Factor -32 + 448*j**3 + 8*j**4 - 624*j**2 - 77*j**4 - v*j**4 + 7*j**4 + 256*j.
-2*(j - 2)**2*(7*j - 2)**2
Factor 4*x - 3*x**2 - 4/3.
-(3*x - 2)**2/3
Let l be (-128)/10*12/(-144). Let b = l + -2/3. Solve -b*y**2 + 0*y + 2/5 = 0 for y.
-1, 1
Let v(f) be the first derivative of 36*f**5/5 + 3*f**4 - 5*f**3 - 3*f**2 - 3. Find t such that v(t) = 0.
-1/2, 0, 2/3
Suppose -5*m - 10 = -0*m. Let u be (-3)/(9/(-1)) - m. Factor -2/3 + u*a + 3*a**2.
(a + 1)*(9*a - 2)/3
Let p(z) be the second derivative of 1/3*z**3 + 2*z + 0 + 0*z**2 - 1/4*z**4. Determine q so that p(q) = 0.
0, 2/3
Let t(y) be the first derivative of y**7/14 - y**6/5 + y**4/2 - y**3/2 + y - 3. Let v(r) be the first derivative of t(r). Suppose v(u) = 0. What is u?
-1, 0, 1
Let c(q) be the second derivative of -q**7/840 + q**6/120 - q**4/6 - 2*q. Let k(y) be the third derivative of c(y). Factor k(t).
-3*t*(t - 2)
Suppose -5 = -g + 2*i, -33 = -4*g - 0*g - 5*i. Let x(y) = -y + 7. Let t be x(5). Suppose 1 + 49/4*p**t - g*p = 0. Calculate p.
2/7
Let i = 11803/12 + -983. Let z(o) be the second derivative of 3/2*o**3 - i*o**4 + o - o**2 + 0. Solve z(t) = 0.
2/7, 1
Let q = -1447 + 7261/5. Factor -8/5 - 2/5*p**4 - 24/5*p - q*p**2 - 12/5*p**3.
-2*(p + 1)**2*(p + 2)**2/5
Let d(z) = -z**2 - 7*z + 12. Let o be d(-8). Suppose p + 4*p = o*h + 18, -4*p = 4*h. Let -2/5*t**4 - 4/5*t**3 + 0*t**p + 2/5 + 4/5*t = 0. What is t?
-1, 1
Suppose 0 = -5*l - 5*q + 5, 0*l = l - 3*q - 9. Factor 3/2*b - 3/2*b**2 + l.
-3*(b - 2)*(b + 1)/2
Let n(w) be the second derivative of -w**7/945 + w**5/90 - w**4/54 + w**2 + 2*w. Let f(c) be the first derivative of n(c). Find s such that f(s) = 0.
-2, 0, 1
Let b(c) = -4*c**3 - 6*c**2 - 2*c + 5. Suppose -l + 0*l + 4 = 0. Let o(w) = -3*w**3 - 5*w**2 - 2*w + 4. Let q(h) = l*b(h) - 5*o(h). Factor q(m).
-m*(m - 2)*(m + 1)
Suppose 2*x + 9 = 5*x. Suppose -4*z + x*i = -26, 2*i - 1 = 4*z - 25. Solve -30*f**3 - 33*f - 14*f**z - 38*f**4 + 4 - 2*f**2 - 4 + 37*f = 0 for f.
-1, 0, 2/7
Suppose 10*c - 8*c = 2. Let m(z) be the first derivative of -2*z - c + 2/3*z**3 + 0*z**2. Factor m(j).
2*(j - 1)*(j + 1)
Let f(p) = -p**2 + 4*p. Let z be f(4). Let o(l) be the first derivative of z*l - 1/16*l**4 + 2 - 1/8*l**2 - 1/6*l**3. What is a in o(a) = 0?
-1, 0
Suppose -v - 16 = -2*v. Factor t**5 - 4*t**2 + 5*t**5 + 10*t**3 + 4*t**3 - v*t**4.
2*t**2*(t - 1)**2*(3*t - 2)
Let p = -1 - -4. Let z(k) = 57*k**3 + 111*k**2 + 75*k + 13. Let h(n) = -1