 1/4*g**2 + 0 + z*g = 0.
-1, 0
Let p(a) be the third derivative of -a**7/315 + a**5/30 + a**4/18 + 27*a**2. Factor p(h).
-2*h*(h - 2)*(h + 1)**2/3
Let r(f) be the first derivative of -f**6/120 - f**5/30 - f**4/24 + f**2/2 - 5. Let b(z) be the second derivative of r(z). Factor b(o).
-o*(o + 1)**2
Let l(x) = -x**2 + 13*x - 12. Let g be ((-12)/5)/((-2)/10). Let z be l(g). Determine i, given that 0 + z*i + 1/5*i**2 = 0.
0
Let y(z) = -9*z**3 + 12*z**2 - 31*z + 16. Let m(x) = -4*x**3 + 6*x**2 - 15*x + 8. Let p(l) = -7*m(l) + 3*y(l). Factor p(s).
(s - 2)**3
Let n = -19 - -19. Let q(d) be the first derivative of 5/3*d**3 - 3 + 1/5*d**5 + d**4 + d**2 + n*d. Factor q(m).
m*(m + 1)**2*(m + 2)
Let a be 2/6 - (-8)/3. Suppose q - 3*q + 2*t = -6, 0 = -a*t - 3. Determine g so that 0 - 2/3*g**q + 2/3*g = 0.
0, 1
Let h(z) be the third derivative of -z**8/504 - z**7/315 + z**6/90 + z**5/45 - z**4/36 - z**3/9 - 5*z**2. Factor h(s).
-2*(s - 1)**2*(s + 1)**3/3
Let w = 4 - 2. Let r(t) be the third derivative of 0*t + 0*t**3 - 1/150*t**5 + 1/60*t**4 + 0 - w*t**2. Factor r(s).
-2*s*(s - 1)/5
Let w be 0 + -2 + (-4)/(-1). Let 5*l**3 - w*l + 0*l - 2*l**3 - l = 0. Calculate l.
-1, 0, 1
Let y(a) be the second derivative of -1/4*a**4 + 5*a + 0 + 4*a**3 - 24*a**2. Determine n, given that y(n) = 0.
4
Let g be (12/(-5))/(-6 - -4). Let y be 4/(-3)*(-9)/30. Suppose -18/5*i**3 - y + 2*i - g*i**2 = 0. What is i?
-1, 1/3
Let b(t) be the first derivative of -3*t**5 - 11*t**4/2 + 3*t**2 - t - 13. Solve b(w) = 0.
-1, 1/5, 1/3
Suppose -6*d + 2*d = 3*j + 7, 4*j - 32 = 5*d. Determine s, given that -2/7*s**j + 1/7*s**2 + 0*s + 0 + 1/7*s**4 = 0.
0, 1
Let j(x) be the third derivative of -x**6/60 + x**5/30 + x**4/12 - x**3/3 + 2*x**2. Factor j(v).
-2*(v - 1)**2*(v + 1)
Let f = -63 - -68. Let w(x) be the second derivative of 0*x**2 + 0*x**3 + 1/21*x**7 - 1/5*x**6 - 1/6*x**4 + 3/10*x**f + 0 - x. Factor w(a).
2*a**2*(a - 1)**3
Let r(f) be the third derivative of f**6/30 - 2*f**4/3 - 33*f**2. Determine n, given that r(n) = 0.
-2, 0, 2
Let o = 133 + -133. Factor -1/2 - p + 1/2*p**4 + p**3 + o*p**2.
(p - 1)*(p + 1)**3/2
Suppose -4*o - 5 + 13 = 0. Factor 4/11*v + 2/11 + 2/11*v**o.
2*(v + 1)**2/11
Let f = 3/56 + 321/280. Suppose -5*h + 16 = -9. Factor 3/5*y + 0*y**4 + 3/5*y**h + 0 + 0*y**2 - f*y**3.
3*y*(y - 1)**2*(y + 1)**2/5
Let o = -12 + 12. Solve 1/2*y**3 + 0*y**2 + o - 1/2*y = 0.
-1, 0, 1
Let j(w) = 11*w**2 - 4*w. Let z(u) = 2*u + 0*u**2 - 7*u**2 + 2*u**2. Let x(v) = -6*j(v) - 13*z(v). Factor x(c).
-c*(c + 2)
Suppose -t = l - 2, -t - 5*l - 2 = -8. Let n be t/(-5) + 2/10. Factor -2/7 + 2/7*y**2 + n*y.
2*(y - 1)*(y + 1)/7
Let l(v) = -4*v**2 + 2. Let r(n) = 12 - n**2 - n**4 - 9 - 4*n**2. Let u(i) = 3*l(i) - 2*r(i). Factor u(y).
2*y**2*(y - 1)*(y + 1)
What is s in 0*s + 9/8 - 1/8*s**2 = 0?
-3, 3
Let r = 157/145 - 14/29. Let b(v) be the first derivative of 3*v**2 - 2*v**6 - 4 - 11*v**3 + r*v**5 + 0*v + 9*v**4. Suppose b(x) = 0. Calculate x.
-2, 0, 1/4, 1
Let g(u) = -2*u**3 - 44*u**2 + 100*u + 152. Let v(p) = -9*p**3 - 219*p**2 + 501*p + 759. Let z(h) = 24*g(h) - 5*v(h). Let z(i) = 0. What is i?
-1, 7
Let u be -23 + 21 - ((-20)/6 + 0). Let p be (-6)/9*-3*1. Factor -u*i**2 + 0 - 4/3*i**4 - 1/3*i - 1/3*i**5 - p*i**3.
-i*(i + 1)**4/3
Let k(x) = -x**5 + 20*x**4 - 32*x**3 + 19*x**2 + 3*x - 3. Let o(n) = -n**5 - n**2 - n + 1. Let h(v) = k(v) + 3*o(v). Determine d so that h(d) = 0.
0, 1, 2
Let t(k) = 4*k**3 - 2. Let r(x) be the first derivative of x**5/5 + x**4/4 + x**3/3 - x**2/2 + 1. Let w(a) = -6*r(a) - 2*t(a). Factor w(j).
-2*(j + 1)**3*(3*j - 2)
Let g(m) be the first derivative of m**6/18 - m**5/15 - m**4/12 + m**3/9 + 4. Suppose g(v) = 0. What is v?
-1, 0, 1
Let c(m) be the first derivative of -2*m**5/5 - m**4 + 2*m**3 + 4*m**2 - 8*m + 12. Factor c(q).
-2*(q - 1)**2*(q + 2)**2
Suppose -z**2 + 4/3 - 4/3*z = 0. Calculate z.
-2, 2/3
Let d(u) = -u**2 - 9*u - 10. Let v be d(-7). Factor -3*r + r**4 + 4*r**3 - r**2 + v*r - 6*r**3 + r.
r*(r - 2)*(r - 1)*(r + 1)
Solve -2*q**4 - 2*q**4 + 8*q**4 + 6*q**3 - 10*q**3 = 0.
0, 1
Let 2/7*o**3 + 0 - 2/7*o**2 - 4/7*o = 0. Calculate o.
-1, 0, 2
Let f(q) be the second derivative of -1/3*q**2 - 1/36*q**4 + 0 - 2*q - 1/6*q**3. Factor f(d).
-(d + 1)*(d + 2)/3
Let z = 274 - 271. Factor -1 - 1/2*f**z + f**2 + 1/2*f.
-(f - 2)*(f - 1)*(f + 1)/2
Let l(a) = a**3 - 4*a**2 + 2*a + 5. Let b be l(3). Factor -2/11 + 0*q**b + 2/11*q**4 + 4/11*q**3 - 4/11*q.
2*(q - 1)*(q + 1)**3/11
Let j(m) be the third derivative of 0*m - 2/3*m**3 - 2*m**2 + 0*m**5 - 1/1440*m**6 + 0 + 1/96*m**4. Let s(a) be the first derivative of j(a). Factor s(n).
-(n - 1)*(n + 1)/4
Let f(m) be the first derivative of m**6/5 + 2*m**5/5 - m**4/3 - 4*m**3/3 - m**2 - m - 2. Let d(t) be the first derivative of f(t). Find c, given that d(c) = 0.
-1, -1/3, 1
Let m be (216/180)/(2/((-20)/(-9))). Solve -10/3*l**5 + 0*l**2 - 14/3*l**4 + 0*l + 0 - m*l**3 = 0.
-1, -2/5, 0
Suppose 5*x - 7*x = -8. Suppose -r + 10 = 3*r - 5*k, -8 = 3*r + x*k. Factor -2/7*w + r + 6/7*w**2 - 6/7*w**3 + 2/7*w**4.
2*w*(w - 1)**3/7
Suppose 3*z = 4*z - 2. Suppose 0 = -5*c - 8 - 7, -16 = -z*h + 4*c. Factor h*p - 2*p - p**4 - 2*p**3.
-p**3*(p + 2)
Let d(c) be the third derivative of 4*c**7/105 + c**6/15 - 7*c**5/30 + c**4/6 - 23*c**2. Factor d(b).
2*b*(b + 2)*(2*b - 1)**2
Solve 32/5*d + 0 + 4/5*d**5 + 28/5*d**4 + 16*d**2 + 72/5*d**3 = 0.
-2, -1, 0
Let q(g) be the third derivative of g**5/300 + g**4/30 + g**3/10 - 7*g**2. Factor q(k).
(k + 1)*(k + 3)/5
Let s be ((-135)/12)/5*8. Let y = -52/3 - s. What is d in 0 - y*d - 2/3*d**2 = 0?
-1, 0
Let z be 2/8 + (-15)/72. Let w(x) be the third derivative of 1/60*x**5 - z*x**4 - 1/210*x**7 + 3*x**2 + 1/120*x**6 + 0*x + 0 + 0*x**3. Factor w(k).
-k*(k - 1)**2*(k + 1)
Let b(c) = 4*c**3 + 7*c**2 + 3*c - 8. Let w(m) = m**3 + 2*m**2 + m - 3. Let t(d) = -3*b(d) + 8*w(d). Determine k, given that t(k) = 0.
-1, -1/4, 0
Determine h, given that 4*h**4 + 15*h**4 - 7*h**4 - 4*h**2 - 6*h**4 + 10*h**3 = 0.
-2, 0, 1/3
Let v(f) be the second derivative of f**5/12 - 5*f**3/6 - 5*f**2/3 + 3*f. Let v(x) = 0. What is x?
-1, 2
Let z(i) be the second derivative of 0*i**2 + 0*i**5 - 1/105*i**6 + 5*i + 1/42*i**4 + 0*i**3 + 0. Factor z(h).
-2*h**2*(h - 1)*(h + 1)/7
Solve 6/5*x - 2*x**2 + 2/5*x**4 + 8/5 - 6/5*x**3 = 0.
-1, 1, 4
Let y(a) be the second derivative of -a**6/30 + 3*a**5/20 - a**4/4 + a**3/6 + 6*a. Suppose y(c) = 0. What is c?
0, 1
Let h be (2/2)/((-4)/(-20)). Let z(q) = 6*q**4 + 2*q**3 + 2*q**2 - 2*q - 4. Let b(d) = 7*d**4 + d**3 + d**2 - 3*d - 5. Let p(l) = h*z(l) - 4*b(l). Factor p(j).
2*j*(j + 1)**3
Determine b, given that 0 - 1/9*b**4 - 1/9*b**2 - 2/9*b**3 + 0*b = 0.
-1, 0
Factor -4/7 + 6/7*j - 2/7*j**2.
-2*(j - 2)*(j - 1)/7
Let j(p) = -3*p**2 + 5*p + 32. Let t(u) = -4*u**2 + 8*u + 48. Let k(l) = 8*j(l) - 5*t(l). Factor k(m).
-4*(m - 2)*(m + 2)
Let w = 361/5 - 72. Let i(z) = -z**3 - 4*z**2 - 2*z - 6. Let q be i(-4). Determine d, given that -w*d**q + 0 - 1/5*d = 0.
-1, 0
Suppose i - 2 = -0*i. Suppose -i*g = -2, 5*r - 3*g - 6 = 6. Factor -l + l**5 + 2*l**2 + 2*l + l - r*l - 2*l**4.
l*(l - 1)**3*(l + 1)
Factor 0 + 6/7*i + 2/7*i**4 + 10/7*i**3 + 2*i**2.
2*i*(i + 1)**2*(i + 3)/7
Factor 11*q**2 - q**2 - 6*q - 8*q**2.
2*q*(q - 3)
Let y(j) be the second derivative of 8*j**4/3 + 8*j**3/3 + j**2 + 8*j. Determine d so that y(d) = 0.
-1/4
Let i = -7 + 9. Find b, given that 12*b + 4*b**2 - 9*b - b**i = 0.
-1, 0
Let z(j) be the second derivative of -1/45*j**6 + 1/9*j**4 + 4*j + 0 + 0*j**5 - 1/3*j**2 + 0*j**3. Let z(v) = 0. Calculate v.
-1, 1
Let d(g) be the third derivative of -g**8/224 - g**7/70 + g**6/40 + g**5/10 - g**4/16 - g**3/2 - g**2. Suppose d(a) = 0. What is a?
-2, -1, 1
Let k(w) = 225*w**4 - 57*w**3 - 38*w**2 + 10*w. Let o(g) = 675*g**4 - 172*g**3 - 113*g**2 + 30*g. Let u(v) = -8*k(v) + 3*o(v). Suppose u(l) = 0. What is l?
-2/5, 0, 1/3
Suppose 8/15*c + 4/15*c**3 + 2/15 + 2/3*c**2 = 0. What is c?
-1, -1/2
Let y be (-3)/(6/(-34)) - 1. Let u be ((-4)/(-6))/(y/42). Factor -a**2 - 3*a**3 + u*a**4 + 0 + 0*a.
a**2*(a - 2)*(7*a + 2)/4
Suppose 2*r = b - 10, -3*r - 14 + 0 = -b. Let q(j) be the first derivative of -1/6*j**6 + j - 2/3*j**3 + b + 1/2*j**4 + 1/5*j**5 - 1/2*j**2. Factor q(f).
-(f - 1)**3*(f + 1)**2
Let l(j) be the first deri