-7
Let t be 0/(-1)*(-2)/(-4). Let b(m) be the first derivative of -1/14*m**4 + t*m**3 + 3/7*m**2 - 4/7*m - 2. Determine h, given that b(h) = 0.
-2, 1
Let p(g) = 4*g**2 - 5*g - 1. Let x(u) = -5*u - u**2 + 0*u + 6*u + 1. Let q(d) = p(d) + 5*x(d). Solve q(y) = 0.
-2, 2
Let h(b) = -28*b**3 - 4*b**2 + 20*b - 8. Let v(q) = -27*q**3 - 3*q**2 + 20*q - 9. Let g(w) = 5*h(w) - 4*v(w). Suppose g(l) = 0. What is l?
-1, 1/4, 1/2
Suppose l - 6 = -2*l. Suppose -13*f + 7 + f + 5*f**2 + 11 - 3*f**l = 0. Calculate f.
3
Let l(o) be the second derivative of -o**10/45360 + o**8/5040 - o**6/1080 + o**4/6 - 3*o. Let n(d) be the third derivative of l(d). Factor n(t).
-2*t*(t - 1)**2*(t + 1)**2/3
Let k = 26/9 + -8/3. Find h, given that 0 + 0*h - 2/9*h**3 + 4/9*h**2 - k*h**4 = 0.
-2, 0, 1
Let b be 4/16*2 - (-14)/4. Let o(w) be the second derivative of w + 0 + 0*w**b + 1/10*w**5 - 2*w**2 - w**3. Factor o(x).
2*(x - 2)*(x + 1)**2
Let f(w) be the first derivative of -4*w**5/35 + 3*w**4/7 - 8*w**3/21 - 7. What is r in f(r) = 0?
0, 1, 2
Let n be (-8)/44 + 3/(264/49). Let c(y) be the first derivative of 0*y + 2 + n*y**2 - 1/4*y**3. Let c(w) = 0. What is w?
0, 1
Let x = -80 + 84. Let d(h) be the first derivative of 0*h**2 + 6*h**x - h**3 + 0*h + 2 - 48/5*h**5. Determine t so that d(t) = 0.
0, 1/4
Suppose 3*z**2 + 51*z + 2*z**2 + 4*z - 5*z + 125 = 0. What is z?
-5
Let v = -974/5 - -196. Factor 2/5 - 8/5*p + v*p**2.
2*(p - 1)*(3*p - 1)/5
Let t(q) be the first derivative of -2/9*q**3 - 1 + 1/6*q**4 + 2/15*q**5 - 1/3*q**2 + 0*q. Factor t(j).
2*j*(j - 1)*(j + 1)**2/3
Let k(w) be the first derivative of -3/7*w**2 - 2/21*w**3 + 0*w + 2. Suppose k(q) = 0. Calculate q.
-3, 0
Suppose k = -1 - 0. Let w = 3 - k. Factor -5 + 4 - 3*l**4 + 2*l**2 + 2*l**w.
-(l - 1)**2*(l + 1)**2
Let j(u) = 2*u - 5. Let z be j(4). Let o be ((-20)/(-3) - z)*2. What is b in 0 - 2/3*b - 4*b**2 - o*b**3 - 4*b**4 = 0?
-1, -1/2, -1/3, 0
Suppose -3*w - w - 4*k + 1496 = 0, w - 354 = 3*k. Suppose -5*d + w = 2*l - 586, 746 = 4*d - 2*l. Factor 4 - 50*g + d*g**2 - 729/2*g**4 - 243/2*g**3.
-(g + 1)*(9*g - 2)**3/2
Suppose 0 = 2*h + h + 3*x, 0 = x + 2. Determine y, given that -26*y + 42*y**2 - h*y**2 + 4 - 26*y**3 + 8*y**3 = 0.
2/9, 1
Let o(a) = -a**2 - 4*a - 1. Let p be o(-4). Let v be 1*(p + 6/4). Find w, given that -1 - 1/2*w + v*w**2 = 0.
-1, 2
Suppose -p = -0*p + 10. Let x be 8/p + 20/25. Factor -1/6*c**2 - 1/6*c + x.
-c*(c + 1)/6
Let h(j) be the first derivative of j**5/80 + j**4/24 + j**3/24 + 2*j + 1. Let l(w) be the first derivative of h(w). Let l(x) = 0. Calculate x.
-1, 0
Let y(g) be the third derivative of -g**9/13440 + g**8/3360 + g**7/3360 - g**6/240 + g**5/15 + 3*g**2. Let l(w) be the third derivative of y(w). Solve l(d) = 0.
-2/3, 1
Let j(k) be the second derivative of 9*k**4/8 + 19*k**3/2 + 6*k**2 - 5*k. Let j(c) = 0. What is c?
-4, -2/9
Let q(m) be the first derivative of 0*m + 1/2*m**4 - 1 - 2/5*m**5 + 0*m**2 + 0*m**3. Factor q(d).
-2*d**3*(d - 1)
Let q be (-3)/7 + (-208)/(-224). Let x(o) be the first derivative of 4/3*o**3 - q*o**4 - o**2 + 0*o + 1. Let x(g) = 0. Calculate g.
0, 1
Let d(p) be the third derivative of -p**8/840 + p**7/525 + p**6/300 - p**5/150 - 8*p**2. What is z in d(z) = 0?
-1, 0, 1
Let r(n) = 2*n**2 - 2*n - 1. Suppose 4*w = 5*w + c + 8, -w + 17 = -4*c. Let z(t) = -5*t**2 + 6*t + 3. Let l(i) = w*z(i) - 8*r(i). Factor l(h).
-(h + 1)**2
Let s(t) be the third derivative of -t**7/525 - t**6/225 - t**5/450 - 2*t**2 - 2. Find h, given that s(h) = 0.
-1, -1/3, 0
Let k(w) be the second derivative of -w**7/105 - w**6/25 - 3*w**5/50 - w**4/30 - 14*w. Factor k(y).
-2*y**2*(y + 1)**3/5
Let f(i) be the first derivative of i**5/20 - i**3/2 - i**2 + 2*i + 3. Let n(c) be the first derivative of f(c). Find b, given that n(b) = 0.
-1, 2
Let n(y) = -3*y**5 + 13*y**4 - 7*y**3 - 6*y**2 + 3*y + 7. Let p(t) = -2*t**5 + 9*t**4 - 5*t**3 - 4*t**2 + 2*t + 5. Let s(c) = -5*n(c) + 7*p(c). Factor s(f).
f*(f - 1)**3*(f + 1)
Suppose -4*d + l = -0*d - 15, -l - 3 = 0. Factor d*w**3 + 1 + 6*w**2 - 9*w**2 - 3*w + 2.
3*(w - 1)**2*(w + 1)
Suppose 3*s**3 + 9*s**2 - 2*s + 15*s - 7*s = 0. What is s?
-2, -1, 0
Let f(v) = v**4 + 3*v**3 - 2*v**2 - 3*v + 7. Let q(p) = 6*p - 5*p**3 - 36 + 10*p**2 + 8*p - 6*p**4 - 6*p**3 - 3*p**3. Let o(w) = -16*f(w) - 3*q(w). Factor o(s).
2*(s - 2)*(s - 1)**2*(s + 1)
Let w = 256/5 + -51. Let s(t) be the first derivative of 0*t**2 + 0*t - w*t**5 + 2 - 1/4*t**4 + 0*t**3. Factor s(a).
-a**3*(a + 1)
What is l in 2*l**3 - 2*l + 13*l**2 + 7*l**2 - 14*l**2 - 6 = 0?
-3, -1, 1
Let r = -1 - -5. Suppose 10 - 2 = r*w. Determine m so that 2/5*m - 6/5*m**w + 0 = 0.
0, 1/3
Let w(t) = 2*t**2 - 9*t + 12. Let h be w(4). Let d be ((-9)/15)/((-12)/h). Suppose 0 + d*x**3 + 2/5*x + 4/5*x**2 = 0. Calculate x.
-1, 0
Let -9*p + 16*p**2 - p**5 - 11 + 6*p**4 - 14*p**3 - 4 + 17 = 0. Calculate p.
1, 2
Let x(d) = -d**2 - 3*d - 15. Let y be x(-10). Let p = y - -173/2. Determine i so that 3/2*i**2 + p*i + 0 = 0.
-1, 0
Suppose -p = 2*p - 9. Factor 6*b**4 - 7*b**4 + b**3 + b**p.
-b**3*(b - 2)
Let w(d) be the first derivative of -d**4/12 + d**3/3 - 4*d + 3. Let m(a) be the first derivative of w(a). Factor m(n).
-n*(n - 2)
Let u(c) = c**2 - 10*c + 11. Let z be u(9). Let -3*s**z - 3 + 0*s + 9*s - 3*s = 0. What is s?
1
Let j be 3 - (-1)/((-2)/22). Let w be ((-2)/(-3))/((-12)/j). Determine c so that -2/3*c - 2/9*c**2 - w = 0.
-2, -1
Let m(r) be the third derivative of -r**7/210 + r**6/45 - r**5/30 - 4*r**3/3 + 5*r**2. Let l(z) be the first derivative of m(z). Factor l(s).
-4*s*(s - 1)**2
Factor 21*s - 14*s - 3 + 48*s**3 + 17*s - 60*s**2.
3*(2*s - 1)**2*(4*s - 1)
Let d be ((-1)/(-6))/(10/120). Let f(h) be the first derivative of 1/15*h**3 + 0*h**d + 0*h + 4 + 1/20*h**4. Factor f(o).
o**2*(o + 1)/5
Factor -4*x**3 + 6*x**3 - 3*x**4 - 5*x**3.
-3*x**3*(x + 1)
Let u(o) = -6*o**5 + 6*o**3 + 6*o**2 - 3*o. Let m(v) = -11*v**5 - v**4 + 11*v**3 + 11*v**2 - 5*v. Let c(r) = 3*m(r) - 5*u(r). Let c(a) = 0. Calculate a.
-1, 0, 1
Let x(s) be the first derivative of s**6/15 + 3*s**5/5 + 2*s**4 + 8*s**3/3 + 4*s - 7. Let k(h) be the first derivative of x(h). Solve k(y) = 0.
-2, 0
Let x be 5*(219/210 - 1). Let p(l) be the second derivative of -3*l**2 + 0 - 3/2*l**5 - 1/5*l**6 - l + x*l**7 + 3*l**4 - 1/2*l**3. Let p(u) = 0. What is u?
-2, -1/3, 1
Find f such that 0 + 4/3*f + 4/3*f**2 + 1/3*f**3 = 0.
-2, 0
Let f = -1110 + 21096/19. Let w = f - -20/57. Suppose -2/3*o**3 - 2/3 + 2/3*o**2 + w*o = 0. Calculate o.
-1, 1
Factor -4*m**2 + 0*m + 2*m**2 + 0*m + 2 - 2*m**3 + 2*m.
-2*(m - 1)*(m + 1)**2
Let n = -87 - -439/5. Let p = n + -11/20. Factor 1/4*r**3 + 0 - 1/4*r**5 + 1/4*r**2 + 0*r - p*r**4.
-r**2*(r - 1)*(r + 1)**2/4
Find o such that 3*o**2 - 32*o + 2*o**2 - 14*o + 60 - 19*o = 0.
1, 12
Let f(b) be the first derivative of -b**6/180 - b**5/18 - 7*b**4/36 - b**3/3 - b**2 + 1. Let g(t) be the second derivative of f(t). Factor g(a).
-2*(a + 1)**2*(a + 3)/3
Let x(m) = -5*m**5 - 41*m**4 - 49*m**3 - 29*m**2 - 11*m. Let d(b) = -b**5 - 8*b**4 - 10*b**3 - 6*b**2 - 2*b. Let u(f) = 11*d(f) - 2*x(f). Factor u(h).
-h**2*(h + 2)**3
Let l(n) be the first derivative of 343*n**6/4 - 588*n**5/5 - 483*n**4/8 + 67*n**3 + 51*n**2 + 12*n - 1. Let l(d) = 0. What is d?
-2/7, 1
Suppose 10 = 4*b + 2. Suppose 12 + 36 = 12*w. Let 0 + 4/11*z**w - 4/11*z**b + 0*z**3 + 2/11*z - 2/11*z**5 = 0. Calculate z.
-1, 0, 1
Let l(j) = -2*j + 7. Let i(m) = m + 1. Let v(d) = -3*i(d) - l(d). Let b be v(-15). Factor -2*u + 3/2*u**3 + 1/4*u**b - u**2 + 0 + 5/4*u**4.
u*(u - 1)*(u + 2)**3/4
Let d(c) = -7*c**2 - 4*c - 1. Let p(v) = v**2 + v. Let r(w) = d(w) + 6*p(w). Let r(t) = 0. What is t?
1
Let z = -855/2 + 428. Factor 1/4*o**3 - 1/2 + z*o**2 - 1/4*o.
(o - 1)*(o + 1)*(o + 2)/4
Let o(v) = 8*v**3 - v**2 - 20*v + 3. Let f(h) be the first derivative of -2*h**4 + 10*h**2 - 4*h + 5. Let x(b) = -5*f(b) - 4*o(b). Let x(c) = 0. Calculate c.
-2, 1/2, 1
Let r be (-4)/(-6) + 34/(-60). Let w(q) be the third derivative of r*q**5 - 5/12*q**4 + q**2 + 0*q + 0 + 2/3*q**3. Suppose w(j) = 0. What is j?
2/3, 1
Let c(r) = 35*r**3 + 580*r**2 + 2220*r - 20. Let s(p) = 5*p**3 + 83*p**2 + 317*p - 3. Let m(q) = 3*c(q) - 20*s(q). Factor m(f).
5*f*(f + 8)**2
Let o be (-32)/64*(2 - 2). Factor o*k + 0 - 3/2*k**2 + 3/2*k**5 - 9/2*k**