culate r.
-1, 0
Let f(r) be the second derivative of 1/10*r**6 + 0*r**3 + 0 - 3/20*r**5 + 0*r**2 + 3*r - 1/2*r**4. Factor f(v).
3*v**2*(v - 2)*(v + 1)
Let i(b) be the third derivative of -1/72*b**4 + 1/180*b**6 + 0*b**7 + 0*b - 4*b**2 - 1/1008*b**8 + 0*b**5 + 0*b**3 + 0. Find k such that i(k) = 0.
-1, 0, 1
Let 6*t**2 - 3*t**2 + 5*t**2 - 4*t**3 = 0. What is t?
0, 2
Let d(w) be the third derivative of -w**6/30 + w**4/6 + 16*w**2. Factor d(q).
-4*q*(q - 1)*(q + 1)
Let w(r) be the first derivative of -1/7*r**2 - 2/21*r**3 + 0*r - 2. Factor w(k).
-2*k*(k + 1)/7
Let a(u) be the first derivative of 3*u**4/4 + 5*u**3/3 + u**2/2 - u + 9. Determine j, given that a(j) = 0.
-1, 1/3
Let r be (-30)/50 + (-26)/(-10). Determine i, given that 0 + 1/2*i**r + 1/2*i = 0.
-1, 0
Factor 2/5*r**2 + 4/5 - 6/5*r.
2*(r - 2)*(r - 1)/5
Let h be (-3)/(-9) + (-1)/5. Let y(m) be the first derivative of 3 - h*m**3 + 0*m**2 + 2/5*m. Solve y(z) = 0 for z.
-1, 1
Let z(o) be the first derivative of o**4/4 + o**3 + o**2/2 + o - 1. Let m be z(-2). Let 2/3*u**2 - 2/3*u**m + 0*u + 0 + 2/3*u**5 - 2/3*u**4 = 0. What is u?
-1, 0, 1
Let f(n) = -n**3 + 7*n**2 + 7*n + 11. Let o be f(8). Let h = 157/735 - 2/147. What is a in -2/5*a**o + 0 - 1/5*a**2 + h*a = 0?
-1, 0, 1/2
Let p(n) = -2*n - 10. Let d be p(-6). Let k be -5*(-4 - (-7)/d). What is f in 5/2*f**3 - 1 - k*f + f**2 = 0?
-1, -2/5, 1
Let v(h) = -h + 1. Let r(p) = -5*p + 4*p + 4 - 5*p + 2*p**3. Let y(t) = -r(t) + 4*v(t). Determine u, given that y(u) = 0.
-1, 0, 1
Let s(p) be the second derivative of 2*p - 1/120*p**5 + 0 + 0*p**3 + 0*p**4 - p**2. Let i(k) be the first derivative of s(k). Factor i(a).
-a**2/2
Determine n so that 1/4*n**4 - 1/4*n + 1/4*n**3 - 1/4*n**2 + 0 = 0.
-1, 0, 1
Suppose -4*m = k + 8 + 1, -4*k = 4*m. Suppose 3*x - 18 = -3*h, k*x + 10 = -2*x + 5*h. Determine l so that -1 - l**2 - l**x + l**2 + 2*l = 0.
1
Factor -86/7*g**2 - 16/7 + 2/7*g**5 + 60/7*g - 18/7*g**4 + 58/7*g**3.
2*(g - 4)*(g - 2)*(g - 1)**3/7
Let h(y) be the first derivative of 25*y**3/27 - 5*y**2/9 + y/9 + 6. Factor h(c).
(5*c - 1)**2/9
Let d be ((-8)/(-7))/((-110)/(-77)). Factor -2/5*a - d*a**2 - 2/5*a**3 + 0.
-2*a*(a + 1)**2/5
Suppose 2*z + 2*z - 8 = 0. Factor -p**5 - z*p**2 + p**4 + p**3 + 0*p**4 + p**2.
-p**2*(p - 1)**2*(p + 1)
Find d, given that -3/5*d + 1/5*d**3 - 2/5 + 0*d**2 = 0.
-1, 2
Let j = 3324 + -16687/5. Let m = -13 - j. Let 0*g**2 + 2/5*g - m*g**3 + 0 = 0. What is g?
-1, 0, 1
Let 0 - 2/3*k**4 + 2/3*k**2 + 0*k - 8/3*k**5 + 8/3*k**3 = 0. What is k?
-1, -1/4, 0, 1
Let j be ((1 - -2)/(-9))/(6/(-276)). Let u(o) be the first derivative of -j*o**3 - 8/3*o - 10/3*o**5 - 28/3*o**2 + 3 - 35/3*o**4. Factor u(z).
-2*(z + 1)**2*(5*z + 2)**2/3
Let h(q) be the first derivative of -q**3/5 + 9*q**2/5 - 24*q/5 + 46. Find u such that h(u) = 0.
2, 4
Let q be (8/(-6))/(-15 + 18 + -9). Factor -2/9*k**4 + q*k**2 - 2/9*k**5 + 0*k + 0 + 2/9*k**3.
-2*k**2*(k - 1)*(k + 1)**2/9
Let r = -57 + 57. Factor 2/5*x**2 + r*x - x**5 - 1/5*x**3 - 8/5*x**4 + 0.
-x**2*(x + 1)**2*(5*x - 2)/5
Determine a so that 6*a**2 - 25*a + 8 + a + 12*a - a**3 = 0.
2
Let x = -5 + 5. Suppose -5*y + y + 8 = x. Determine s, given that 4/3*s + 0 + 2/3*s**y = 0.
-2, 0
Factor v**2 - 75 + 70*v - 40*v - 4*v**2.
-3*(v - 5)**2
Let d(z) be the second derivative of 1/42*z**4 - 2*z + 1/210*z**5 + z**2 + 1/21*z**3 + 0. Let v(s) be the first derivative of d(s). Factor v(f).
2*(f + 1)**2/7
Let x = 15 + -14. Let v be 2/(-4) + 2/x. Factor 1 + v*b + 0*b**2 - 1/2*b**3.
-(b - 2)*(b + 1)**2/2
Let f(j) be the second derivative of -j**5/60 + j**4/9 - 5*j**3/18 + j**2/3 + 6*j. Factor f(z).
-(z - 2)*(z - 1)**2/3
Let o(z) be the first derivative of -z**7/1400 - z**6/200 - z**3 - 4. Let f(i) be the third derivative of o(i). Find p such that f(p) = 0.
-3, 0
Let j(k) be the third derivative of k**2 + 0*k - 1/270*k**6 + 1/945*k**7 + 0 + 0*k**3 + 0*k**4 + 1/270*k**5. Determine d, given that j(d) = 0.
0, 1
Let n = 71/222 + 1/74. Factor w**4 + 0 + n*w**2 - w**3 - 1/3*w**5 + 0*w.
-w**2*(w - 1)**3/3
Let r be (112/(-140))/((-6)/5). Determine g, given that 0*g**2 + r*g**4 + 4/9*g**3 + 0 + 0*g + 2/9*g**5 = 0.
-2, -1, 0
Let i = -71 + 73. Let m(h) be the first derivative of 9/5*h**5 + 16*h - 24*h**i + 56/3*h**3 - 1 - 1/6*h**6 - 8*h**4. Factor m(u).
-(u - 2)**4*(u - 1)
Let c(u) be the first derivative of -8*u**2 + 16*u + 4/3*u**3 + 4. Factor c(v).
4*(v - 2)**2
Let o(g) be the first derivative of g**4/20 - 11*g**3/15 + 12*g**2/5 + 36*g/5 - 22. Factor o(q).
(q - 6)**2*(q + 1)/5
Let j(f) = f**2 + 3. Let k be j(0). Suppose 2*n**3 + 6*n**2 + 1 + k - 10*n - 3*n**3 - 2*n**4 + 3*n**3 = 0. What is n?
-2, 1
Let d(b) = 5*b**2 + 101*b + 23. Let w be d(-20). Suppose -3/2*t**3 - w*t**2 - 3/2*t + 0 = 0. What is t?
-1, 0
Let z(q) be the third derivative of -q**6/24 + q**5/12 + 15*q**2. Factor z(v).
-5*v**2*(v - 1)
Let r be ((-100)/(-6))/(16/(-48)). Let n = r + 301/6. Suppose 0 + n*i**3 - 1/3*i**2 + 1/6*i = 0. What is i?
0, 1
Let p = -5 + 5. Suppose -4*n + 3*j - j = p, -j + 14 = 5*n. Solve 4 - 3*o**n + o + 0*o**2 - o - o**3 = 0 for o.
-2, 1
Let h be 2/(-6) + (-1)/(-3). Suppose n - 5*w + w - 20 = h, -n = 3*w + 15. Find x such that -1/3*x**3 + 1/3*x + n*x**2 + 0 = 0.
-1, 0, 1
Find f, given that -3/2*f**3 + 9/4*f - 3/2*f**2 - 3/4 + 9/4*f**4 - 3/4*f**5 = 0.
-1, 1
Factor 3/2*k - 1/2*k**2 + 0.
-k*(k - 3)/2
Let h(n) = 2*n**2 + 4*n. Let g(t) = t**2 + 2*t. Let d(o) = -4*g(o) + h(o). Factor d(q).
-2*q*(q + 2)
Suppose -l - 2*c - 1 = 0, 0 = -2*l - 4*c + c. Factor 1/5 + 3/5*j**2 - 1/5*j**l - 3/5*j.
-(j - 1)**3/5
Solve -2/5 + 2/5*b - 2/5*b**3 + 2/5*b**2 = 0 for b.
-1, 1
Let d(a) be the second derivative of a**6/160 + 11*a**5/240 + a**4/12 - a**3/6 + a**2/2 + 5*a. Let q(x) be the first derivative of d(x). Solve q(g) = 0.
-2, 1/3
Let x(j) = -2*j**2 + 13*j - 13. Suppose 4 = 3*y - 5. Let w(z) = 4 - 4*z - 3*z + z**2 + y. Let p(u) = -10*w(u) - 6*x(u). Factor p(o).
2*(o - 2)**2
Determine k so that 55*k**2 - 3 - 58*k**2 - 10*k + 4*k = 0.
-1
Suppose 10 = -d + 5*q, -4*q + 0 = 2*d - 22. Factor -d*a - a + 4*a + 2*a**5 + 4*a**4 - 4*a**2.
2*a*(a - 1)*(a + 1)**3
What is g in -2/3*g**4 + 4/3 + 10/3*g + 2*g**2 - 2/3*g**3 = 0?
-1, 2
Let v = 84 - 82. Factor 0*w**v - w - 2/3 + 1/3*w**3.
(w - 2)*(w + 1)**2/3
Let -1 + 7/4*h**2 + 3*h = 0. Calculate h.
-2, 2/7
Let x(r) be the first derivative of -3*r**4/16 + r**3 - 15*r**2/8 + 3*r/2 + 27. Determine f so that x(f) = 0.
1, 2
Suppose 2*r + 60 = 66. Let l(v) be the third derivative of 1/60*v**4 - 2*v**2 + 0 + 1/150*v**5 + 0*v**r + 0*v. Suppose l(o) = 0. Calculate o.
-1, 0
Let r(q) = -q**2 - 8*q - 5. Let m be r(-6). Let z(w) = 2*w**2 - 11*w + 7. Let t be z(m). Let -25*a**2 - a**3 + 0*a**3 + t*a**2 - 4 = 0. What is a?
-1, 2
Suppose 5*p + 3*k + k - 3 = 0, -2*p = 4*k + 6. Factor 2/9*a**2 + 2/9*a - 2/9*a**p - 2/9.
-2*(a - 1)**2*(a + 1)/9
Let q(c) be the first derivative of c**4/2 - 9. Factor q(a).
2*a**3
Let l(p) be the first derivative of -3*p**2 + 0*p - p**3 + 3/4*p**4 - 3. Let l(k) = 0. Calculate k.
-1, 0, 2
Find k, given that -1/3*k**5 - 1/3*k**2 + 1/3*k**4 + 5/3*k**3 - 8/3*k - 4/3 = 0.
-1, 2
Let o(t) be the first derivative of 0*t + 4/3*t**6 - 1 + 0*t**2 - 2/3*t**3 + 14/5*t**5 + t**4. Find w such that o(w) = 0.
-1, 0, 1/4
Let u(b) = 6*b**2 + 4 - 5*b**2 + 3 + 4*b + 0*b**2. Let s(k) = -2*k - 4. Let n(x) = 7*s(x) + 4*u(x). Let n(a) = 0. What is a?
-1/2, 0
Solve 0*f**2 + 0*f**2 + 8*f**2 - 3*f**3 - 11*f**2 = 0 for f.
-1, 0
Let o = -12 - -7. Let i(t) = -8*t**2 + 12*t + 6. Let k(h) = 7*h**2 - 11*h - 5. Let m(y) = o*i(y) - 6*k(y). Determine s, given that m(s) = 0.
0, 3
Suppose -2*j + 3*j = -3*t + 3, -3*j - 1 = 4*t. Let h(o) be the second derivative of o + 2/15*o**3 + 0 + 1/30*o**4 + 1/5*o**t. Suppose h(g) = 0. What is g?
-1
Factor w**2 - 6*w**2 - 5 - 2*w - 8*w.
-5*(w + 1)**2
Let w(x) be the third derivative of -x**8/26880 + x**7/2016 - 7*x**6/2880 + x**5/160 + x**4/6 + 3*x**2. Let a(i) be the second derivative of w(i). Factor a(y).
-(y - 3)*(y - 1)**2/4
Let o = 9/10 - 3/10. Factor -7/5*y**3 - 12/5*y**2 - o*y + 2/5.
-(y + 1)**2*(7*y - 2)/5
Let w(b) be the third derivative of -1/60*b**5 + 2*b**2 + 0*b**3 + 0 + 0*b + 0*b**4. Factor w(v).
-v**2
Let z(j) be the second derivative of -1/72*j**5 - 1/270*j**6 + 0 - 1/72*j**4 + 0*j**2 - 1/3*j**3 + j. Let o