d - 2)/2
Let o(x) be the third derivative of 0*x**3 - 1/36*x**5 + 0 + 1/36*x**4 - 1/630*x**7 - 2*x**2 + 0*x + 1/90*x**6. Find g, given that o(g) = 0.
0, 1, 2
Let a(r) be the first derivative of -r**6/12 - r**5/10 + r**4/4 + r**3/3 - r**2/4 - r/2 + 5. Factor a(y).
-(y - 1)**2*(y + 1)**3/2
Let m(f) be the second derivative of -f**4/6 + f**2 - 6*f. Factor m(g).
-2*(g - 1)*(g + 1)
Let u be (-5)/25 - 36/(-5). Let k = 7 + -5. Find s, given that -10*s**k + 4 + 4*s - u + 3 = 0.
0, 2/5
Let l(c) be the first derivative of c**8/560 - c**7/140 + c**5/20 - c**4/8 + 2*c**3/3 - 8. Let f(p) be the third derivative of l(p). Factor f(a).
3*(a - 1)**3*(a + 1)
Let x(h) = h**2 + 10*h + 16. Let a(j) = 3*j**2 + 31*j + 48. Let q(c) = 2*a(c) - 7*x(c). Suppose q(r) = 0. Calculate r.
-4
Let b = 4 + 1. Let m be (-10)/(-3) + (-2)/(-3). Factor -2*t**3 - b*t**4 + 2*t + 3 + m*t**4 - 2.
-(t - 1)*(t + 1)**3
Let t(b) be the third derivative of -b**5/20 + 3*b**4/4 - 9*b**3/2 - 7*b**2. Let t(p) = 0. Calculate p.
3
Suppose -8*u**3 - 3 + 8*u + 6*u**2 - 4*u**4 + 3 - 2*u**2 = 0. What is u?
-2, -1, 0, 1
Let h be 1/(-1)*5 + (-705)/(-105). Factor -8/7*b - 8/7*b**3 - h*b**2 - 2/7 - 2/7*b**4.
-2*(b + 1)**4/7
Let z(x) be the third derivative of x**7/150 - 2*x**6/75 + 11*x**5/300 - x**4/60 + 6*x**2. Factor z(g).
g*(g - 1)**2*(7*g - 2)/5
Let j(i) = i**2 + 8*i + 4. Let f(x) = -2*x**2 - 24*x - 12. Let y(a) = -3*f(a) - 10*j(a). Factor y(s).
-4*(s + 1)**2
Suppose 7*t - 16 = -2. Suppose 1/2*c**t - 3*c + 9/2 = 0. Calculate c.
3
Let q(v) be the third derivative of -v**6/1260 - v**5/210 - v**4/84 + v**3/2 + v**2. Let f(m) be the first derivative of q(m). Find d, given that f(d) = 0.
-1
Let o(r) be the second derivative of r**5/30 + r**4/12 - 2*r**3/3 - r**2/2 - 4*r. Let s(h) be the first derivative of o(h). Factor s(f).
2*(f - 1)*(f + 2)
Suppose -2*u - 13 = -37. Let j = 17 - u. Factor -1/2 + 3/2*i - i**3 - 1/2*i**j + 3/2*i**4 - i**2.
-(i - 1)**4*(i + 1)/2
Let c(k) = -7*k**3 - 24*k**2 + 48*k - 32. Let z(i) = 4*i**3 + 12*i**2 - 24*i + 16. Let p(y) = 6*c(y) + 11*z(y). Determine v so that p(v) = 0.
2
Let s(q) = -4*q**2 - 66*q. Let c(j) = -j**2 - 13*j. Let i(v) = -28*c(v) + 6*s(v). Factor i(x).
4*x*(x - 8)
Suppose -55*r**2 + 4*r**3 - 4*r + 55*r**2 = 0. What is r?
-1, 0, 1
Let h be 1 - 10/8 - 9/(-12). Determine r, given that 0*r**2 + h*r - 1/2*r**3 + 0 = 0.
-1, 0, 1
What is w in -3/7*w - 3/7*w**2 + 6/7 = 0?
-2, 1
Let y be 16/(-18)*5/(-10). Let o(p) be the first derivative of -5/6*p**4 + 3 + 0*p**2 - y*p**3 + 0*p. Suppose o(x) = 0. Calculate x.
-2/5, 0
Let q(k) be the first derivative of -k**6/6 + k**4/2 - k**2/2 + 4. Factor q(h).
-h*(h - 1)**2*(h + 1)**2
Determine f so that 3*f**3 + f**2 + 0*f + 2*f**4 - f**3 - 2*f - 3*f**2 = 0.
-1, 0, 1
Let p(j) = -j**3 - j - 1. Let m(h) = -2*h**3 + 2*h**2 - 8*h - 7. Let f = -23 - -33. Let w be (f/(-5))/(4/(-10)). Let v(t) = w*p(t) - m(t). Factor v(b).
-(b - 1)*(b + 1)*(3*b + 2)
Let i(q) = -48*q**3 + 192*q**2 - 225*q - 33. Let l(f) = -3*f**3 + 12*f**2 - 14*f - 2. Let c(h) = 2*i(h) - 33*l(h). Solve c(s) = 0 for s.
0, 2
Let x = 17411/28 + -2461/4. Let r = -124/21 + x. Determine p so that -r*p - 1/3*p**4 + 2/3*p**3 + 0*p**2 + 1/3 = 0.
-1, 1
Let n(z) = -z**3 + z**2. Let k(h) = -14*h**5 - 46*h**4 - 40*h**3 - 40*h**2 - 4*h. Let x(o) = -2*k(o) - 28*n(o). Factor x(g).
4*g*(g + 1)**3*(7*g + 2)
Find t, given that -4*t**2 + 2*t + 11 - 11 + t**3 + 2*t = 0.
0, 2
What is i in -4/5 - 4/5*i**4 + 8/5*i**2 - 8/5*i**3 + 4/5*i**5 + 4/5*i = 0?
-1, 1
Let l(k) = 6*k**2 + 6*k - 4. Let m(c) be the first derivative of 5*c**3/3 + 5*c**2/2 - 4*c - 1. Let i(j) = -3*l(j) + 4*m(j). Factor i(w).
2*(w - 1)*(w + 2)
Let 26/11*k**2 - 14/11 + 4/11*k**3 - 16/11*k = 0. What is k?
-7, -1/2, 1
Let z = 25 - 21. Suppose -4*b - z*a + 20 + 16 = 0, -a = -4. Let 0 - 1/4*j**b + 0*j + 0*j**3 + 0*j**2 + 1/4*j**4 = 0. Calculate j.
0, 1
Suppose 0 = 2*x - 0*x - 10. Suppose -x*j + 5 = -0. Factor 5 + 2 - 6 + j - 10*a**2 + 8*a.
-2*(a - 1)*(5*a + 1)
Let r(p) be the first derivative of 2/3*p**3 + 6/5*p**5 + 0*p + 3/2*p**4 - 6 + 1/3*p**6 + 0*p**2. Find y such that r(y) = 0.
-1, 0
Let k(m) be the second derivative of 0 + 3/100*m**5 + 0*m**3 + 1/10*m**4 + 4*m + 0*m**2. Factor k(y).
3*y**2*(y + 2)/5
Let h be ((-1425)/(-102))/5 + -2. Let v = h - -681/170. Let -14/5*d**4 + v*d**3 - 4/5*d - 6/5*d**2 + 0 = 0. Calculate d.
-2/7, 0, 1
Let b = 1 + 1. Let s be (-1)/b - (2 - 3). Factor -1/2*d**4 + 1/2*d**3 + 0 - 1/2*d + s*d**2.
-d*(d - 1)**2*(d + 1)/2
Let 15*i**4 + i + 10*i**3 - 6*i - 30*i**2 + 15 - 71*i**5 + 66*i**5 = 0. What is i?
-1, 1, 3
Let n(k) be the third derivative of -k**5/90 + k**4/9 + k**2. Let n(w) = 0. What is w?
0, 4
Let b(q) = -q**3 + q + 1. Let m(k) = 4*k**3 + 10*k**2 - 4*k - 9. Let d(o) = b(o) - m(o). Find t such that d(t) = 0.
-2, -1, 1
Let n(c) be the second derivative of -c**5/20 + c**4/4 + 2*c**3/3 + c**2 + 4*c. Let w be n(4). Determine l so that 2*l**w - 4*l**2 + 1 + 9*l - l**2 - 7 = 0.
1, 2
Determine r so that -6*r**2 - 11*r - 2 + r**2 + 5 - 5 = 0.
-2, -1/5
Let m = -312 + 312. Factor 0*k**2 + 1/3*k**3 - 1/3*k + m.
k*(k - 1)*(k + 1)/3
Let r be (-10)/(-4) - 2 - (-129)/30. Solve r*o**2 - 16/5*o**3 + 2/5 - 12/5*o = 0.
1/2
Let -6*s**2 + 8 - 25*s + 11*s**2 + 7 + 5 = 0. Calculate s.
1, 4
Let h = -857/2 + 449. Let b = h + -20. What is m in -m + b*m**2 + 0 = 0?
0, 2
Suppose k = 0, 2*k - 8 + 28 = 2*u. Let i be (40/25)/(4/u). Factor 2/3*c**i - 4/3*c**3 + 0*c + 0 + 2/3*c**2.
2*c**2*(c - 1)**2/3
Suppose -2*j + 20 = 2*l, 0*j + 4*l = -2*j + 30. Let u = 12 - j. Factor -9*g**2 + 9*g - u*g - 3*g**4 - 5*g - 9*g**3.
-3*g*(g + 1)**3
Let s(y) be the third derivative of -y**8/5040 - y**7/1260 - y**5/30 + 7*y**2. Let l(w) be the third derivative of s(w). Factor l(c).
-4*c*(c + 1)
Suppose -8 = 7*r - 43. Let c(i) be the second derivative of 0*i**3 + 1/10*i**6 - 1/42*i**7 - 3/20*i**r + 0*i**2 + 1/12*i**4 + i + 0. Let c(s) = 0. Calculate s.
0, 1
Let d(m) be the third derivative of m**6/1080 - m**5/180 + m**3/3 + 2*m**2. Let x(b) be the first derivative of d(b). Factor x(u).
u*(u - 2)/3
Let n(j) = j + 8. Let g be n(7). Suppose -6 = -2*s - 3*a, -2*s - 3*s + g = 2*a. Let 0*r + 0*r**2 + 0 + 1/3*r**s = 0. What is r?
0
Let k(w) be the third derivative of -w**5/120 - w**4/12 - w**3/3 - 8*w**2. Factor k(d).
-(d + 2)**2/2
Factor 13*b**2 - 4*b**3 - 2*b**3 - 5*b - 5*b + b**4 - 2*b + 4.
(b - 2)**2*(b - 1)**2
What is l in -2/11*l - 6/11*l**4 + 6/11*l**2 + 4/11*l**5 + 0 - 2/11*l**3 = 0?
-1, 0, 1/2, 1
Let b(r) be the first derivative of -14*r**3/15 + 26*r**2/5 + 16*r/5 - 17. Factor b(c).
-2*(c - 4)*(7*c + 2)/5
Let g(n) be the first derivative of -n**4/16 + n**3/12 - 1. Solve g(o) = 0 for o.
0, 1
Let q(y) be the third derivative of y**7/280 + y**6/160 - y**5/80 - y**4/32 - 16*y**2. Factor q(z).
3*z*(z - 1)*(z + 1)**2/4
Let a = 11 + -8. What is d in 5*d**3 - d**5 - 2*d - d**a - d**5 = 0?
-1, 0, 1
Let y(i) be the third derivative of i**5/100 + 3*i**4/20 + 9*i**3/10 - i**2. Factor y(n).
3*(n + 3)**2/5
Let c(p) be the second derivative of -p**6/20 + 3*p**5/20 - p**4/8 - p. Determine u so that c(u) = 0.
0, 1
Suppose -5*t = 4*y + 2, -5*t - 9*y = -4*y + 5. Factor 16/3 + 2*h**3 + 40/3*h + 28/3*h**t.
2*(h + 2)**2*(3*h + 2)/3
Find t, given that 1/2*t + 0 + 1/4*t**2 = 0.
-2, 0
Let u(d) = 2*d**3 - 2*d + 2. Let j(p) = -2*p**3 + p**2 + 3*p - 3. Let g(t) = 2*j(t) + 3*u(t). Factor g(k).
2*k**2*(k + 1)
Let g(d) = -14*d**3 - 28*d**2 - 8*d + 4. Let l(s) = 14*s**3 + 27*s**2 + 8*s - 5. Let u(p) = 5*g(p) + 4*l(p). Suppose u(f) = 0. Calculate f.
-2, -2/7, 0
Let b(y) be the second derivative of y**4/30 - 4*y**3/15 + 4*y**2/5 + 7*y. Factor b(u).
2*(u - 2)**2/5
Let i = 49 - 49. Let g(k) be the third derivative of k**2 - 2/15*k**3 + 1/300*k**6 + 1/75*k**5 - 1/60*k**4 + 0*k + i. Factor g(d).
2*(d - 1)*(d + 1)*(d + 2)/5
Let g(x) = -x**3 - 1. Let f(w) = 6*w**3 + w**2 - 3*w + 1. Let u(k) = f(k) + 4*g(k). Let l(b) = -b**3 + b + 1. Let q(m) = 3*l(m) + u(m). Factor q(s).
-s**2*(s - 1)
Suppose -2*n - n + 15 = 5*f, -1 = -f - n. Let t(i) be the second derivative of 0*i**3 + 1/10*i**5 - i + 0 + 1/15*i**f + 0*i**2 + 0*i**4. Factor t(j).
2*j**3*(j + 1)
Suppose -2*i - 4*m = 18 - 2, 4*i - 3*m = 23. Determine a, given that -a - 3*a**4 + a**3 - a - 4 + a**4 + a**3 + 6*a**i = 0.
-1, 1, 2
Suppose 4*n