first derivative of 1/2*j**2 + 0*j - 7 + 1/3*j**3 - 1/4*j**4 - 1/5*j**5. Suppose k(r) = 0. What is r?
-1, 0, 1
Let y(t) = 18*t**2 - 20*t - 63. Let c(x) = 8*x**2 - 10*x - 31. Let f(z) = -7*c(z) + 3*y(z). Factor f(b).
-2*(b - 7)*(b + 2)
Suppose 2*o + 3*o + 4*h = 3, 0 = o + 4*h + 9. Solve -c - 3*c**2 - o*c + 0*c + 3*c = 0.
-1/3, 0
Let s(f) be the second derivative of -f**6/10 - 3*f**5/5 - 5*f**4/4 - f**3 + 12*f. Factor s(h).
-3*h*(h + 1)**2*(h + 2)
Suppose -3*y + 7 = 4*b, 4*y + 5*b + 1 = 12. Let c be 15/y - 3/18. Let -j - 1/2*j**3 + c*j**2 + 0 = 0. Calculate j.
0, 1, 2
What is y in 2/9*y**4 + 2/9*y**2 + 0*y + 0 + 4/9*y**3 = 0?
-1, 0
Factor -2/9*y**2 + 0 - 2/9*y**4 - 4/9*y**3 + 0*y.
-2*y**2*(y + 1)**2/9
Factor 4*j**2 - 2 - 2 + 0*j**2.
4*(j - 1)*(j + 1)
Suppose -1/8 - 3/8*m**2 + 1/8*m**3 + 3/8*m = 0. Calculate m.
1
Let x(b) be the second derivative of b**7/21 + 7*b**6/90 - b**5/20 - b**4/12 + b**3/18 + 5*b. Let x(c) = 0. Calculate c.
-1, 0, 1/3, 1/2
Let q be (1/3)/(-1)*-12. Find v such that -3*v**4 + q*v**4 - 3*v**4 + 2*v**2 + 2*v**5 - 2*v**3 = 0.
-1, 0, 1
Let t(d) = -d**2 - 4*d + 3. Let q be t(-4). Suppose q*g - 4*g = 0. Determine x so that 3*x**2 - x**2 + g*x**2 + 2*x = 0.
-1, 0
Let n = -20 + 22. Let l(h) be the second derivative of 0 + 0*h**3 + 1/6*h**4 - h**2 - n*h. Factor l(w).
2*(w - 1)*(w + 1)
Suppose 88 = -6*r + 8*r. Find a such that -10*a**3 + 10*a**3 + 36 - r*a**2 - 8*a**4 - 44*a**3 + 60*a = 0.
-3, -1/2, 1
Suppose -4*o - 2*r = 4 - 10, -o + 2*r = -4. Let u be (2 + -1)*o + -2. Let -1/5*b**3 - 1/5*b**4 + 0*b + 0*b**2 + u = 0. Calculate b.
-1, 0
Let i = 0 - -3. Let y be 2/(-4) + (-5)/(-2). Determine a, given that -7*a**3 + 4*a - a**4 + 4 - y + 3*a**i - a**4 = 0.
-1, 1
Let c(d) be the first derivative of -d**3 + 2*d**2 + 1/6*d**4 - d - 1. Let k(h) be the first derivative of c(h). Determine s, given that k(s) = 0.
1, 2
Let h(n) = -6. Let m(k) = k**2 - 1. Let y(a) = -2*h(a) - 4*m(a). Suppose y(c) = 0. What is c?
-2, 2
Let v(n) be the second derivative of -n**7/840 + n**3/2 + 3*n. Let b(s) be the second derivative of v(s). Factor b(i).
-i**3
Factor 75*t**2 - 22*t**2 - 29*t**2 - 12*t - 12 - 27*t**2.
-3*(t + 2)**2
Let m(g) be the third derivative of g**6/30 - 13*g**5/60 + g**4/6 + 2*g**3 - 11*g**2. Factor m(b).
(b - 2)**2*(4*b + 3)
Let a(d) be the first derivative of -d**6/6 + 4*d**5/5 - d**4/4 - 10*d**3/3 + 2*d**2 + 8*d + 23. Factor a(l).
-(l - 2)**3*(l + 1)**2
Let q(a) be the first derivative of -4*a**3/3 - 4*a**2 - 4*a - 2. What is t in q(t) = 0?
-1
Let b(d) be the second derivative of 0 - 1/10*d**5 - 3*d - 5/12*d**4 - 1/2*d**2 - 2/3*d**3. Solve b(l) = 0.
-1, -1/2
Let s(m) be the second derivative of 1/12*m**4 + 1/2*m**3 + m**2 - 3*m + 0. Factor s(t).
(t + 1)*(t + 2)
Let f(z) be the second derivative of z**7/105 - z**5/10 + 4*z**3/15 - 22*z. Let f(t) = 0. Calculate t.
-2, -1, 0, 1, 2
Let f be 33/90 - (-69)/230. Solve 0*p**3 + 2/3*p**2 + 0 - f*p**4 + 0*p = 0.
-1, 0, 1
Let h(n) be the first derivative of 9*n**5/10 + 7*n**4/8 - 11*n**3/6 - 7*n**2/4 + n - 14. Solve h(o) = 0 for o.
-1, 2/9, 1
Let p = 3 + 0. Let k(y) be the second derivative of -7/3*y**4 + 0 + 0*y**2 - 2/3*y**p + y - 49/20*y**5. Factor k(x).
-x*(7*x + 2)**2
Let f(a) be the first derivative of -a**4 + 7*a**3/3 - a**2 - a + 4. Let f(d) = 0. What is d?
-1/4, 1
Let s = -64 + 68. Let v(f) be the third derivative of 0 + 3*f**2 - 7/30*f**s + 0*f + 49/300*f**5 + 2/15*f**3. Find k, given that v(k) = 0.
2/7
Suppose 5*u - 3*v - 3 = 12, 3*u - 9 = -5*v. Factor -6*a**2 + u*a + 6*a**3 - a + 2*a**4 - a**4 - 3*a**4.
-2*a*(a - 1)**3
Let p = -62 + 64. Factor -2/7*i + 0 + 1/7*i**p.
i*(i - 2)/7
Let a = -6 - -8. Let i = -12/7 - -31/14. Find d, given that -i*d**a + 0*d + 1/2 = 0.
-1, 1
Factor -1 + 2*q + 7 + 3*q**2 + 7*q.
3*(q + 1)*(q + 2)
Suppose -4*h = 4*h. Let j(p) be the third derivative of 2/175*p**7 + 0*p**3 + 1/560*p**8 + 1/25*p**5 + h*p + 0 + 4*p**2 + 3/100*p**6 + 1/40*p**4. Factor j(k).
3*k*(k + 1)**4/5
Let j(v) = v**4 + v**3. Let h be -1 + 1 - (3 + -2). Let r be 20/70 - (-23)/(-7). Let m(c) = -5*c**4 - 3*c**3 + 2*c**2. Let u(f) = h*m(f) + r*j(f). Factor u(n).
2*n**2*(n - 1)*(n + 1)
Let q be (-15)/(-10)*(-4)/2. Let y be q + 0 + 5 + -2. Factor -2/3*k**3 + 0*k + y - 1/3*k**2.
-k**2*(2*k + 1)/3
Let v(j) be the first derivative of 3*j**4/4 - 8. Solve v(w) = 0.
0
Let w(m) be the first derivative of 6 + 1/2*m**4 + 2/3*m**3 - 2*m - m**2. Suppose w(n) = 0. What is n?
-1, 1
Factor -10*b**2 - 3*b**5 + 4*b**2 - 44*b**3 + 29*b**3 - 12*b**4.
-3*b**2*(b + 1)**2*(b + 2)
Let f(x) = 3*x**3 - 18*x**2 - 3*x. Let k(a) = 2*a**3 - 9*a**2 - a. Let r be (-1 + -5)/(12/18). Let q(p) = r*k(p) + 5*f(p). Factor q(y).
-3*y*(y + 1)*(y + 2)
Let r(l) be the third derivative of l**5/105 - 5*l**4/42 - 8*l**2. Determine q, given that r(q) = 0.
0, 5
Let n(l) = -6*l**2 - 17*l + 8. Let f(s) = 2*s**2 + 6*s - 3. Let q(g) = -8*f(g) - 3*n(g). Let k be q(-2). Factor -o**2 + o - k*o + 3*o.
-o*(o - 2)
Let s(j) be the second derivative of j**6/1440 - j**5/160 - 4*j**3/3 - 5*j. Let r(u) be the second derivative of s(u). Suppose r(c) = 0. Calculate c.
0, 3
Let h(i) be the third derivative of 0 + 0*i**3 - 1/72*i**4 + 2*i**2 - 1/180*i**5 + 0*i. Factor h(y).
-y*(y + 1)/3
Suppose 0 = 86*n - 83*n. Find p, given that 0*p**2 + 0 + n*p + 2/7*p**3 = 0.
0
Suppose -2*n + 2*x - 3*x - 2 = 0, 3*x = 5*n - 6. Suppose n = 3*o - 7 - 5. Find f such that 0*f + 0 - 2/9*f**5 + 2/3*f**o + 2/9*f**2 - 2/3*f**3 = 0.
0, 1
Factor 15*b + 6*b**2 - 4*b**3 - 2*b**3 - 9*b**3 - 5*b**4 - 20 + 19*b**2.
-5*(b - 1)**2*(b + 1)*(b + 4)
Let x(z) = z**4 - 6*z**3 + 10*z**2 + 6*z - 5. Let n(j) = 4*j**4 - 18*j**3 + 31*j**2 + 18*j - 14. Let u(c) = -2*n(c) + 7*x(c). Factor u(s).
-(s - 1)**2*(s + 1)*(s + 7)
Let s(w) be the first derivative of w**3/2 + 3*w**2/4 + 6. Suppose s(r) = 0. Calculate r.
-1, 0
Let d(i) = -5*i**3 + 9*i**2 + 3*i + 7. Let r = 0 - -2. Let z(q) = 7*q - 7*q - q**3 + q**r + 1. Let n(t) = d(t) - 6*z(t). Factor n(u).
(u + 1)**3
Let z = -2 - -3. Suppose 2*r - 3 = z. Factor -2*n + 17*n**4 + 13*n**r + 6*n**4 - 8*n**5 + n**5 - 27*n**3.
-n*(n - 1)**3*(7*n - 2)
Let i(p) = 1. Let f(y) = -5*y**2 - 7. Let n(m) = 2*m**2 + 2 + 0 - m**2. Let r(a) = -2*f(a) - 9*n(a). Let c(b) = -3*i(b) - r(b). Factor c(q).
-(q - 1)*(q + 1)
Let w be (-2 + 4)*10/(-4). Let q be (3/4)/(w/(-20)). Factor 2*d**q - 5*d**3 - 2*d**4 + d**3.
-2*d**3*(d + 1)
Let -40/3 - 2/3*k**3 - 2/3*k**2 + 32/3*k = 0. Calculate k.
-5, 2
Let o(p) be the first derivative of p**6/200 + p**5/75 - p**4/120 - p**3/15 - p**2 + 2. Let t(i) be the second derivative of o(i). Solve t(f) = 0.
-1, 2/3
Let s(k) = -4*k + 12. Let a be s(3). Let m(f) be the second derivative of a + f - 1/12*f**3 + 5/48*f**4 - 3/80*f**5 + 0*f**2. Suppose m(h) = 0. Calculate h.
0, 2/3, 1
Let a be ((-2)/(-1 + 2))/(-2 - -1). Find n such that -8/11 + 6/11*n**a + 8/11*n**3 + 2/11*n**4 - 8/11*n = 0.
-2, -1, 1
Let v = -89458 - -808096/9. Let m = v - 330. Solve -m*a - 2/9*a**2 + 0 + 2/9*a**3 = 0 for a.
-1, 0, 2
Suppose 0*i - 2 = -i. Factor 2*g**i + 15*g - 15*g - 2*g**4 + 2*g**5 - 2*g**3.
2*g**2*(g - 1)**2*(g + 1)
Suppose 11 = 2*v + 5*u + 28, -4*u = 20. Let q(c) = c**3 - 3*c**2 - 4*c + 2. Let m be q(v). Factor 5*l + l**3 + l**m - 3 + 3*l**2 + 5.
(l + 1)**2*(l + 2)
Let k(n) = 5*n**2 - n + 2. Let p(z) be the second derivative of z**4/12 + z**3/6 + z. Let w = 21 - 22. Let r(y) = w*k(y) + 3*p(y). Factor r(g).
-2*(g - 1)**2
Let o = -39/7 - -209/35. Let l(j) = -j**2 + 3*j + 3. Let t be l(3). Suppose 2/5 + 2/5*z**t - o*z - 2/5*z**2 = 0. What is z?
-1, 1
Suppose -t + 135 = 2*t. Let x be t/12 - 15/20. Factor 1/3 - 4/3*b**2 - 2/3*b + 2/3*b**x + b**4.
(b - 1)*(b + 1)**2*(3*b - 1)/3
Let q be 0 - 44/(-8)*2. Suppose -2*p = -3*u + q, 0 = 2*p + 2 - 0. Factor 0 + 1/3*o**u - 2/3*o**2 + 1/3*o.
o*(o - 1)**2/3
Let m(n) be the second derivative of 0*n**2 - 2/21*n**3 - n + 0 - 1/70*n**5 + 1/14*n**4. Factor m(f).
-2*f*(f - 2)*(f - 1)/7
Let x be ((-3)/12)/(2/(-16)). Let j(m) be the first derivative of 0*m - 1/8*m**4 + 1/6*m**3 + 0*m**2 - x. Factor j(z).
-z**2*(z - 1)/2
Let 694 - 694 - 10*r + 5*r**2 = 0. Calculate r.
0, 2
Let q = 29/106 - -12/53. Factor 5/2*v - 2*v**3 - 2*v**4 + v**2 + 1 - q*v**5.
-(v - 1)*(v + 1)**3*(v + 2)/2
Let i(h) = -2*h**2 + 3*h - 3*h - 2. Let f = 2 + -3. Let k(r) = -r**3 + r