d**2 = 0.
-3/5, 1
Factor -30 - 21*h**2 - 3*h**3 + 76*h - 26 + 20*h**2 - 15*h**2 - h**3.
-4*(h - 2)*(h - 1)*(h + 7)
Let z(g) be the first derivative of -3*g**6/40 - g**5/5 + g**4/8 + g**3 - 2*g**2 + 12. Let n(s) be the second derivative of z(s). Factor n(w).
-3*(w + 1)**2*(3*w - 2)
Determine d, given that 1/4*d**5 + 0 + 5/4*d**4 + 7/4*d**2 + 1/2*d + 9/4*d**3 = 0.
-2, -1, 0
Let t be ((-4)/(-70))/(1264/4424). Factor 0 - t*r + 1/5*r**3 - 1/5*r**2 + 1/5*r**4.
r*(r - 1)*(r + 1)**2/5
Let g be ((-2)/12)/(4/(-32)). Let q(b) = 5*b**2 - 342*b + 139. Let a be q(68). Determine d, given that 0 + 2/3*d**a - g*d + 2/3*d**2 = 0.
-2, 0, 1
Suppose 2*d + 15 = 7*d. Let s(i) be the second derivative of 0 + 1/7*i**2 + 0*i**d - 1/21*i**4 + 0*i**5 + 1/105*i**6 + 5*i. Factor s(r).
2*(r - 1)**2*(r + 1)**2/7
Let i = 55/2 - 27. Let u = -142 + 575/4. Find o such that i + 5/4*o**2 + u*o = 0.
-1, -2/5
Suppose 8 = -2*p + 6*p. Suppose -3*z = -5*f + 10, -p*z = -z - 4*f + 8. Let z*c + 2/3*c**2 - 4/3*c**3 + 2/3*c**4 + 0 = 0. Calculate c.
0, 1
Let h = -18 - -20. Suppose 5*k - 5 = -z, -5*k + 4*z + 16 + 14 = 0. Factor 9*m**3 - k*m**3 + 3*m**2 + 5*m**4 - 3*m**2 + 2*m**h.
m**2*(m + 1)*(5*m + 2)
Let h(t) be the first derivative of 1/2*t**2 + 5 + 3*t + 1/3*t**3 + 1/12*t**4. Let o(j) be the first derivative of h(j). Factor o(m).
(m + 1)**2
Let 4/3*z**3 + 0 - 1/3*z**2 - z = 0. Calculate z.
-3/4, 0, 1
Let t(n) be the second derivative of -2*n**3 + n**2 - 1/20*n**5 - 1/2*n**4 + 0 + 7*n. Let d(i) be the first derivative of t(i). Solve d(w) = 0 for w.
-2
Suppose -5*i = 378 - 398. Let n(d) be the second derivative of -4*d + 8/3*d**3 + 0*d**2 + 0 - 4/3*d**i + 4/15*d**6 + 2/21*d**7 - 3/5*d**5. Factor n(y).
4*y*(y - 1)**2*(y + 2)**2
Let y be -215 + -3 + 1 + 0. Let m = y + 1955/9. Solve -2/9*p + 0 - m*p**2 = 0.
-1, 0
Let y(k) be the third derivative of -k**7/945 - k**6/180 + k**5/54 + k**4/36 - 4*k**3/27 + 11*k**2 + 1. Solve y(n) = 0 for n.
-4, -1, 1
Suppose 0 = -w + 2. Let t be 5 + w*2/(-4). Factor -5*b**3 + 0*b**3 - t + 0*b - 4 + 6*b**2 + b**4 + 4*b.
(b - 2)**3*(b + 1)
Let g(i) = -i**3 - 1. Let o(f) = 4*f - 8 - 9 + 0 - f**2 + 15 - 7*f**3. Let v(n) = -6*g(n) + o(n). Solve v(q) = 0.
-2, -1, 2
Let o be 9/((-6)/21 + 201/42). Factor 1/2*c**3 - 1 - 1/2*c + c**o.
(c - 1)*(c + 1)*(c + 2)/2
Let c = 33 - 30. Suppose -2217 + 2217 + c*g**3 - 6*g**2 - 9*g = 0. What is g?
-1, 0, 3
Let v(b) be the second derivative of -1/8*b**3 + 0 + 3/8*b**2 + 6*b - 1/16*b**4 + 3/80*b**5. Factor v(x).
3*(x - 1)**2*(x + 1)/4
Let q(w) = 5*w - 18. Let j be q(4). Suppose 4*i**3 - 4*i**4 - 6*i**3 + i**j - 2*i + 3*i**4 + 4*i**3 = 0. What is i?
-1, 0, 1, 2
Suppose -t = -2*x + 173 - 171, 9*t = 4*x - 18. Determine u, given that x + 2/11*u**2 + 4/11*u = 0.
-2, 0
Let o be -4*(27/14)/(-27). Suppose o*l**2 + 2/7 - 4/7*l = 0. What is l?
1
Let z(y) be the second derivative of y**5/5 - 4*y**4 + 24*y**3 - 64*y**2 + 168*y. Solve z(b) = 0 for b.
2, 8
Let y = 1720 + -5156/3. Determine k so that -y*k - 13/2*k**3 + 0 - 10/3*k**4 - 5*k**2 - 1/2*k**5 = 0.
-4, -1, -2/3, 0
Let p be -18*(-1678*3/(-1170) - 4). Let w = 28/5 + p. What is n in -w + 14/13*n**2 + 4/13*n + 8/13*n**3 = 0?
-1, 1/4
Let t(v) be the first derivative of -11/5*v**4 - 8 + 8/5*v + 2/5*v**5 + 22/5*v**3 - 4*v**2. Solve t(a) = 0.
2/5, 1, 2
Factor -12 - 6*o - 14*o**2 + 6*o + 18*o**2 - 8*o.
4*(o - 3)*(o + 1)
Suppose 4*u - 4*f = 40, -2*u + 4*f = -8 - 20. Factor u + 0*x - 3/2*x**2.
-3*(x - 2)*(x + 2)/2
Solve 0 + 105/2*q**2 - 63/4*q**3 - 36*q - 3/4*q**4 = 0.
-24, 0, 1, 2
Let u be 6/4 - (-3)/(-6). Let d = u - -1. Suppose -6 + 2 + 2*h - 4*h**2 + h**d + 5*h**2 = 0. Calculate h.
-2, 1
Let c(k) = -5*k**4 + 205*k**3 - 495*k**2 - 95*k + 655. Let m(f) = f**4 - 51*f**3 + 124*f**2 + 24*f - 164. Let j(i) = -4*c(i) - 15*m(i). Factor j(p).
5*(p - 8)*(p - 2)**2*(p + 1)
Let n(m) = 50*m**2 - 15*m + 5. Let s(f) = 25*f**2 - 7*f + 2. Let t(x) = 2*n(x) - 5*s(x). Suppose t(c) = 0. Calculate c.
0, 1/5
Let v(c) be the first derivative of -4*c**3/9 + 13*c**2/3 + 14*c/3 - 89. Find f such that v(f) = 0.
-1/2, 7
Let l(w) = -5*w**3 - 188*w**2 - 1621*w + 1799. Let c(z) = z**2 + 2*z + 2. Let h(m) = 3*c(m) + l(m). Let h(s) = 0. Calculate s.
-19, 1
Let l(t) be the second derivative of -t**4/42 - 8*t**3/3 - 55*t**2/7 + 87*t + 1. Factor l(z).
-2*(z + 1)*(z + 55)/7
Let b(o) = o**2 - 32*o + 91. Let l be b(29). Let x(p) be the first derivative of 4/3*p**3 - 4*p**2 + 0*p + 6 + p**l. Factor x(s).
4*s*(s - 1)*(s + 2)
Factor 75*c**2 - 42*c + 60*c + 22*c + 9*c**4 + 30*c**3 - 14*c**4.
-5*c*(c - 8)*(c + 1)**2
Let q = 1 - -8. Let n = q + -6. Factor -10*h**n + h**3 + 4*h**3 + 20*h.
-5*h*(h - 2)*(h + 2)
Let q(z) be the third derivative of -z**7/735 - 3*z**6/140 - 2*z**5/15 - 3*z**4/7 - 16*z**3/21 + 2*z**2 + 51*z. Determine m, given that q(m) = 0.
-4, -2, -1
Let g = -25 + 44. Let d = g - 16. Find s such that -d*s - 2*s + 2*s**2 + 4 + 0 - s = 0.
1, 2
Factor -8*i**3 + 37*i**3 - 30 - 17*i + 14*i**2 - 28*i**3.
(i - 2)*(i + 1)*(i + 15)
Let c(l) be the first derivative of l**7/14 - 3*l**6/10 + 3*l**5/10 - 4*l - 12. Let i(g) be the first derivative of c(g). Factor i(k).
3*k**3*(k - 2)*(k - 1)
Let y = -86 + 66. Let b be y/(-100) + (-6)/(-70). Suppose 0*u - 10/7*u**3 - 8/7*u**4 - 4/7*u**2 - b*u**5 + 0 = 0. What is u?
-2, -1, 0
Let x(l) be the first derivative of -4/3*l**2 - 16/9*l - 8 + 4/3*l**3 - 5/18*l**4. Factor x(n).
-2*(n - 2)**2*(5*n + 2)/9
Let a(o) be the second derivative of -1/30*o**5 + 4/9*o**3 + 0 + 1/18*o**4 - 4/3*o**2 + 14*o. Find v such that a(v) = 0.
-2, 1, 2
Factor -n**2 - 1/4*n + 0.
-n*(4*n + 1)/4
Let f(l) be the first derivative of 5*l**6/6 + l**5 - 35*l**4/4 - 5*l**3/3 + 15*l**2 + 166. Suppose f(y) = 0. What is y?
-3, -1, 0, 1, 2
Let s(w) = 39*w**2 - 3*w - 2. Let x be s(-1). Suppose -t + 42 = x. Factor 0 + 4/3*h**2 + 0*h**4 - t*h**3 + 0*h + 2/3*h**5.
2*h**2*(h - 1)**2*(h + 2)/3
Let b(p) be the second derivative of p**6/75 - p**5/50 - p**4/30 + p**3/15 - 916*p. Solve b(s) = 0.
-1, 0, 1
Let v(m) be the second derivative of m**5/20 - m**4/6 - 2*m**3/3 + 3*m**2 + 8*m. Let a be v(3). Factor -2*s - 9*s**2 - s + 4*s**4 - 9*s**a - 11*s**4 + 4*s**4.
-3*s*(s + 1)**3
Let q(x) = x**2 - x. Suppose 4*z - 8 = 4*o, 0 = -4*o - 5*z + 1. Let p(i) = 2*i**3 + 8*i**2 + 26*i + 12. Let w(t) = o*p(t) - 4*q(t). Factor w(k).
-2*(k + 1)*(k + 2)*(k + 3)
Let k(x) = 17*x**2 - 19*x - 6. Let l(o) = 3*o**2 + o - 1. Let p(y) = k(y) - 6*l(y). Factor p(v).
-v*(v + 25)
Let o be 7/(-42) + (16/(-4))/(-8). Factor 1/6*p**3 + 0 + o*p**2 + 1/6*p.
p*(p + 1)**2/6
Let y(k) be the first derivative of 2*k**3 + 72*k + 1/12*k**4 + 18*k**2 - 11. Factor y(v).
(v + 6)**3/3
Suppose -c = 14*f - 9*f - 5, -4*c - 10 = 5*f. Factor 2*w - 4 - 1/4*w**f.
-(w - 4)**2/4
Let h = -27797 + 194612/7. Factor -15*x**2 + h*x**3 + 75/7*x - 3/7*x**4 + 0.
-3*x*(x - 5)**2*(x - 1)/7
Determine a so that 2 + 14/9*a**2 - 2/9*a**3 - 10/3*a = 0.
1, 3
Let h = -34 - -36. Factor -355*d**2 - 148*d**h + 42*d**2 - 208*d - 16 - 215*d**2.
-4*(13*d + 2)**2
Let r = 28 + -26. Solve -3*h**2 + 3*h**r + 3*h**3 + 21*h - 15*h**2 - 9 = 0 for h.
1, 3
Let s(t) = -10*t**3 + 178*t**2 - 736*t + 388. Let x(n) = -20*n**3 + 359*n**2 - 1472*n + 777. Let k(j) = 9*s(j) - 4*x(j). Solve k(m) = 0 for m.
3/5, 8
Let v be (-14)/(-49) - ((-176)/(-77) + -4). Factor -2/3*i + 1 - 1/3*i**v.
-(i - 1)*(i + 3)/3
Let c(a) be the second derivative of a**6/120 - 7*a**5/80 + a**4/4 + a**3/6 - 2*a**2 + 28*a - 6. Determine q, given that c(q) = 0.
-1, 2, 4
Suppose -2*q + 359 = 3*q + g, 3*q = -4*g + 229. Let x be 1/1*(-7 + 7) - -3. Factor -1 - x - 4*y**2 - 79*y + q*y.
-4*(y + 1)**2
Let v be (-378)/98 + 2/(-14). Let y be v/(-3)*15/5. Suppose 2 - 3*r**4 - y*r**5 + 8*r**4 - 155*r**3 - 7*r**2 + 166*r**3 - 7*r = 0. Calculate r.
-1, 1/4, 1, 2
Let n be (-124)/(-56) - (-87)/(-406). Determine r so that 2/7*r**n - 2*r**4 + 4/7*r**3 + 0*r + 0 + 8/7*r**5 = 0.
-1/4, 0, 1
Let u = -45 - -48. Solve 6*m + 972*m**4 + u*m**2 - 3*m - 3*m**3 - 975*m**4 = 0.
-1, 0, 1
Determine r, given that -12 - 534/5*r - 1386/5*r**2 + 96/5*r**4 - 816/5*r**3 = 0.
-1, -1/4, 10
Let j(s) = 35*s**2 + 207*s - 8. Let g(u) = 137*u**2 + 830*u - 31. Let f(c) = -4*g(c) + 18*j(c). Determine r so that f(r) = 0.
-5, 2/41
Let h = 28 - 26. Determine g so that -5*g**2 - g**2 + 4 + g**h + g**2 = 0.
-1, 1
Let 