hat o(a) = 0.
-1/3, 0, 2
Solve -11/4*c**4 + 0 + 81/2*c - 117/2*c**2 + 165/8*c**3 + 1/8*c**5 = 0.
0, 1, 6, 9
Let u = -19 - -39. Suppose 4*s + u - 32 = 0. Factor 4*x**2 + 3*x**3 + 2*x**3 + s*x**3 + 4*x**4.
4*x**2*(x + 1)**2
Let f = -1858 + 1860. Factor 2/9*k**f + 4/9 + 2/3*k.
2*(k + 1)*(k + 2)/9
Let n(a) be the third derivative of -2*a**7/105 - 9*a**6/10 - 56*a**5/5 + 98*a**4/3 + 136*a**2. Factor n(k).
-4*k*(k - 1)*(k + 14)**2
Suppose -h + p - 28 = 0, -5*h + 4*p = -3*h + 64. Let q = h - -27. Solve -2/9*m**q + 2/9*m + 0*m**2 + 1/9 - 1/9*m**4 = 0 for m.
-1, 1
Let s = -7932 - -23804/3. Factor 1 + s*l - l**2.
-(l - 3)*(3*l + 1)/3
Suppose -8/11*z**4 + 28/11*z**2 - 2/11*z**5 + 16/11*z + 6/11*z**3 + 0 = 0. What is z?
-4, -1, 0, 2
Suppose 3*v - 4 = -3345*j + 3349*j, 0 = 2*j - v. Factor 2/3*o**2 + j*o + 0.
2*o*(o + 3)/3
Suppose 0 = 12*t - 16*t + 80. Determine x, given that 5*x**2 - 2*x**2 + 20*x - 8*x**2 - t = 0.
2
Let k = 509 - 347. Factor 82*s - 3*s**2 + 2*s**2 + 76*s - k*s + 5.
-(s - 1)*(s + 5)
Let m be (-2)/(-4) + (-1240)/(-400). Factor -3*p + 3/5*p**2 + m.
3*(p - 3)*(p - 2)/5
Solve 105*y**2 - 102*y**2 + 2*y - 32*y = 0 for y.
0, 10
Let o(m) be the first derivative of m**2/2 - 19. Let n(y) = 15*y**3 - 85*y**2 + 40*y + 25. Let i(f) = -n(f) - 5*o(f). Factor i(r).
-5*(r - 5)*(r - 1)*(3*r + 1)
Suppose 0 = q + 4*q + 25, t + q = -121. Let y = t + 118. Factor 16/5*l - 4/5*l**4 - 24/5*l**y + 16/5*l**3 - 4/5.
-4*(l - 1)**4/5
Let s be 1/1 - (-1 - (6 + -5)). Suppose -2*h - s = -3*h + p, h = 2*p + 4. Factor -4/11*g**h - 2/11*g + 4/11 + 2/11*g**3.
2*(g - 2)*(g - 1)*(g + 1)/11
Suppose -l - 5 = 0, -32 - 11 = -2*z + 5*l. Suppose z*h = 8*h + 4. Determine u, given that -2/11*u**h - 4/11*u**3 + 0 + 0*u + 0*u**2 = 0.
-2, 0
Let n be (-1170)/(-297) - (-9)/((-891)/(-6)). Factor 0 - 2/7*v**3 - 4/7*v**5 + 0*v**2 + 6/7*v**n + 0*v.
-2*v**3*(v - 1)*(2*v - 1)/7
Let f(h) = 3*h**2 - 27*h + 44. Let o be f(7). Factor -2*n**4 - n**o + 0 + 1/2*n**5 + 0*n + 5/2*n**3.
n**2*(n - 2)*(n - 1)**2/2
Suppose 3*b = -2*k + 7 + 4, -15 = -4*k + b. Suppose -4*u = j - 8, -j = 2*u - 4*j - k. What is a in -3/2*a + 1/4*a**u + 9/4 = 0?
3
Let b(k) be the first derivative of -k**8/6720 - k**7/1680 - k**6/1440 + k**3 - 11. Let q(d) be the third derivative of b(d). Solve q(t) = 0.
-1, 0
Let o(l) be the first derivative of -3*l**4/8 + 8*l**3 - 177*l**2/4 + 66*l - 61. Find j such that o(j) = 0.
1, 4, 11
Suppose 62 = -19*w - 71. Let d(b) = -2*b**2 - 11*b + 26. Let g be d(w). Suppose -1/2*p**4 + 1/2*p + p**2 - p**3 + 1/2*p**g - 1/2 = 0. Calculate p.
-1, 1
Let z(p) be the first derivative of -3*p**3 + 141*p**2/2 - 90*p - 521. Factor z(l).
-3*(l - 15)*(3*l - 2)
Let b(k) be the first derivative of -k**4/4 - 11*k**3 - 144*k**2 - 256*k + 615. Suppose b(m) = 0. Calculate m.
-16, -1
Let p = 69473/9 + -7719. What is j in -4/9*j - p*j**2 - 2/9 = 0?
-1
Let a(l) = -l + 6. Let m be a(6). Suppose 7 + 4 = 6*f - 13. Factor -2/5*j**5 + m*j - 2/5*j**f + 2/5*j**2 + 2/5*j**3 + 0.
-2*j**2*(j - 1)*(j + 1)**2/5
What is f in -f**4 + 6*f**4 + 5*f**3 - 5*f**2 + 12424 - 12424 - 5*f = 0?
-1, 0, 1
Let s = 48 + -34. Let z be 20/6 - (s + -12). Determine u, given that -1/3*u**2 + z*u - 4/3 = 0.
2
Solve 0 - 222/17*c + 2/17*c**2 = 0 for c.
0, 111
Let z = 77 - 70. Let p(n) be the third derivative of -n**2 + 0*n**3 + 0*n + 1/120*n**5 + 0*n**4 - 1/160*n**6 + 1/840*n**z + 0. Let p(w) = 0. Calculate w.
0, 1, 2
Let t(r) = -13*r**3 + 238*r**2 + 11880*r + 11671. Let p(m) = -2*m**3 + 3*m**2 + 1. Let s(g) = 14*p(g) - 2*t(g). Suppose s(d) = 0. Calculate d.
-108, -1
Let b(u) = -161*u - 8691. Let n be b(-54). Solve -4/17*q**2 - 30/17*q**n - 32/17*q**5 + 64/17*q**4 + 2/17*q + 0 = 0.
-1/4, 0, 1/4, 1
Let y(a) be the first derivative of 5*a**7/42 - a**6/6 - 3*a**5/4 + 5*a**4/12 + 5*a**3/3 + 25*a + 12. Let j(h) be the first derivative of y(h). Factor j(r).
5*r*(r - 2)*(r - 1)*(r + 1)**2
Let k(w) = -w**2 - 1. Let b(r) be the third derivative of -r**5/5 - 5*r**4/4 + 10*r**3 - 8*r**2. Let j(d) = b(d) - 15*k(d). Factor j(c).
3*(c - 5)**2
Let f(d) be the third derivative of d**8/33600 - d**7/2100 - 37*d**4/24 + 7*d**2. Let b(h) be the second derivative of f(h). Let b(g) = 0. What is g?
0, 6
Let i(n) = -5*n**4 - 2*n**3 - 5*n**2. Let h(a) = 6*a**4 + 3*a**3 + 6*a**2. Let o(x) = 4*h(x) + 5*i(x). Determine b so that o(b) = 0.
0, 1
Let s = -1351/5 - -271. Let k be (-52)/20*(0 - 2). Factor 22/5*f + s - k*f**2.
-2*(f - 1)*(13*f + 2)/5
Let k(p) be the third derivative of 0*p**3 + 1/12*p**5 + 0*p - 1/24*p**6 - 1/42*p**7 + 0*p**4 + 5/336*p**8 + 0 - 16*p**2. Factor k(i).
5*i**2*(i - 1)**2*(i + 1)
Let x(m) be the first derivative of -2*m**5/55 - 9*m**4/22 - 16*m**3/33 - 37. Factor x(j).
-2*j**2*(j + 1)*(j + 8)/11
Let a(p) be the second derivative of p**4/12 - 25*p**3/18 + 4*p**2/3 - 23*p + 2. Factor a(g).
(g - 8)*(3*g - 1)/3
Suppose 11*y + 21 = 18*y. Let x(j) be the second derivative of 0*j**2 + 1/3*j**4 + 1/10*j**5 + 0 + 1/3*j**y - 2*j. Let x(p) = 0. What is p?
-1, 0
Factor -1/7 - 7*s**2 - 2*s.
-(7*s + 1)**2/7
Let p be (-546)/30 + 9 + 10. What is k in 0 - 2/5*k**3 - 6/5*k**2 + p*k - 2/5*k**5 + 6/5*k**4 = 0?
-1, 0, 1, 2
Let o(x) be the second derivative of x**9/7560 + 13*x**4/12 + 6*x. Let k(a) be the third derivative of o(a). Find h such that k(h) = 0.
0
Let p be (2/4)/((-3)/(-18)). Suppose 0 = -2*q - 2*q - 4*f + 24, 2*q - 3*f = -p. Find l such that -6*l**2 - q*l**2 + 3 + 6*l**2 = 0.
-1, 1
Let f(r) be the first derivative of 0*r**2 + 1/36*r**4 - 9 + 4/27*r**3 + 0*r. Let f(p) = 0. Calculate p.
-4, 0
Let u(m) be the second derivative of -m**4/6 - 29*m**3/3 - 28*m**2 + 273*m. Let u(c) = 0. What is c?
-28, -1
Let y(j) be the first derivative of -5*j**3/3 - 10*j**2 - 15*j + 126. Solve y(x) = 0 for x.
-3, -1
Determine o so that 0 + 61/5*o**3 + 18/5*o**4 + 28/5*o + 72/5*o**2 + 1/5*o**5 = 0.
-14, -2, -1, 0
Let g = -3379 + 27197/8. Let d = g - 1453/72. Let -d + 2/9*n**3 - 2/9*n + 4/9*n**2 = 0. What is n?
-2, -1, 1
Let q(p) be the third derivative of 3/11*p**3 + 0 - 1/660*p**6 + 4*p**2 - 1/44*p**4 - 1/66*p**5 + 0*p. Factor q(r).
-2*(r - 1)*(r + 3)**2/11
Let t = 30 + -26. Factor 3*h**2 + t*h - 8*h - 4*h**2 - 4.
-(h + 2)**2
Let w(s) = -14*s**2 - 1171*s + 422. Let t be w(-84). Factor 0*g**3 - 2/7*g**4 + 0*g + 4/7*g**t - 2/7.
-2*(g - 1)**2*(g + 1)**2/7
Factor 0*h + 8*h**2 + 2/9*h**4 + 0 - 8/3*h**3.
2*h**2*(h - 6)**2/9
Let s be 10/8*(-3)/(-5). Let a = -3/17642 - -26469/35284. Factor a*v**2 - s*v**4 + 0 + 3/4*v**3 + 0*v - 3/4*v**5.
-3*v**2*(v - 1)*(v + 1)**2/4
Let o be (3/20)/(2/28*42/12). Determine m, given that -12/5 + o*m**3 + 24/5*m - 3*m**2 = 0.
1, 2
Suppose 0 = -3*s + 95 - 77. Let z(i) be the third derivative of 0*i**4 + 0*i**3 + 1/420*i**5 + 1/420*i**s + 6*i**2 + 0*i + 0 + 1/1470*i**7. Factor z(y).
y**2*(y + 1)**2/7
Let g(n) = 16*n**3 - 34*n**2 + 100*n + 6. Let o(p) = -2*p**3 - p**2 - 1. Let x(j) = -g(j) - 6*o(j). Determine f so that x(f) = 0.
0, 5
Let p(b) be the first derivative of -243*b**6/8 + 837*b**5/20 + 673*b**4/8 - 53*b**3/3 + b**2 + 169. Let p(z) = 0. Calculate z.
-1, 0, 2/27, 2
Let d(x) be the third derivative of -x**8/5040 - x**7/1260 + x**6/90 - 23*x**5/60 + 15*x**2. Let g(o) be the third derivative of d(o). Let g(r) = 0. What is r?
-2, 1
Let f(i) be the second derivative of 5/42*i**3 + 1/210*i**6 + 0 - 1/140*i**5 - 1/7*i**2 - 26*i - 1/28*i**4. Factor f(g).
(g - 1)**3*(g + 2)/7
Suppose 0 = 3*s - 2*s - 8. Suppose 0 = 3*x + f + 3*f + 7, -s = 2*f. Factor 2*h**3 - x*h**2 + 3*h - 4*h**3 + 6 - 4.
-(h - 1)*(h + 2)*(2*h + 1)
Solve -1 - 28*t**4 + 4*t**5 + 64*t - 15 + 35203*t**2 + 76*t**3 - 35303*t**2 = 0 for t.
1, 2
Let x(q) be the third derivative of q**5/60 + q**4/8 - q**3/3 + 11*q**2. Let v(j) = -j + 1. Let a(w) = -2*v(w) - x(w). Factor a(f).
-f*(f + 1)
Let j be (1/3)/((-7)/(-84)). Suppose -2*l - j + 12 = 0. Find f, given that 2*f**l - 4*f**5 - 12*f**3 + 0*f**5 - 4*f**2 - 14*f**4 = 0.
-1, 0
Let s(h) be the first derivative of h**9/1008 - h**8/280 + h**3 + 13. Let m(p) be the third derivative of s(p). Suppose m(u) = 0. Calculate u.
0, 2
Suppose 2*d + 42 = 5*d - 4*b, 2*b - 4 = -d. Suppose -2*p - 2*k + 18 = 0, -1 = -k + 2. Determine z, given that -4*z**2 - d*z - p*z + 4*z = 0.
-3, 0
Let t be (-9 - (-10)/2)/(-2). Factor 1/7*n**t - 4/7*n + 4/7.
(n - 2)**2/7
Let m(p) be the third d