 + -1218. Suppose 2*l - 3 - p*l**2 = 0. What is l?
3
Factor -4802/9 - 2744/9*i - 196/3*i**2 - 56/9*i**3 - 2/9*i**4.
-2*(i + 7)**4/9
Solve 2/7*y**3 + 9126/7*y - 234/7*y**2 - 118638/7 = 0 for y.
39
Let c(j) be the first derivative of -16*j**3/21 - 2*j**2 + 8*j/7 - 17. Factor c(u).
-4*(u + 2)*(4*u - 1)/7
Let l(p) be the second derivative of p**4/20 - 3*p**3/10 + 3*p**2/5 + 5*p + 4. Factor l(b).
3*(b - 2)*(b - 1)/5
Let x(a) = 3*a**2 + 2*a - 9. Suppose 45 = 3*c - 8*c. Let m = c + 8. Let y(k) = -k**2 + k. Let g(i) = m*x(i) - 4*y(i). What is z in g(z) = 0?
3
Suppose -201*o + 27 = -375. Find n, given that -8/11 + 1/11*n**o + 7/11*n = 0.
-8, 1
Suppose -5*h + 8 = 4*w - 24, 0 = -2*w + 2*h - 2. Factor 3/2*o**w + 33/8*o**2 + 0 - 9/8*o.
3*o*(o + 3)*(4*o - 1)/8
Let o(w) be the first derivative of -w**6/24 - 11*w**5/20 - 5*w**4/8 + 53*w**3/6 - 133*w**2/8 + 49*w/4 + 59. Factor o(r).
-(r - 1)**3*(r + 7)**2/4
Suppose 3*l + 6 = -3*l. Let a(q) = -q - 1. Let t(p) = 5*p**2 + 49*p + 124. Let f(h) = l*a(h) + t(h). Find b, given that f(b) = 0.
-5
Let w = 3994/3 - 1331. Factor -w*j - 1/3 + 1/3*j**2 + 1/3*j**3.
(j - 1)*(j + 1)**2/3
Let w = -4335 - -4338. Factor -3/2*v**w + 0 + 0*v**2 + 3/2*v.
-3*v*(v - 1)*(v + 1)/2
Let i(f) = -2*f**2 - 19*f + 12. Let m be i(-10). Factor 1/6*a**3 + 0 + 1/3*a**m + 1/6*a.
a*(a + 1)**2/6
Let h = -31/19 - -355/171. Let i = 82424/9 + -9158. Factor 2/3*q - h - i*q**2.
-2*(q - 2)*(q - 1)/9
Suppose -5*t = -5*g, 0 = -4*g + t + t. Suppose 2*w = -g*w. What is d in -4*d**3 + 8*d**3 + w*d**3 + 4*d - 8*d**2 = 0?
0, 1
Find o, given that -26/3*o - 2/3*o**5 - 4/3*o**2 + 14/3 - 10/3*o**4 + 28/3*o**3 = 0.
-7, -1, 1
Let x(b) = 6*b**3 - 63*b**2 + 84*b - 27. Let z(d) = 4*d**3 - 42*d**2 + 56*d - 18. Suppose 0 = -12*h - 5*h + 136. Let u(m) = h*z(m) - 5*x(m). Factor u(y).
(y - 9)*(y - 1)*(2*y - 1)
Let b(a) = -3*a - 12. Let c be b(-5). Find v, given that 9*v + 6 + 6*v**c + v**3 - 10*v**3 + 0*v**3 = 0.
-1, 2
Find t such that -13*t**3 + 26*t**3 - 12*t**2 - t**2 - 5*t**2 - 11*t**3 = 0.
0, 9
Let d(q) be the third derivative of -2*q**7/735 + 11*q**6/210 + 2*q**5/5 + 2*q**4/21 - 16*q**3/3 - 380*q**2. Find m such that d(m) = 0.
-2, 1, 14
Solve 609*j**2 + 13 - 2 - 66*j + 147*j**3 + 618*j + 133 = 0 for j.
-3, -4/7
Let a be 0 - (-7 + 4 + 3). Let h(o) be the second derivative of 0*o**3 + 6*o + a + 1/12*o**4 - 1/2*o**2. Factor h(k).
(k - 1)*(k + 1)
Let c be 1 + 2/(((-8)/(-3))/4). Factor 6 + 2*g**2 - 4*g**2 + c*g + 0*g**2.
-2*(g - 3)*(g + 1)
Let l = 15 + -20. Let f(r) = -7*r**4 + 5*r**3 + r**2 + r - 6. Let g(b) = -6*b**4 + 4*b**3 + b**2 + b - 5. Let d(o) = l*f(o) + 6*g(o). Solve d(z) = 0 for z.
-1, 0, 1
Find y, given that 321/5*y**2 + 3/5*y**4 - 264/5*y - 12*y**3 + 0 = 0.
0, 1, 8, 11
Let n(z) be the third derivative of -3/10*z**3 + 0*z + 18*z**2 + 1/20*z**4 + 0 - 1/300*z**5. Factor n(x).
-(x - 3)**2/5
Let m = 11474 - 11471. Factor -14/3*u**2 + 98/9*u**m - 8/9 - 16/3*u.
2*(u - 1)*(7*u + 2)**2/9
Let d(m) be the third derivative of m**5/100 - 5*m**4/8 - 13*m**3/5 - 299*m**2. Suppose d(u) = 0. What is u?
-1, 26
Let n = 1457 - 1453. Let 4/3*t**3 + 2/9*t - 8/9*t**n + 0 - 8/9*t**2 + 2/9*t**5 = 0. What is t?
0, 1
Let g(h) be the first derivative of 5 + 2/5*h**2 + 2*h + 1/10*h**3 - 1/60*h**4. Let x(s) be the first derivative of g(s). Factor x(j).
-(j - 4)*(j + 1)/5
Let t(q) be the third derivative of -q**5/16 - 7*q**4/4 - 11*q**3/8 - 138*q**2. Find p, given that t(p) = 0.
-11, -1/5
Let g(x) = 8*x**4 - 2*x**3 - 19*x**2 - 21*x. Let s(h) = -h**4 + h**3 - h**2 - 3*h. Let b(q) = -g(q) - 5*s(q). Factor b(u).
-3*u*(u - 3)*(u + 2)**2
Let q(j) be the first derivative of -j**8/2100 - j**7/525 + j**6/450 + j**5/75 - 2*j**3 - 11. Let h(n) be the third derivative of q(n). Factor h(p).
-4*p*(p - 1)*(p + 1)*(p + 2)/5
Let o(s) = -29*s**3 - 503*s**2 + 649*s - 132. Let x(i) = 14*i**3 + 251*i**2 - 325*i + 66. Let q(c) = -2*o(c) - 5*x(c). Factor q(m).
-3*(m - 1)*(m + 22)*(4*m - 1)
Let x(q) = -q**2 + q + 1. Let p(f) = -5*f**3 - 16*f**2 + 55*f - 8. Let r(j) = p(j) - 2*x(j). Let r(c) = 0. What is c?
-5, 1/5, 2
Let d = 128 - 128. Let q(w) be the first derivative of 2/13*w**2 + d*w - 2/39*w**3 + 2. Determine t so that q(t) = 0.
0, 2
Let p(s) = 2*s**2 - 10*s - 30. Let q be p(10). Find b, given that -115*b - 5*b**3 - b**3 - 130*b + q*b**2 + b**3 = 0.
0, 7
Let l(m) = 4*m**3 - 12*m**2 + 4*m + 22. Let f(h) = 13*h**3 - 36*h**2 + 11*h + 67. Let p(c) = 2*f(c) - 7*l(c). Factor p(j).
-2*(j - 5)*(j - 2)*(j + 1)
Let k = -2858/3 - -1907/2. Let 5/6 + 1/6*n**3 - k*n**2 - 1/6*n = 0. Calculate n.
-1, 1, 5
Let q(f) be the third derivative of -f**8/504 - 4*f**7/315 + f**6/10 - 2*f**5/9 + 7*f**4/36 - 81*f**2. Factor q(h).
-2*h*(h - 1)**3*(h + 7)/3
Suppose 46*q - 29*q = 34. Solve 1/7*h**5 + 0*h + 0*h**3 - 1/7*h**4 + 0 + 0*h**q = 0 for h.
0, 1
Let k(q) be the second derivative of -q**6/50 + 39*q**5/100 - 12*q**4/5 + 18*q**3/5 + q - 62. Factor k(d).
-3*d*(d - 6)**2*(d - 1)/5
Let t(b) = b**2 + 6*b - 41. Let d be t(-10). Let o(r) = 1. Let n(i) = -3*i**2 + 9*i + 3. Let f(h) = d*n(h) - 9*o(h). Factor f(y).
3*(y - 4)*(y + 1)
Let p(z) be the first derivative of -15*z**4/8 - 349*z**3/2 - 18165*z**2/4 + 3675*z/2 - 794. Factor p(s).
-3*(s + 35)**2*(5*s - 1)/2
Let a(p) be the third derivative of 0*p - 13/18*p**4 + 38/315*p**7 + 41/360*p**6 + 0 - 4/9*p**3 + 1/48*p**8 - 7*p**2 - 13/30*p**5. Solve a(s) = 0.
-2, -1/3, -2/7, 1
Let p(x) = -x**2 + 7*x - 4. Let k(d) = d**4 - 2*d**3 - 2*d**2 + d. Let u(h) = 3*k(h) + 3*p(h). Factor u(g).
3*(g - 2)*(g - 1)**2*(g + 2)
Let d(i) = -i**2 + 30*i + 79. Let g = 16 + -12. Let h(x) = x**2 - 60*x - 157. Let y(p) = g*h(p) + 7*d(p). Find r such that y(r) = 0.
-5
Determine v so that 0 - 47916*v**2 - 395307*v - 2178*v**3 - 44*v**4 - 1/3*v**5 = 0.
-33, 0
Let f = -513 - -41041/80. Let a(v) be the third derivative of 1/840*v**7 + 0*v + 0 - 1/12*v**3 - 1/480*v**6 + 5/96*v**4 - 7*v**2 - f*v**5. Factor a(x).
(x - 1)**3*(x + 2)/4
Let l(f) = -125*f**3 + 225*f**2 + 101*f - 237. Let a(t) = -500*t**3 + 900*t**2 + 405*t - 950. Let n(r) = -4*a(r) + 15*l(r). Let n(v) = 0. What is v?
-1, 7/5
Let g(k) = -10*k - 12. Let d be g(-2). Let z be (1/(-18))/((-2)/d). Factor 2/3*x + 4/9 + z*x**2.
2*(x + 1)*(x + 2)/9
Let c(k) be the first derivative of k**5/390 - 5*k**4/156 + 6*k**2 - 31. Let z(s) be the second derivative of c(s). Find i such that z(i) = 0.
0, 5
Let z(k) = -k**3 - 69*k**2 - 135*k - 65. Let m be z(-67). Let f(a) be the first derivative of -8 - 1/2*a**4 + m*a + a**2 - 2/3*a**3. Find v such that f(v) = 0.
-1, 1
Let u(c) be the third derivative of c**6/40 - c**5/5 + c**4/8 + 3*c**3 - 39*c**2 + 1. Factor u(j).
3*(j - 3)*(j - 2)*(j + 1)
Suppose 28 = -11*b - 38. Let t be (-14)/b - 2/6. Factor 1/3*q**t - 2/3 + 1/3*q.
(q - 1)*(q + 2)/3
Let d(r) be the first derivative of r**6/24 + 51*r**5/20 + 97*r**4/8 + 143*r**3/6 + 189*r**2/8 + 47*r/4 - 399. Let d(c) = 0. What is c?
-47, -1
Let c(d) be the second derivative of -d**7/420 - d**6/300 + 7*d**5/100 - 13*d**4/60 + 19*d**3/60 - d**2/4 - 64*d + 1. Factor c(g).
-(g - 1)**4*(g + 5)/10
Let v(i) be the third derivative of -i**6/135 + 761*i**5/270 - 18145*i**4/54 + 9025*i**3/27 + i**2 - 306*i. Let v(u) = 0. What is u?
1/4, 95
Let c(s) be the first derivative of 17 - 1/6*s**4 + 1/3*s**2 + 0*s**3 - 1/15*s**5 + 1/3*s. Factor c(j).
-(j - 1)*(j + 1)**3/3
Suppose 6*a - 55 = a. Let v be -3 + 2 + -2 + 9. Factor -a*o + 0*o + v*o**2 + 1 + 3 - 3*o.
2*(o - 2)*(3*o - 1)
Let k = -29 - -31. Solve 2*o**2 + 0*o**k + 2*o**2 - 4*o = 0 for o.
0, 1
Let d(y) = 5*y - 1. Let w be d(1). Suppose -w = v - 12. Factor -2*h**2 - 3*h - 5*h - v + 0*h**2.
-2*(h + 2)**2
Let s(r) be the first derivative of -r**6/14 + 36*r**5/35 + 117*r**4/28 - 398*r**3/7 - 2610*r**2/7 - 5400*r/7 - 78. Suppose s(k) = 0. Calculate k.
-3, -2, 10
Suppose -3*f = -3*p - 27, -6*f + 2*p + 43 = 17. Factor 42/5*z - 147/5 - 3/5*z**f.
-3*(z - 7)**2/5
Let h(l) be the second derivative of l**4/12 - l**3/3 - 3*l**2/2 - l + 56. Factor h(v).
(v - 3)*(v + 1)
Let v(t) = 13*t**3 + 33*t**2 + 261*t - 289. Let b(l) = 11*l**3 + 33*l**2 + 260*l - 289. Let d(k) = -6*b(k) + 5*v(k). Solve d(o) = 0 for o.
-17, 1
Let q(n) be the second derivative of 0*n**2 - 12*n + 1/6*n**5 + 0*n**3 + 1/3*n**4 + 0 - 1/45*n**6. Determine d so that q(d) = 0.
-1, 0, 6
Suppose -57 - 30 = -4