 + 34*a**2 + 8830 + 52507 = 0.
-300
Suppose -5*i + 8 = -3*a, -2*a + 4 = 2*i - 3*i. What is t in 0 + t**a - 3*t**2 - t**3 - 2 - 6*t + 11*t + 0*t**4 = 0?
-2, 1
Let u = -1503/8 + 1507/8. What is t in 0 - t + u*t**3 + 1/2*t**2 = 0?
-2, 0, 1
Suppose 0 = -11*b - 20 + 75. Let x(t) be the third derivative of -1/330*t**b + t**2 + 0*t + 0*t**4 + 1/660*t**6 + 0 + 0*t**3. Determine h, given that x(h) = 0.
0, 1
Suppose -17*a - 3*x + 18 = -16*a, -3*a = 3*x - 24. What is w in 14/17*w - 6/17 + 2/17*w**a - 10/17*w**2 = 0?
1, 3
Let t be 7*3/(-1)*17/(-3). Let 3 + 1 + 40*m - t*m**2 + 75*m**2 = 0. Calculate m.
-1/11, 1
Factor 27/2*u**2 + 9/2*u - 3/2 + 15/2*u**3.
3*(u + 1)**2*(5*u - 1)/2
Let u(h) be the second derivative of h**7/56 + 23*h**6/40 + 177*h**5/40 - 12*h**4 - 36*h**3 + 189*h - 1. Determine n so that u(n) = 0.
-12, -1, 0, 2
Let n be -4 - 1614/36 - (-2)/(-4). Let i = n - -50. Find s such that 0*s + 4/3*s**2 - 2/3*s**4 - i*s**3 + 0 = 0.
-2, 0, 1
Factor -32 + 2/9*k**2 + 14/9*k.
2*(k - 9)*(k + 16)/9
Let u(m) = -m**2 + 7*m + 10. Let s be u(8). Let f be (s/4)/((-3)/(-24)). Factor -4*h**3 - 3*h**5 - h**4 + 7*h**3 - 3*h**2 + f*h**4.
-3*h**2*(h - 1)**2*(h + 1)
Factor -7/2*t**2 - 5/2*t**4 + t + 9/2*t**3 + 0 + 1/2*t**5.
t*(t - 2)*(t - 1)**3/2
Let c be (20/5 + -3)/1. Factor 3 + 1 - 2*p**3 - p**3 + 3*p - 3*p**2 - c.
-3*(p - 1)*(p + 1)**2
Let z(o) = -o**2 - 13*o + 30. Let a be z(-15). Let r(k) be the first derivative of 6 + k**6 + a*k + 21/5*k**5 - 6*k**2 - 8*k**3 + 9/4*k**4. Solve r(p) = 0.
-2, -1/2, 0, 1
Let i(w) = -w**2 - 15*w - 19. Let a be i(-14). Let h = a + 8. Determine d, given that 9*d**3 - h - 6*d**2 - 4*d - 11*d**3 + 3 = 0.
-2, -1, 0
Let m(r) be the first derivative of 2*r**5/75 + r**4/10 + 2*r**3/15 + r**2/15 - 29. Factor m(s).
2*s*(s + 1)**3/15
Let m = 1137 - 1134. Determine j, given that -6/11*j**m + 8/11*j**2 + 2/11*j - 4/11 = 0.
-2/3, 1
Let t(w) = w**2 - 14*w + 52. Let p be t(6). Suppose 75*a**3 + 4*a**5 - 3*a**3 + 32*a - 28*a**p + 16*a**2 + 0*a**4 - 96*a**2 = 0. Calculate a.
0, 1, 2
Let x(b) be the second derivative of b**6/480 - b**4/32 + b**3/12 - 3*b**2/2 + 9*b. Let g(r) be the first derivative of x(r). Factor g(v).
(v - 1)**2*(v + 2)/4
Let a(n) = 70*n**2 + 165*n + 45. Let j(f) = -22 - 53*f + 21*f - 22*f - 35*f**2 - 28*f. Let q(m) = 2*a(m) + 5*j(m). Factor q(w).
-5*(w + 2)*(7*w + 2)
Solve 1568/15 - 112/15*d + 2/15*d**2 = 0.
28
Let y = 20 - 28. Let f(b) = b + 11. Let p be f(y). Let 0*q + 6*q - 2*q - p*q - q**3 - 1 + q**2 = 0. What is q?
-1, 1
Suppose 5*r = -2*i + 7 + 5, -2*r - 5*i = -9. Factor -z**2 + 9*z**2 + 2 - 11*z**r - 8 - 9*z.
-3*(z + 1)*(z + 2)
Let d(u) = u**2 - 2*u + 1. Let k(i) = -i**3 + 10*i**2 + 12*i - 4. Let o be k(11). Let p(x) = -1 - o + 4 + 3. Let r(n) = d(n) + 4*p(n). Factor r(g).
(g - 3)*(g + 1)
Let d(h) = 4*h**2 + 13*h - 10. Let o(x) = 3*x**2 + 12*x - 11. Let z(s) = 4*d(s) - 5*o(s). Solve z(t) = 0.
3, 5
Let o be 3/((-6)/(-4)) - -2 - (-12947)/214. Let 330*b + 3*b**3 + 363/2 - o*b**2 = 0. Calculate b.
-1/2, 11
Let c(k) be the first derivative of -96/5*k**2 + 512/5*k + 8/5*k**3 - 1/20*k**4 - 8. Determine q, given that c(q) = 0.
8
Suppose 2*u + 29 = 33. Let h be u + -6*(-2)/(-8). Determine k so that -2/3 + h*k**2 - 1/6*k**3 + 0*k = 0.
-1, 2
Let b = -3903/2 - -1953. Factor b*w**3 - 3/2*w + 1/2 - 1/2*w**2.
(w - 1)*(w + 1)*(3*w - 1)/2
Let -52/3 - 50*f**2 + 2/3*f**4 + 154/3*f + 46/3*f**3 = 0. Calculate f.
-26, 1
Let u = -201 + 201. Let x(s) be the third derivative of -3*s**2 + 0*s**3 + 0*s**5 + 0*s**4 - 1/315*s**7 - 1/180*s**6 + u + 0*s. Factor x(y).
-2*y**3*(y + 1)/3
Let x(p) = -8*p**3 - 2*p - 1. Let g be x(-1). Suppose g*d**3 + 6 - 16*d + 2*d**3 - 7*d**3 - 4*d**2 + 10 = 0. What is d?
-2, 1, 2
Let m(h) be the third derivative of -h**7/42 - 3*h**6/8 - h**5/3 + 15*h**4/2 + 80*h**3/3 - 14*h**2 + 2*h. Find q such that m(q) = 0.
-8, -2, -1, 2
Let g(w) = -11*w**2 - 62*w. Let d(n) = -21*n**2 - 123*n - 4. Let u(i) = -4*d(i) + 7*g(i). What is x in u(x) = 0?
-8, -2/7
Let h(c) be the first derivative of 17 - 15*c + 10*c**2 - 5/3*c**3. Factor h(s).
-5*(s - 3)*(s - 1)
Let p be (-3 + -2)/((-2)/8). Factor 64*u**3 + 6*u**5 + 13*u - 40*u**2 - 4 - p*u**2 - 32*u**4 + 13*u.
2*(u - 2)*(u - 1)**3*(3*u - 1)
Let j be ((-60)/(-70))/((-3)/(-42)*8). Factor 4*l + 2 + j*l**2.
(l + 2)*(3*l + 2)/2
Let w(q) = q**2 + 8*q + 2. Let y be w(-8). Let c(o) = -o**2 - o. Let i(j) = -j**2 - j. Let f be 7/3 + (-3)/9. Let m(k) = f*i(k) + y*c(k). Factor m(x).
-4*x*(x + 1)
Let z = -7892 - -11703. Let v = 26722/7 - z. Determine m, given that 375/7 + 3/7*m**3 + v*m**2 + 225/7*m = 0.
-5
Let t(u) be the first derivative of -u**4/10 - 2*u**3/5 + 4*u**2/5 + 324. Find q such that t(q) = 0.
-4, 0, 1
Let y(c) be the second derivative of 0*c**4 + 1/6*c**6 + 0*c**2 + 0*c**5 + 0 + 8*c + 0*c**3. Factor y(q).
5*q**4
Let j(f) be the first derivative of -32*f + 11 - 2/3*f**6 + 40/3*f**3 - 16/5*f**5 - f**4 + 8*f**2. Factor j(v).
-4*(v - 1)**2*(v + 2)**3
Solve 480/7*s**2 + 512 + 2432/7*s + 8/7*s**3 - 4/7*s**4 = 0 for s.
-4, 14
Let h(v) = 23*v**2 - 3*v + 7. Let x be h(2). Factor x + 35*m**3 + 50*m**2 - 93 + 15*m.
5*m*(m + 1)*(7*m + 3)
Let r(y) be the first derivative of -8 + 0*y**2 - 2/9*y**3 + 3*y - 1/18*y**4. Let g(f) be the first derivative of r(f). Determine d so that g(d) = 0.
-2, 0
Let z = -212 - -107. Let k = z + 110. Let -24*s - 432*s**2 - 2916*s**3 - 19683/2*s**k + 0 - 8748*s**4 = 0. Calculate s.
-2/9, 0
Let l be (-4 - (-9)/3)*(-4)/2. Let -4*r**4 + 3*r**4 + l + 12*r**2 - 14*r - 2*r**3 + 2 + 1 = 0. What is r?
-5, 1
Suppose 0 = -2*p + 5 + 25. Factor p*l + 4*l**2 + 32*l**3 + 32*l**2 + 4*l + 10*l**4 + 2 - 3*l.
2*(l + 1)**3*(5*l + 1)
Suppose 26*l**2 + 742 + 15*l**3 - 385 - 372 + 25*l + 29*l**2 = 0. What is l?
-3, -1, 1/3
Let w(s) = -3*s**5 + s**4 + 2*s**2 + s. Let c(r) = -3*r**5 + 43*r**4 + 22*r**3 - 50*r**2 - 23*r + 13. Let d(n) = c(n) - 2*w(n). Solve d(f) = 0.
-13, -1, 1/3, 1
Let h(k) be the first derivative of 1/2*k**3 + 1/5*k**5 - 1/2*k**4 + 3/2*k**2 + 0*k - 1. Let o(m) be the second derivative of h(m). Factor o(q).
3*(2*q - 1)**2
Let u = -5272/3 + 1758. Suppose -2/3*j + 0*j**3 + 0 - 4/3*j**2 + u*j**5 + 4/3*j**4 = 0. What is j?
-1, 0, 1
Let j(p) be the first derivative of p**4/6 + 8*p**3/3 + 15*p**2 + 36*p - 156. Factor j(v).
2*(v + 3)**2*(v + 6)/3
Suppose 0 = 7*t + 13 - 97. Determine p, given that -28*p**3 - t*p**2 + 82*p**5 - 11*p**4 - 86*p**5 - 9*p**4 = 0.
-3, -1, 0
Let u(f) be the first derivative of -7*f**2 - 52/7*f**3 - 9/14*f**4 + 23 - 16/7*f. Factor u(y).
-2*(y + 8)*(3*y + 1)**2/7
Let w(h) = h**3 - 29*h**2 + 89*h - 284. Let t be w(26). Determine v, given that 0 + 1/3*v**5 - 2/3*v**4 + 0*v + 2/3*v**t - 1/3*v**3 = 0.
-1, 0, 1, 2
Let f be 1426/155 + -8*4/4. Let 3/5*d**3 + 0 + f*d + 9/5*d**2 = 0. Calculate d.
-2, -1, 0
Let l(f) = f**3 + f**2 - f. Let u(r) = -r**4 + 10*r**3 - 3*r**2 - 16*r. Let x(o) = -2*l(o) + u(o). Factor x(i).
-i*(i - 7)*(i - 2)*(i + 1)
Let q(a) be the first derivative of 75*a**4/4 + 145*a**3 + 156*a**2 + 60*a - 8. Factor q(r).
3*(r + 5)*(5*r + 2)**2
Suppose -7*y - 2 + 23 = 0. Factor -233 + 233 - 3*w**y + 6*w**2 + w - 4*w.
-3*w*(w - 1)**2
Let q = 195 - 190. Let m(s) be the third derivative of -4*s**2 - 3/140*s**q - 1/120*s**6 + 0*s + 0 + 0*s**3 - 1/84*s**4. Factor m(h).
-h*(h + 1)*(7*h + 2)/7
Let r(a) be the first derivative of 4*a**3/3 + 26*a**2 + 131. Factor r(d).
4*d*(d + 13)
Let v be (-4)/18 - (-6012)/81. Let f(c) = c**3 + 16*c**2 + 25*c - 34. Let a be f(-14). Let -82*g**3 + 0*g + 4*g**4 + a*g - 4*g**2 + v*g**3 = 0. What is g?
-1, 0, 1, 2
Suppose 5*z - 7 = 8. Let w(c) be the third derivative of 0*c + 5*c**2 + 1/6*c**4 + 2/15*c**5 + 0 - 2/3*c**z. Factor w(n).
4*(n + 1)*(2*n - 1)
Factor 96/7*w + 32/7 + 18/7*w**4 + 16*w**2 + 64/7*w**3 + 2/7*w**5.
2*(w + 1)*(w + 2)**4/7
Let a = 236 - 234. Let w(f) be the first derivative of 0*f - 1/8*f**a - 3 + 1/12*f**3. Find q, given that w(q) = 0.
0, 1
Let h(n) = -7*n**3 - 53*n**2 + n + 41. Let w(r) = 20*r**3 + 156*r**2 - 4*r - 124. Let u(g) = -8*h(g) - 3*w(g). Factor u(q).
-4*(q - 1)*(q + 1)*(q + 11)
Let y(u) be the first derivative of -u**3/15 + 7*u**2/2 + 36*u/5 + 91. Find p, given that y(p) = 0.
-1, 36
Let n(r) be the first derivative of -2*r**3/3 + 86*r**2 - 3698*r - 363. Determine o, given that n(o) = 0.
43
Let m(k) be the th