hat 21/4*g**2 - 195/4*g + 27/2 = 0.
2/7, 9
Let c be (-2)/3*-3 - (-7353)/(-63). Let w = 115 + c. Find t such that 0*t + w*t**2 - 2/7 = 0.
-1, 1
Let k(v) be the first derivative of -v**5/20 + v**4/2 - 3*v**3/2 - 13*v - 1. Let j(a) be the first derivative of k(a). Factor j(m).
-m*(m - 3)**2
Suppose -4*z + 9 = -5*g, 3*g + 15 = 5*z - z. Let c(l) = 3*l - 18. Let x be c(z). Factor -2/9*s**3 + 0 + 2/9*s**2 + x*s.
-2*s**2*(s - 1)/9
Suppose 0 = -32*w + 136*w. Find r such that 2/9*r**3 + 0 + 4/9*r**4 - 2/9*r**5 - 4/9*r**2 + w*r = 0.
-1, 0, 1, 2
Let n(p) = 5*p**3 - 8*p**2 + 11*p. Let s(a) be the first derivative of 65/2*a**2 + 29/4*a**4 - 16*a**3 - 4 + 0*a. Let m(h) = 34*n(h) - 6*s(h). Factor m(b).
-4*b*(b - 2)**2
Let l(s) be the second derivative of s**6/15 + 28*s**5/5 + 196*s**4 + 10976*s**3/3 + 38416*s**2 + 20*s - 1. Factor l(z).
2*(z + 14)**4
Let m(d) be the first derivative of d**3/4 + 99*d**2/8 + 93*d/2 + 24. Let m(i) = 0. What is i?
-31, -2
Let n(b) be the second derivative of -4/75*b**6 + 0*b**2 + 0 - 16*b + 0*b**4 - 1/50*b**5 + 0*b**3. Factor n(g).
-2*g**3*(4*g + 1)/5
Suppose 7*s - 10 = 4*l, -s + 24*l - 28*l + 6 = 0. Factor 0*x + 16*x**3 + 0 + 50/3*x**5 + 30*x**4 + 8/3*x**s.
2*x**2*(x + 1)*(5*x + 2)**2/3
Suppose -39*r = -29*r. Suppose r = 17*o - 10*o. Factor -2*l**2 - 35/2*l**4 - 13*l**3 + 49/4*l**5 + 0 + o*l.
l**2*(l - 2)*(7*l + 2)**2/4
Let y(d) be the third derivative of -d**8/1344 + d**7/504 + d**4/2 + 17*d**2. Let x(t) be the second derivative of y(t). Determine c, given that x(c) = 0.
0, 1
Let x = 37852 - 870594/23. Let x*d**3 - 1458/23 + 486/23*d - 54/23*d**2 = 0. Calculate d.
9
Let z = -2567/3 - -10343/12. Factor 5*t + 5/4*t**2 - z.
5*(t - 1)*(t + 5)/4
Let y be 8/(-7)*(-2)/8. Let w(t) = -2*t**3 - 37*t**2 + 18*t - 17. Let g be w(-19). Solve y*q + 4/7 - 2/7*q**g = 0.
-1, 2
Let j(o) be the third derivative of o**6/300 + o**5/50 - o**4/6 - 55*o**2. Suppose j(h) = 0. What is h?
-5, 0, 2
Suppose -3*w - 2 = 4. Let d(o) = -6*o**4 - o**3 + 6*o**2 + o + 7. Let x(z) = -2 - 2*z**4 - 8 + 12 + 0 + 2*z**2. Let j(k) = w*d(k) + 7*x(k). Factor j(l).
-2*l*(l - 1)**2*(l + 1)
Let t = -4 - -12. Let k(a) = 22*a - 4. Let z be k(7). Factor t*g - 2*g**2 + z - 150.
-2*g*(g - 4)
Let o = -17 - -22. Factor -8 + 2*c + o*c**2 - 3*c**2 - 2 + 6.
2*(c - 1)*(c + 2)
Let k(d) be the first derivative of -d**5/10 + 7*d**4/8 + 3*d**3/2 - 115*d**2/4 + 50*d + 328. Factor k(y).
-(y - 5)**2*(y - 1)*(y + 4)/2
Let q(x) be the third derivative of -x**6/360 - 7*x**3/3 + x**2. Let w(z) be the first derivative of q(z). Factor w(i).
-i**2
Let z(m) be the third derivative of m**7/14 + 8*m**6/3 + 71*m**5/2 + 180*m**4 + 405*m**3/2 + 153*m**2. Suppose z(f) = 0. Calculate f.
-9, -3, -1/3
Factor 2/3*a - 2/3*a**2 + 40/3.
-2*(a - 5)*(a + 4)/3
Let o(v) be the second derivative of -v**4/12 + 37*v**3/24 - 9*v**2/8 - 81*v. Factor o(q).
-(q - 9)*(4*q - 1)/4
Suppose -2*p = 3*l - 22, 7 = -5*p - 5*l + 47. Factor 25 - 11/4*h**p + 1/4*h**4 - 15*h + 3/2*h**3.
(h - 2)**2*(h + 5)**2/4
Let o = -4792/3 - -1689. Let s = -89 + o. Suppose 56/3*h - 98/3*h**2 - s = 0. Calculate h.
2/7
Let o be 0/(-1 - -7) - 1/(-6). Let t(u) be the second derivative of 0 + 0*u**2 - o*u**4 + 1/3*u**3 - 8*u. Factor t(l).
-2*l*(l - 1)
Let w(r) = -3*r**3 + r**2 + r. Suppose -5*p + p - 5*y = 29, 5*y = 3*p - 22. Let l be w(p). Solve h**2 - h + h**4 + 8*h**3 - 2*h - 5*h**l - 2 = 0 for h.
-2, -1, 1
Let z = -18 + 21. Factor v**z - 3*v**3 - 2*v**3 + 12*v**2 + v**3.
-3*v**2*(v - 4)
Let q = 301 + -299. Let v(x) be the third derivative of 0 + 0*x**3 - 1/120*x**5 + 0*x**4 + 2*x**q + 0*x. Factor v(h).
-h**2/2
Let q be 38/(-5) + (-768)/(-96). Solve -4/5 + 2/5*g**2 - q*g = 0.
-1, 2
Let o be (-4)/((-24)/(-10))*-3. Let x(n) be the second derivative of 7*n + 0 + 2/3*n**3 + 1/10*n**o + 0*n**2 - 1/2*n**4. What is j in x(j) = 0?
0, 1, 2
Let o be -229 - -235 - (1 + (2 - -1)). Factor 2/13*y**o + 10/13*y + 0.
2*y*(y + 5)/13
Let l(w) = -w**2 + 5*w - 4. Let d be l(2). Solve 8*a - 7*a + 0*a - 5*a - 8*a**d = 0 for a.
-1/2, 0
Let p(s) = 12*s**2 + 16*s + 14. Let x(o) = 2 - 1 + 2 - 2 - o. Let u be x(-5). Let d(c) = c**2 + 1. Let t(a) = u*d(a) - p(a). Solve t(r) = 0.
-2, -2/3
Let t = -10 - -12. Suppose 4*u = 3*u + 3. Solve -7 + 15*g + 2 + u*g**3 - 1 - 12*g**t = 0 for g.
1, 2
Let x(o) be the first derivative of -4/3*o + 3 + 2/3*o**2 + 1/9*o**3 - 1/12*o**4. Suppose x(d) = 0. What is d?
-2, 1, 2
Let l = -139682/15 - -9318. Let c = l + -8/15. Find x, given that 64/3*x + 56/3*x**3 - c - 4*x**4 - 92/3*x**2 = 0.
2/3, 1, 2
Let o(i) be the first derivative of 2*i**2 + 2 - i**2 + 9*i + i**3 + 5*i**2. Let o(z) = 0. Calculate z.
-3, -1
Suppose n + 1 = 4*s, -3*s - 228*n + 34 = -224*n. Factor -2/5*y**5 - 6*y**3 - 10*y**s + 18/5*y**4 + 0 + 0*y.
-2*y**2*(y - 5)**2*(y + 1)/5
Let t(d) be the third derivative of -d**8/63 + 44*d**7/35 + 511*d**6/90 + 929*d**5/90 + 121*d**4/12 + 52*d**3/9 - 380*d**2. Suppose t(l) = 0. Calculate l.
-1, -1/2, 52
Let w(u) be the first derivative of -2*u**5/15 + 20*u**4/3 - 238*u**3/3 - 294*u**2 - 194. Suppose w(i) = 0. Calculate i.
-2, 0, 21
Let t(k) be the first derivative of k**4/7 + 40*k**3/21 + 66*k**2/7 + 144*k/7 + 6. Factor t(v).
4*(v + 3)**2*(v + 4)/7
Let n(u) be the first derivative of u**6/33 - 32*u**5/55 + 41*u**4/22 + 452*u**3/33 - 180*u**2/11 - 1296*u/11 + 479. Determine d, given that n(d) = 0.
-2, 2, 9
Let j(h) be the first derivative of -h**3/3 + 5*h**2/2 - 88. Determine n, given that j(n) = 0.
0, 5
Let t(a) = a**3 - a**2 + 3*a - 1. Suppose 4 = 43*h - 45*h. Let n(m) = 4*m**3 - 4*m**2 + 10*m - 3. Let s(o) = h*n(o) + 7*t(o). Suppose s(z) = 0. What is z?
-1, 1
Suppose -3*p + 17 = 5*f - 126, f + 45 = p. Determine l so that 3*l**3 - p + 46 - l**3 + 6*l**2 = 0.
-3, 0
Let i be (-1 + (-1)/(-3))*-6. Suppose 7*v - 64 + 36 = 0. Factor -145*f + i*f**3 + 145*f + 8*f**4 - v*f**2.
4*f**2*(f + 1)*(2*f - 1)
Let u = -317/14 - -156/7. Let p = u + 17/28. Factor p*i**3 + 1/2 - 3/4*i + 0*i**2.
(i - 1)**2*(i + 2)/4
Let m(f) be the first derivative of 3*f**4/4 - 5*f**3 + 9*f**2 - 61. Factor m(t).
3*t*(t - 3)*(t - 2)
Suppose -10 = 3*j + 2*b, -2*j - 39*b = -37*b + 10. What is h in j*h**2 - 7/5*h - 6/5 + 1/5*h**3 = 0?
-2, -1, 3
Suppose 155*n**2 + 1187*n**4 - 327*n**3 + 76*n**3 + 25*n**5 - 1222*n**4 - 64*n**3 - 120 + 290*n = 0. Calculate n.
-3, -1, 2/5, 1, 4
Let l(r) = -13*r**5 - 32*r**4 - 43*r**3 - 15*r**2 + 9*r + 9. Let o(w) = -3*w**5 - 8*w**4 - 11*w**3 - 4*w**2 + 2*w + 2. Let g(m) = -2*l(m) + 9*o(m). Factor g(x).
-x**2*(x + 1)**2*(x + 6)
Let z be 2142/595 + (-4)/(-10). Let d(i) be the first derivative of -2/3*i**3 + 3/4*i**z - 8 + 1/4*i**2 + 0*i - 2/5*i**5 + 1/12*i**6. Factor d(g).
g*(g - 1)**4/2
Let x(j) be the third derivative of -1/630*j**7 + 0*j**3 + 1/45*j**5 + 0 + 3*j**2 + 0*j + 1/2016*j**8 + 0*j**4 - 1/180*j**6. Factor x(m).
m**2*(m - 2)**2*(m + 2)/6
Let i(t) = 5*t**3 + 71*t**2 + 362*t - 432. Let p(u) = -26*u**3 - 356*u**2 - 1811*u + 2160. Let o(a) = -11*i(a) - 2*p(a). Factor o(s).
-3*(s - 1)*(s + 12)**2
Suppose 0 = 5*w + 25 - 65. Let p(k) = 8*k**2 + 65*k - 67. Let s(c) = 23*c**2 + 195*c - 202. Let b(n) = w*p(n) - 3*s(n). Factor b(i).
-5*(i - 1)*(i + 14)
Let d(v) be the second derivative of -9*v**7/98 + 18*v**6/35 - 36*v**5/35 + 16*v**4/21 - 4*v - 3. Suppose d(b) = 0. What is b?
0, 4/3
Let d(m) be the third derivative of 13*m**6/420 - 22*m**5/105 + 5*m**4/21 + 32*m**3/21 - 214*m**2. Suppose d(z) = 0. What is z?
-8/13, 2
Factor 330*c + 48 + 242*c - 110*c + 57*c**2.
3*(c + 8)*(19*c + 2)
Let n(t) be the second derivative of -t**7/4200 + t**6/1800 + t**5/120 + t**4/40 + t**3/6 + 20*t. Let u(d) be the second derivative of n(d). Factor u(p).
-(p - 3)*(p + 1)**2/5
Let y be (-1834)/(-9432) - (1 - 5/4). Let -10/9*k - 4/9*k**2 + 8/9*k**3 + 8/9*k**4 - y + 2/9*k**5 = 0. Calculate k.
-2, -1, 1
Determine q so that -3*q**2 - 70 + 171 + 32*q + 2*q**2 - 132*q = 0.
-101, 1
Let q(n) be the second derivative of -2*n**6/15 - 2*n**5/5 + 4*n**4/3 + 4*n**3/3 - 6*n**2 - 101*n. What is g in q(g) = 0?
-3, -1, 1
Suppose 0 = -4*z + 8, 3*z + 6 = 2*k + k. Suppose -l - k*l = -20. Suppose l*m + m**2 + 0 - 6*m + 1 = 0. What is m?
1
Let j = -34 + 38. Factor 4*a**2 - 5 + j - 3.
4*(a - 1)*(a + 1)
Let r(b) = -b**4 + b**2 + b - 1. Let x(l) = l**2 + 8. Let p be x(6). Let v(d) = -10*d**4 - 5*d**3 +