 - 30*g**2 - 2*g. Suppose m(n) = 0. What is n?
-7, -1, 1
Let b(g) be the second derivative of -g**8/336 + g**6/20 + 2*g**5/15 + g**4/8 + 3*g**2/2 + 29*g. Let o(r) be the first derivative of b(r). Factor o(k).
-k*(k - 3)*(k + 1)**3
Let q be (-5555)/(-605) - 27/(4 + -1). Let 0*p**2 + 2/11*p + 1/11*p**4 - q*p**3 - 1/11 = 0. What is p?
-1, 1
Let a(g) = -2*g**3 - 2*g**2 + 1. Let r be a(-1). Suppose r = -4*s + 2*f + 15, -5 = -s + f. Suppose 14*c - 2*c + 8 - c**2 + 5*c**s = 0. What is c?
-2, -1
Let u(h) be the first derivative of h**6/69 + 12*h**5/115 + 7*h**4/23 + 32*h**3/69 + 9*h**2/23 + 4*h/23 - 124. Determine a so that u(a) = 0.
-2, -1
Factor -4/3*q**3 - 8/3 - 2/3*q**4 + 8/3*q + 2*q**2.
-2*(q - 1)**2*(q + 2)**2/3
Factor -49*o**4 + 32*o**4 + 19*o**4 + 2*o**5.
2*o**4*(o + 1)
Let z be (-3 - -6 - -8) + 32/(-3). Suppose z*y + y**4 - 2/3*y**3 + 1/3*y**5 - 2*y**2 + 1 = 0. What is y?
-3, -1, 1
Let o be 3*4/(-84) + (-132)/(-140). Let d(y) be the first derivative of 10 + 12/5*y**2 + 56/15*y**3 + 36/25*y**5 + 4/15*y**6 + o*y + 16/5*y**4. Factor d(r).
4*(r + 1)**4*(2*r + 1)/5
Factor -111/7*p + 3/7*p**2 + 108/7.
3*(p - 36)*(p - 1)/7
Let c = 1682 - 1679. Factor -1/6 - 1/6*x**4 + 1/3*x**2 + 0*x + 0*x**c.
-(x - 1)**2*(x + 1)**2/6
Let s = 578 + -572. Let x(m) be the first derivative of -9 - s*m**4 + 4/5*m**5 + 16*m - 24*m**2 + 52/3*m**3. Determine c, given that x(c) = 0.
1, 2
Let p = 36 - 40. Let a be (0 - p)/(-5 + 6). Factor -2*o**2 - 4 + 5*o + 0*o**2 + 5*o**2 - a*o**2.
-(o - 4)*(o - 1)
Let v be 1058/28 + ((-33)/(-7) - 5). Let f = v - 963/26. Factor -2/13*w**3 - f*w**2 + 8/13 + 0*w.
-2*(w - 1)*(w + 2)**2/13
Suppose 4*k + 3*t = 12, 5*t = 4*k + 14 + 6. Suppose -5*z - 19 = -3*l + 6, k = -3*l + z + 5. Find f such that -f + l*f + 5*f - 6*f**3 + 2*f**3 = 0.
-1, 0, 1
Let w(b) be the first derivative of b**6/10 - 12*b**5/25 - 33*b**4/20 - 6*b**3/5 - 80. Suppose w(z) = 0. Calculate z.
-1, 0, 6
Let m(s) = -7*s**3 - 159*s**2 + 1434*s - 1280. Let k(a) = 9*a**3 + 158*a**2 - 1433*a + 1280. Let z(x) = 6*k(x) + 7*m(x). Factor z(j).
5*(j - 16)**2*(j - 1)
Suppose 0 = 3*j - j + 8. Let g = 0 - j. Let h(c) = -5*c**2 + 4*c - 3. Let f(i) = 6*i**2 - 5*i + 4. Let a(k) = g*f(k) + 5*h(k). Factor a(m).
-(m - 1)*(m + 1)
Let u be (-4)/(-10) + 11 + (-1449)/135. Factor -u*k**3 + 2/3*k - 2/3*k**4 + 2/3*k**2 + 0.
-2*k*(k - 1)*(k + 1)**2/3
Suppose -152*x**2 - 112*x**3 + 16 - 1577*x**4 + 112*x**5 - 92*x**2 + 1805*x**4 = 0. What is x?
-2, -1, -2/7, 1/4, 1
Let o = -1072 + 1073. Suppose 0 = -5*s - 3*g + 2*g + 5, -s + 7 = -g. Solve -3 - o - 6*z**2 - 3*z**2 + 10*z + z**2 + s*z**3 = 0.
1, 2
Suppose 0 = -13*u + 21*u - 32. Find n such that 12*n**3 + 8*n**4 - 3*n**3 - 24*n**u + 4*n**5 + 3*n**3 = 0.
0, 1, 3
Let j(z) = 18*z**3 - 16*z**2 - 25*z - 5. Let w(o) = 7*o**3 - 8*o**2 - 13*o - 2. Let c(l) = 4*j(l) - 10*w(l). Factor c(g).
2*g*(g + 3)*(g + 5)
Let n(d) be the second derivative of -5*d**4/4 + 205*d**3/6 + 35*d**2 + 9*d - 1. Determine o so that n(o) = 0.
-1/3, 14
Let a(d) be the third derivative of 1/84*d**8 + 0*d + 2*d**2 + 0*d**3 + 1/6*d**4 - 1/15*d**6 + 0*d**7 + 0*d**5 + 0. Factor a(o).
4*o*(o - 1)**2*(o + 1)**2
Factor g**3 - 19388 - g + 19388.
g*(g - 1)*(g + 1)
Factor 20*z**2 - 5*z**2 - 4*z**3 - 7*z**2 + 0*z**2 + 2*z**4 - 6*z**2.
2*z**2*(z - 1)**2
Suppose 0 = 3*q - 5*s - 34, -13*q - 21 = -15*q + 3*s. Let 5*y**2 - 15/4*y - 5/4*y**q + 0 = 0. Calculate y.
0, 1, 3
Find m, given that 8/3*m**4 + 16/3*m**3 + 1/3*m**5 - 17/3*m - 10/3 + 2/3*m**2 = 0.
-5, -2, -1, 1
Suppose -5*r - g = -118, -4*r = -2*g - 2*g - 80. Factor 7*q**3 - r*q**5 + 11*q**5 + 13*q**5 + 5*q**4 + 3*q**2.
q**2*(q + 1)**2*(q + 3)
Let k(t) be the third derivative of 0*t - 1/1344*t**8 + 0*t**3 + 1/480*t**6 + 0 + 0*t**4 - 37*t**2 + 1/240*t**5 - 1/840*t**7. Determine u, given that k(u) = 0.
-1, 0, 1
Suppose -2*h = 1 - 9. Suppose -5*j = -5*i - 7*j - 8, 2*j + 8 = 4*i. Factor 0 - 8/7*z + 2/7*z**h + 6/7*z**3 + i*z**2.
2*z*(z - 1)*(z + 2)**2/7
Let l(c) be the first derivative of -c**4 - 44*c**3/3 + 47*c**2/2 - 12*c + 1. Find i such that l(i) = 0.
-12, 1/2
Let z = 62254/3 - 20739. Factor 0 - 13/3*k**5 - 11*k**3 + 2/3*k + z*k**4 + 7/3*k**2.
-k*(k - 1)**3*(13*k + 2)/3
Let z(a) = a**3 + 111*a**2 + 434*a + 647. Let r be z(-107). Determine p, given that -20/3*p**4 + 38/3*p**2 + 11/3*p**r + 8/3 - 37/3*p**3 + 52/3*p = 0.
-1, -2/11, 2
Let g be (-133)/(-42) + -8 + 141/18 - 1. Determine s so that 32/3*s + 8 + 2/9*s**3 + 26/9*s**g = 0.
-6, -1
Let j(c) = -c**2 + 2. Let o be j(0). Factor -o*v**3 + 13*v**2 + 4*v**3 + 96*v + 24*v**2 + 128 - 13*v**2.
2*(v + 4)**3
Let o(q) be the second derivative of -q**6/25 + 31*q**5/30 - 17*q**4/45 - 26*q + 10. Factor o(b).
-2*b**2*(b - 17)*(9*b - 2)/15
Suppose 2*u - 6*u + 146 = 5*z, 0 = 2*u + 3*z - 72. Suppose 3*b - u = 4*v, -3*b + 3*v + 42 = 6. Determine f so that -f**2 + b*f - 5 - 1 - 24*f - 8*f**2 = 0.
-1, -2/3
Let d be (-245)/(-30) - 8 - (-1)/(-24). Suppose 1/4*w**2 + 1/8*w**3 + 0 + d*w = 0. What is w?
-1, 0
Factor 8*m**2 - 10*m**2 + 100*m - 64*m.
-2*m*(m - 18)
Let x(r) be the first derivative of 2/15*r**5 - 2/3*r**2 + 0*r + 10/9*r**3 - 18 - 2/3*r**4. Factor x(p).
2*p*(p - 2)*(p - 1)**2/3
Let t(c) be the second derivative of c**5/45 - 23*c**4/27 - 10*c - 1. Factor t(n).
4*n**2*(n - 23)/9
Suppose -r - 24 = -4*r. Find k, given that 3*k**2 + 12*k - k**2 - 6 - r*k = 0.
-3, 1
Let n = -11387 - -11389. Suppose -5 = 4*s - 13. Factor n*x**s + 2/3 + 2/3*x**3 + 2*x.
2*(x + 1)**3/3
Let d = 6 + -4. Suppose 2*r + r - 6 = d*h, 5*r = -3*h + 29. Find a such that 5*a**r - 4*a**2 + 11 - 11 - a**4 = 0.
-1, 0, 1
Let n be 76/12 + -6 + (-74)/276. Let p = 36/23 - n. Solve p + 1/2*z**2 + 2*z = 0 for z.
-3, -1
Let x = -50 - -52. Find n, given that 392*n**x - 48 - 2408*n**2 - 2940*n**3 - 282*n - 1029*n**4 - 246*n = 0.
-2, -2/7
Let i be ((-5170)/90)/(-11) - 5. Solve -2/9*k**2 + 4/9 + i*k = 0 for k.
-1, 2
Let i be ((-10)/30)/((-1)/18). Let h be i - (-3 - -7 - 3). Factor -3*u - 1 + 8*u**2 - u**2 + 4*u**3 + h*u.
(u + 1)**2*(4*u - 1)
Let p(j) be the second derivative of 0 + 1/90*j**5 + 0*j**2 - 1/540*j**6 - 1/36*j**4 - 3*j - 7/6*j**3. Let q(a) be the second derivative of p(a). Factor q(f).
-2*(f - 1)**2/3
Find k such that -8*k + 27*k**2 - 23*k**2 + 36*k + 4 + 37 + 7 = 0.
-4, -3
Let 0*y + 115/4*y**4 + 15/2*y**3 - 21*y**5 - 65/4*y**2 + 1 = 0. Calculate y.
-2/3, -1/4, 2/7, 1
Let f = 33 - 3. Let a = f - 28. Factor -1/3*j - j**a + 2/3.
-(j + 1)*(3*j - 2)/3
Suppose -3*g - 38 = -5*s, -8*g + 18 = -13*g - 3*s. Let k be 2 - 2 - 17/(51/g). Factor 0 + 3/4*b**k - 1/2*b.
b*(3*b - 2)/4
Let l be 5/(-40)*(-8 + 9)*(6 - 18). Find v such that -1/2*v**5 + l*v**3 + 0 + v**4 + 0*v**2 + 0*v = 0.
-1, 0, 3
Let o(j) = j**2 + 10*j + 16. Let k be o(-8). Let v = 5 + 0. Factor 34/7*b**4 + 10/7*b**v + k + 6*b**3 + 22/7*b**2 + 4/7*b.
2*b*(b + 1)**3*(5*b + 2)/7
Let d = 306737/11 + -27885. Solve 0*a**2 + 0*a - d*a**4 + 0*a**3 + 0 = 0.
0
Let f(z) = 21*z**3 - 314*z**2 - 453*z - 94. Let i(u) = -7*u**3 + 104*u**2 + 151*u + 31. Let r(q) = 3*f(q) + 8*i(q). Factor r(g).
(g - 17)*(g + 1)*(7*g + 2)
Solve 763*s**5 - 32*s**4 + 23*s**2 + 60*s**3 - 827*s**5 + 13*s**2 = 0.
-3/4, 0, 1
Suppose -266 + 32 = -9*j. Factor -3*r**2 + 2*r**2 - 3*r**2 - 2 + j - 4*r.
-4*(r - 2)*(r + 3)
Let u be (-12)/(-3) - 573/382. Let -u*b**3 + 15/2*b + 5 + 0*b**2 = 0. What is b?
-1, 2
Let i = -14 + 2. Let h be ((-6)/i)/(1/8). Factor -3*p**3 + h*p**3 - 5 + 1 + 3*p**2.
(p - 1)*(p + 2)**2
Let l(u) be the second derivative of -u**7/28 + u**6/20 + 27*u**5/40 + 11*u**4/8 + u**3 - 327*u. Factor l(w).
-3*w*(w - 4)*(w + 1)**3/2
Let c(y) be the first derivative of -2/15*y**3 + 0*y - 1/5*y**2 + 14. Suppose c(h) = 0. What is h?
-1, 0
Let o(t) = 7. Let d(r) = 2. Let y(g) = 6*d(g) - 2*o(g). Let c(z) = -z**3 + 3. Let n(h) = -2*c(h) - 3*y(h). Factor n(u).
2*u**3
Let d(h) be the second derivative of h**7/7 + 46*h**6/75 - 3*h**5/50 - 13*h**4/5 - 4*h**3/15 + 24*h**2/5 + 7*h + 2. Suppose d(n) = 0. Calculate n.
-2, -2/3, 3/5, 1
Find o, given that -45 - 8*o**3 - 3*o**3 - 9*o - 6*o + 26*o**3 + 5*o**3 + 40*o**2 = 0.
-3/2, 1
Let g = 35/31 + 117/775. Let m(a) be the first derivative of -3 + 4*a**4 + 3/5*a**2 + 46/15*a**3 + 0*a - g*a**5. Factor m(z).
-2*z*(z - 3)*(4*z + 1)**2/5
Let u(h) be the second derivative of 0 + 0*h**2 + 1/24*h**4 + 1/40*h**5 + 0*h*