*2 - b - 20*a - 4 + 72*a**2.
5*(a - 2)*(3*a + 2)
Let k(r) be the first derivative of -5*r**6/36 + 17*r**5/2 - 2405*r**4/12 + 19435*r**3/9 - 32955*r**2/4 - 142805*r/6 + 2011. Factor k(y).
-5*(y - 13)**4*(y + 1)/6
Suppose -y + 4*l = -3, 2*y - 19 = 9*l - 14*l. Solve 78*p**3 - 131*p**4 + 132*p**4 + 6 - 73*p**3 - y*p**2 - 5*p = 0.
-6, -1, 1
Find o, given that -o**5 - 30*o**3 - 86*o**2 + 7*o**4 + 2*o + 7*o**4 + 20*o + 72*o**4 + 9*o**5 = 0.
-11, -1, 0, 1/4, 1
Let g(n) be the third derivative of -n**7/15 - 31*n**6/20 + 12*n**5/5 + 7*n**4/3 - 5*n**2 - 8. Let g(l) = 0. What is l?
-14, -2/7, 0, 1
Let -224 + 1016/5*l**3 - 154/5*l**4 + 2/5*l**5 + 2816/5*l - 512*l**2 = 0. What is l?
1, 2, 70
Let a be ((-6)/10)/((-6)/15). Let s be (-3)/(-99)*((-105)/30 + (-36)/(-4)). Solve 5/6*b**4 + 1/3*b + s*b**5 + 0 + a*b**3 + 7/6*b**2 = 0.
-2, -1, 0
Suppose 3*t - 198 = -33. Factor 16*i**4 + 4*i**3 - 16*i**2 - t*i + 121*i - 70*i.
4*i*(i - 1)*(i + 1)*(4*i + 1)
Suppose 2269 = -664*y + 4261. Solve 20/13*f - 102/13*f**2 + 10/13*f**y + 0 = 0 for f.
0, 1/5, 10
Let y = 2003/130 - 878/65. Let p(l) be the second derivative of 40/3*l**4 + 0*l**2 + y*l**5 + 1/15*l**6 + 42*l + 0 - 100/3*l**3. Let p(k) = 0. What is k?
-10, 0, 1
Let y(u) be the second derivative of -288*u**2 - 2*u + 1 - 1/12*u**4 - 8*u**3. Suppose y(h) = 0. What is h?
-24
Suppose 18 = 2*g + 10. Suppose g*r = -13 + 21. Factor 2 - 4*d**3 - 10*d**r - d**3 + 6*d - d**3 + 8*d**4.
2*(d - 1)**2*(d + 1)*(4*d + 1)
Factor -48*x**4 - 546*x**2 + 996*x**3 + 3*x**5 - 39 + 564*x - 753*x**3 - 177.
3*(x - 9)*(x - 2)**3*(x - 1)
Let c(r) be the third derivative of r**7/210 + r**6/90 - r**5/30 - r**4/6 + 112*r**3/3 - 87*r**2 - r. Let j(l) be the first derivative of c(l). Factor j(i).
4*(i - 1)*(i + 1)**2
Let s(m) be the first derivative of m**4/10 - 722*m**3/5 + 390963*m**2/5 - 94091762*m/5 + 1832. Factor s(i).
2*(i - 361)**3/5
Suppose 0 = 4*u - g + 24, 0 = u - 3*g - g - 9. Let m be (u - 29/(-4))*15. Factor m*p - 5/4*p**2 + 5.
-5*(p - 4)*(p + 1)/4
Let s(v) be the third derivative of v**5/15 + 53*v**4/2 + 312*v**3 + 285*v**2 - v + 2. Factor s(f).
4*(f + 3)*(f + 156)
Suppose 763*f - 759*f - 1 = k, 3*k - 4*f = 5. Suppose -3*i**3 - 1/6*i + 1/2*i**5 - 1/6*i**4 - k*i**2 + 1/2 = 0. What is i?
-1, 1/3, 3
Suppose -18*d - 46 = -41*d. Find r, given that r**3 - 63*r**d + 22*r**5 - 36*r**3 + 15*r + 8*r**2 + 55*r**4 - 2*r**5 = 0.
-3, -1, 0, 1/4, 1
Let n(z) be the second derivative of 8*z**6/15 - 2*z**5 - 29*z**4/4 - 35*z**3/6 - 2*z**2 + 481*z. Factor n(h).
(h - 4)*(h + 1)*(4*h + 1)**2
Suppose 5*p + 2*g = -4*g, 3*g - g = 0. Let j(w) be the first derivative of 1/20*w**4 - 1/10*w**2 - 7 + p*w**3 + 0*w. What is x in j(x) = 0?
-1, 0, 1
Suppose -14*d = -9*d + 5*r + 20, -20 = 4*d + 5*r. Suppose -q + 5*x = -4*q + 5, -4*x + 4 = d. Factor 1/4*p**2 - 1/4*p**3 + 0*p + q.
-p**2*(p - 1)/4
Solve 1824/7*x - 240/7*x**2 + 2/7*x**3 - 512 = 0.
4, 112
Suppose -4*h = -7*h - 6*i + 18, -3*i - 2 = -4*h. Factor -4*q**h + q**4 - 2*q + 1/2*q**5 - 3/2*q**3 + 0.
q*(q - 2)*(q + 1)**2*(q + 2)/2
Let w(s) be the first derivative of -109 + 4/55*s**5 - 4/33*s**3 - 1/22*s**4 + 0*s**2 + 0*s + 1/33*s**6. Let w(y) = 0. Calculate y.
-2, -1, 0, 1
Let k(u) = -2*u**2 + u + 42. Let l be k(0). Determine q so that 13*q**2 - 18 + 15*q**2 - l - 5*q - 23*q**2 = 0.
-3, 4
Let r(x) be the second derivative of 0*x**2 + 28/15*x**6 + 1/3*x**4 - 3 + 8/3*x**3 - 113/10*x**5 - 2*x. Find z such that r(z) = 0.
-1/4, 0, 2/7, 4
Let v(j) be the first derivative of 2/3*j**2 + 5/3*j + 43 - 1/9*j**3. Let v(u) = 0. What is u?
-1, 5
Let d(a) be the second derivative of a**6/135 - 13*a**5/18 + 121*a**4/18 - 59*a**3/3 - 2828*a. Suppose d(r) = 0. What is r?
0, 3, 59
Suppose -3*b - 27 = -3*q, 3*q - 28 = -5*b + 7. Factor -267*g**2 + 137*g**2 - q*g - 40 + 135*g**2.
5*(g - 4)*(g + 2)
Find v such that -7/2*v**4 + 193/4*v + 237/4*v**2 + 15/4*v**3 - 15/4 = 0.
-3, -1, 1/14, 5
Let a(d) be the first derivative of -d**7/2520 - d**6/72 + 98*d**3/3 - 14. Let m(p) be the third derivative of a(p). Solve m(x) = 0.
-15, 0
Let 2/7*h + 19/7*h**2 - 3/7 + 6/7*h**3 = 0. Calculate h.
-3, -1/2, 1/3
Let f(w) = -2*w**2 + 1. Let q(k) = -5*k**2 + 5*k + 7. Let p = 59 + -64. Let x(h) = p*q(h) + 15*f(h). Suppose x(m) = 0. What is m?
-4, -1
Suppose -14 = 5*i - 2*o, 4*i + 2*o + 5 + 17 = 0. Let q be 0/(-2) + i + 6. What is r in -40*r**3 - 3*r**2 + 83*r**q + 4*r**5 - 60*r + 23 - 7 = 0?
-4, 1
Factor 64*p**4 - 40*p**4 + 1 - 6*p**2 + 21*p**4 + 7*p**3 + 7 - 12*p - 42*p**4.
(p - 1)*(p + 2)**2*(3*p - 2)
Let t(y) be the third derivative of y**7/525 - 9*y**6/100 + 81*y**5/50 - 279*y**4/20 + 324*y**3/5 + 4*y**2 - 322. Solve t(q) = 0 for q.
3, 9, 12
Let c be 45/(-1125)*(1 - -2)*(-250)/25. Find r, given that c*r**2 + 2/5*r**3 + 2/5 + 6/5*r = 0.
-1
Determine i so that -2/5*i**2 - 1492/5*i - 278258/5 = 0.
-373
Let s be 205/18 - ((-124)/(-216) + 110/(-1485)). Suppose 2 + s*v**4 - 40/3*v - 280/9*v**3 + 284/9*v**2 = 0. Calculate v.
3/7, 1
Factor -3824*s**2 - 414*s**3 + 419*s**3 - 2421*s**2.
5*s**2*(s - 1249)
Let m(v) = 57*v + 399. Suppose 0 = 7*f + 14, -10*f = 4*u - 8*f + 32. Let b be m(u). Find z, given that b - 16/7*z**2 + 4/7*z**3 + 16/7*z = 0.
0, 2
Find q such that 96/7*q**4 - 2/7*q**5 + 208/7*q**3 - 396/7*q**2 + 300/7 - 206/7*q = 0.
-3, -1, 1, 50
Suppose -151 = 8*i - 31. Let q(c) = c**3 + 14*c**2 - 16*c - 13. Let h be q(i). Factor -m**h - 8*m + 7*m**2 - 2*m**2.
4*m*(m - 2)
Let y(a) be the third derivative of -15/8*a**4 + 0*a - 15*a**2 - 35/3*a**3 - 7 - 1/12*a**5. Factor y(s).
-5*(s + 2)*(s + 7)
Let w = -2407 + 36112/15. Let b(p) be the second derivative of -2/3*p**3 + 25*p + 0*p**2 - 1/2*p**4 + 0 + 6/5*p**5 - w*p**6. Factor b(v).
-2*v*(v - 1)**2*(7*v + 2)
Let j be (-16)/((-4)/2) - (19 - 2929/261). Let l(c) be the second derivative of 5/9*c**3 + j*c**4 + 1/3*c**2 + 0 - 4*c. Factor l(x).
2*(x + 1)*(4*x + 1)/3
Let y = 20885/2 - 10442. Factor 1/4*s**3 + 0 - 3/4*s**2 + y*s.
s*(s - 2)*(s - 1)/4
Let b(g) be the first derivative of 0*g + 5/2*g**3 + 16*g**2 - 5/48*g**4 - 1/24*g**5 - 32. Let o(v) be the second derivative of b(v). Factor o(t).
-5*(t - 2)*(t + 3)/2
Suppose -557 + 4288 - 6357 - 11738 - 9612*p - 1333*p**2 - 287*p**2 - 4*p**3 = 0. What is p?
-399, -3
Factor 2/3*c**2 - 1564/3 + 1562/3*c.
2*(c - 1)*(c + 782)/3
Factor -3364/3*p - 2/3*p**2 - 1414562/3.
-2*(p + 841)**2/3
Let q(j) be the third derivative of j**8/40320 + j**7/2016 + 73*j**5/30 + 8*j**2 - 8*j. Let d(y) be the third derivative of q(y). Factor d(a).
a*(a + 5)/2
Let t = -1529 - -1531. Let f be (0/(-2 + -2))/t. Factor -2*j + f + 1/2*j**2.
j*(j - 4)/2
Let x(c) = 7*c - 46. Let m be x(6). Let n be (-3)/m*(-7)/((-63)/8). Find u such that -2*u**5 - 14/3*u - n - 26/3*u**4 - 12*u**2 - 44/3*u**3 = 0.
-1, -1/3
Let s(a) be the first derivative of -3*a**4/20 - a**3/5 + 24*a**2/5 + 48*a/5 - 224. What is t in s(t) = 0?
-4, -1, 4
Let k be 58/7656*-240 + 1*2. Factor -6/11*s**2 + 0 + 6/11*s**3 + k*s - 2/11*s**4.
-2*s*(s - 1)**3/11
Let q(u) be the first derivative of u**6/33 + 4*u**5/55 - 12*u**4/11 - 12*u**3/11 + 135*u**2/11 - 1312. Suppose q(h) = 0. Calculate h.
-5, -3, 0, 3
Let i(u) be the first derivative of -u**3/4 - 3*u**2/2 + 1356. What is t in i(t) = 0?
-4, 0
Suppose -3*h + 163 = c, 2*c - 6*c = 2*h - 612. Find w such that 2 - c*w + 79*w + 68*w + 2*w**2 = 0.
1
Let c(t) be the first derivative of 2*t**3/15 - 407*t**2/5 + 812*t/5 + 392. What is j in c(j) = 0?
1, 406
Let y(i) = -4*i + 16. Let j be y(-2). Factor -11*f**3 - 8*f + 24*f + 7*f**3 + j*f**2 - 4*f**4 - 32.
-4*(f - 2)*(f - 1)*(f + 2)**2
Let l(a) = a**3 + 7*a**2 - 27*a - 10. Let i be l(-6). Let t = i - 183. Solve 1/5*o**3 + 7*o + t + 11/5*o**2 = 0.
-5, -1
Let g(n) be the second derivative of 2*n**6/15 + 54*n**5/5 + 276*n**4 + 5300*n**3/3 + 3750*n**2 + 1002*n. Let g(x) = 0. Calculate x.
-25, -3, -1
Let q(w) be the second derivative of -w**7/420 + w**6/90 + 15*w**3/2 + 76*w. Let z(c) be the second derivative of q(c). Factor z(j).
-2*j**2*(j - 2)
Let q(a) be the third derivative of 2/35*a**7 - 73*a**2 + 5/8*a**4 - 1/10*a**6 + 0*a - 1/112*a**8 + 0 - 1/10*a**5 - a**3. Suppose q(j) = 0. What is j?
-1, 1, 2
Factor -3*g**4 + 43*g**2 + 22*g**3 - 13 + 15*g**3 - 27 - 3*g**4 - 37*g + 3*g**4.
-(g - 1)*(g + 1)**2*(3*g - 40)
Let x(k) = 4*k**2 - k - 2. Let w be x(-3). Let u = -3