y - 27)*(y - 3)*(y - 1)**2
Let i(z) be the third derivative of z**6/180 - z**5/10 + 3*z**4/4 + 2*z**3 - 7*z**2. Let s(f) be the first derivative of i(f). Solve s(o) = 0.
3
Factor -9*y**2 + 6 + 2*y - 13*y**4 + 5*y**3 - 2*y**3 - 3*y + 16*y**4 - 2*y.
3*(y - 1)**2*(y + 1)*(y + 2)
Let i(k) = k**3 + k**2. Let c(t) = -t**3 - 16*t**2 + 5*t. Let j(a) = c(a) + 6*i(a). Suppose j(x) = 0. Calculate x.
0, 1
Suppose 15*q - 440 = 7*q. Let o be (-1)/(-4) + (-1 - q/(-60)). Suppose -o*r - 1/3 + 1/6*r**2 = 0. What is r?
-1, 2
Let j(q) be the second derivative of -1/70*q**7 - 27/100*q**5 + q + 0*q**2 + 0 - 1/10*q**6 - 1/5*q**3 - 7/20*q**4. Factor j(w).
-3*w*(w + 1)**3*(w + 2)/5
Solve 116*x**2 - 18*x**2 - 6*x**3 + 6*x - 156*x**2 + 56 + 2*x**4 = 0.
-4, -1, 1, 7
Let y(t) = -4*t + 2. Let q be y(-1). Suppose 20 = g + 3*b + q, 0 = 2*b - 8. Factor -4*r - 67*r**2 + g*r**3 + 0*r**3 + 69*r**2.
2*r*(r - 1)*(r + 2)
Let c(y) = 5*y + 10*y**2 + 1 - y**3 - 3 + 2*y**3 - 10. Let g be c(-9). Determine p, given that g*p - p**2 + 14 + 16*p**2 + 3*p**3 - 1 - 1 = 0.
-2, -1
Let p(i) be the second derivative of i**7/42 + 4*i**6/15 - i**5/10 - 31*i**4/3 - 215*i**3/6 - 50*i**2 + 4*i - 41. Factor p(c).
(c - 4)*(c + 1)**2*(c + 5)**2
Factor -1700 + 24*n - 25*n**3 - 70*n**2 - 2*n**4 + 1772 + n**3.
-2*(n - 1)*(n + 1)*(n + 6)**2
Let i(v) = -9*v**2 - 5*v. Let c(o) = -4*o**2 - 2*o. Let p be -4*((-1)/(-1))/(-1). Suppose p*d + 15 = -5. Let h(u) = d*c(u) + 2*i(u). Factor h(k).
2*k**2
Suppose -2*p = -10, 3*n + 30 = n + 2*p. Let f be 1/n*135/(-6). Factor -3/2 - f*m**3 + 3/4*m + 3*m**2.
-3*(m - 1)**2*(3*m + 2)/4
Let v = -2/81611 + 2203507/408055. Find l such that 24/5*l + 3/5*l**2 - v = 0.
-9, 1
Let w = -1484 - -16326/11. Let w*x**2 - 2/11*x + 0 = 0. What is x?
0, 1
Factor -720/17*g + 648/17 + 74/17*g**2 - 2/17*g**3.
-2*(g - 18)**2*(g - 1)/17
Let f(s) be the second derivative of -s**6/120 + s**5/20 - s**4/8 + s**3/3 + 2*s. Let w(m) be the second derivative of f(m). Factor w(x).
-3*(x - 1)**2
Let i(y) be the first derivative of 5/6*y**2 + 2*y - 28 + 1/9*y**3. Determine l, given that i(l) = 0.
-3, -2
Suppose 2*k - 270 = 5*x, 5*k + x = -0*x + 621. Let m = k - 122. Let 3/5*p**5 + 0 + 1/5*p**m - p**4 + 1/5*p**2 + 0*p = 0. Calculate p.
-1/3, 0, 1
Let j(h) be the third derivative of h**9/5040 - h**7/840 + 17*h**4/12 + 27*h**2. Let q(b) be the second derivative of j(b). Factor q(i).
3*i**2*(i - 1)*(i + 1)
Let i(v) be the second derivative of v**6/6 + 3*v**5 + 35*v**4/4 + 25*v**3/3 + 19*v. Factor i(f).
5*f*(f + 1)**2*(f + 10)
Let w(x) be the second derivative of 75*x**4/4 + 31*x**3/2 + 3*x**2 - 2*x - 57. Factor w(o).
3*(3*o + 1)*(25*o + 2)
Let b(s) be the third derivative of 27*s**6/8 - 12*s**5 + 40*s**4/3 + 246*s**2. Factor b(d).
5*d*(9*d - 8)**2
Let a(c) be the second derivative of -1/15*c**6 + 1/6*c**4 + 0 + 2/3*c**3 + 10*c + 0*c**2 - 1/5*c**5. Find f, given that a(f) = 0.
-2, -1, 0, 1
Let w(k) = -k**2. Let o(q) = 12*q**2 - q. Let i be ((-80)/(-4) - 4)/2. Let r = 10 - i. Let d(x) = r*o(x) + 22*w(x). Factor d(b).
2*b*(b - 1)
Let q(p) be the third derivative of 49*p**6/480 + 1393*p**5/240 - 101*p**4/12 + 29*p**3/6 - 10*p**2 - 7*p. Factor q(t).
(t + 29)*(7*t - 2)**2/4
Let p be (2/4)/((-45)/(-10) + -5). Let k be ((-26)/(-12) - p) + 20/120. Factor 14/9*b**2 + 2 - 2/9*b**3 - k*b.
-2*(b - 3)**2*(b - 1)/9
Let b(d) be the second derivative of 389017*d**5/5 - 5329*d**4 + 146*d**3 - 2*d**2 + 266*d. Factor b(c).
4*(73*c - 1)**3
Suppose -57*p + 34*p - 167*p**2 + 23*p - 103*p**2 + 3*p**3 = 0. What is p?
0, 90
Factor 63 - 50*y + 5*y**2 - y**2 - 10*y - 7*y**2.
-3*(y - 1)*(y + 21)
Let z(c) = 3*c**2 - 6*c + 6. Let d be z(2). Let w be 81/27 + (-14)/d. Factor 2/3 + w*m + 1/6*m**2.
(m + 2)**2/6
Let k(d) be the first derivative of -15*d + 5*d**3 - 3/4*d**4 + 3/2*d**2 + 53. Factor k(p).
-3*(p - 5)*(p - 1)*(p + 1)
Let u(d) = 544*d + 2. Let y be u(0). Factor 0 - 3/5*h**3 - 12/5*h + 12/5*h**y.
-3*h*(h - 2)**2/5
Let h be 0 + 0*(-4)/12. Let x(t) = t**2 + 4. Let u be x(h). What is a in -3*a**2 - 2*a**u + 5*a**2 + 0*a**2 = 0?
-1, 0, 1
Factor -9 + 3*v**3 - 4*v**2 - 8*v**2 - 3*v + 24 - 3*v**2.
3*(v - 5)*(v - 1)*(v + 1)
Let s(q) be the first derivative of q**3/3 - q - 15. Let o(a) = a**3 - 5*a**2 - a + 5. Let t(l) = -o(l) - 5*s(l). Suppose t(m) = 0. Calculate m.
-1, 0, 1
Determine f so that 608*f + 952*f - 2443 + 130*f**3 + 1723 - 965*f**2 - 5*f**4 = 0.
1, 12
Let i(m) = m**3 + 9*m**2 + m + 13. Let d(k) = -k**2 - 4*k + 3. Let b be d(-6). Let c be i(b). Determine r so that 2*r**2 + 2*r**3 - c*r + 312 - 312 = 0.
-2, 0, 1
Let s = -530 + 5832/11. Solve s*k**2 + 18/11 + 12/11*k = 0 for k.
-3
Let g = -3938 - -3940. Factor -24/7*t**3 - 12/7 + 6*t + 30/7*t**g.
-6*(t - 2)*(t + 1)*(4*t - 1)/7
Suppose -g + 5*d - 3*d - 8 = 0, -4*d = -5*g - 10. Factor 0*i**g - 12*i**2 + 9*i + 5 - 2.
-3*(i - 1)*(4*i + 1)
Suppose 0 - 3*f**3 + 5/2*f**2 + 1/2*f = 0. Calculate f.
-1/6, 0, 1
Let x(b) be the first derivative of -9 + 0*b**4 - 1/3*b**3 + 1/12*b**6 - 1/4*b**2 + 0*b + 1/5*b**5. Determine m, given that x(m) = 0.
-1, 0, 1
Let o be 8/(-10) + (-504)/(-180). Let t(w) be the first derivative of -2/9*w**3 - 3 - 2/3*w + 2/3*w**o. Determine k, given that t(k) = 0.
1
Let b = 38 - 39. Let m be 5/b - (11 - 19). What is h in -1/2*h**m - 3/2*h**2 + 0 + 0*h = 0?
-3, 0
Let s(q) = -13*q**3 + 5*q**2 + 8*q + 18. Let o(y) = -11*y**3 + 4*y**2 + 8*y + 17. Let c(w) = 6*o(w) - 5*s(w). Factor c(h).
-(h - 3)*(h + 2)**2
Suppose 12*o - 16*o = -276. Let -o*g + 3*g**4 + 69*g - 3*g**2 = 0. Calculate g.
-1, 0, 1
Let q(u) be the third derivative of 5/12*u**5 + 10/3*u**3 + 0*u - 17*u**2 - 5/3*u**4 + 0 - 1/24*u**6. Let q(w) = 0. Calculate w.
1, 2
Suppose l = 2*m, -3*m - 2 = -2*l + 2. Factor 22*d**3 + d + l*d**3 - 15*d**3 + 7*d**2 + 9*d**4.
d*(d + 1)*(3*d + 1)**2
Suppose -4*x - 4*b + 12 = -8, -32 = -4*x - b. Factor -l**2 - 395 - x*l + 395.
-l*(l + 9)
Let z(m) be the first derivative of 0*m - 4/9*m**3 + 2 - 5/12*m**4 + 1/6*m**2. Let z(i) = 0. What is i?
-1, 0, 1/5
Let f be 544/60 - (-171)/(-19). Let i(r) be the second derivative of f*r**5 + 0 - 16/9*r**3 - 4*r - 1/9*r**4 + 8*r**2. Find y such that i(y) = 0.
-3, 2
Suppose 2*g - q = 8, -3*g + 0*g = q - 12. Suppose 0 = -g*y - 5*b + 23 - 3, -4*b = -4*y - 16. Factor 6*x**2 + y*x - 3*x - x**3 - x**3 - x.
-2*x*(x - 2)*(x - 1)
Let a = -186 + 186. Let d(n) be the second derivative of 0*n**2 + 2*n + 1/18*n**3 + a*n**4 - 1/60*n**5 + 0. Determine y so that d(y) = 0.
-1, 0, 1
Let x = -5073 + 5077. What is c in 0 - 6/5*c**x + 4/5*c - 2/5*c**5 - 2/5*c**3 + 6/5*c**2 = 0?
-2, -1, 0, 1
Find j, given that -50*j**2 + 7*j - 7*j + 36 + 46*j**2 = 0.
-3, 3
Let z = 128 - 118. Suppose 18*p - z = 13*p. Factor -4/7*b**p - 2/7*b + 0 - 2/7*b**3.
-2*b*(b + 1)**2/7
Suppose -5*y = -6*y + 3. Factor 2*q + 2*q**3 - 2*q**2 + 5*q**2 - q**y.
q*(q + 1)*(q + 2)
Suppose 0 = -190*t + 195*t - 4*b, 0 = 4*t - 4*b. Factor -1/2*a**4 + 1/6*a**3 + t + 1/2*a**2 - 1/6*a.
-a*(a - 1)*(a + 1)*(3*a - 1)/6
Let r(n) be the first derivative of -3*n - 9/2*n**2 - 22 - 2*n**3. Factor r(f).
-3*(f + 1)*(2*f + 1)
Let v(o) be the first derivative of 5*o**3/3 + 55*o**2 + 82. Suppose v(m) = 0. Calculate m.
-22, 0
Let i = 4 - 2. Suppose -2*c + 3*f + 3 = 0, -8*c + 3*c + 4*f = -11. Find u such that -4*u**2 + u**5 - 6*u**i + 2 + 5*u + 10*u**c - 3 - 5*u**4 = 0.
1
Suppose f + 2*f - 2*n = -432, -5*f = -4*n + 720. Let j = -144 - f. Suppose 0 - 1/2*k**3 + j*k + k**4 + 0*k**2 - 1/2*k**5 = 0. Calculate k.
0, 1
Let q = 51719390/938457 - -2/104273. Let g = q + -55. Let 0*i**3 + 2/9*i**2 - g + 0*i - 1/9*i**4 = 0. Calculate i.
-1, 1
Let c(q) = 2*q + 0*q**3 - 3*q + 4*q**3. Let o be c(1). Factor 14*v**2 - o*v + 3 - 11*v**2 - 2 - v**3.
-(v - 1)**3
Let c(d) = 3*d**2 - 162*d - 2034. Let l(g) = g**2 - g - 1. Let p(r) = c(r) - 6*l(r). Factor p(w).
-3*(w + 26)**2
Factor -338*s**5 + 3*s**4 - 3*s**2 + 341*s**5 - 15*s**3 + 3*s**2 + 9*s**2.
3*s**2*(s - 1)**2*(s + 3)
Let l = 14 + -11. Factor -2*u**3 + 3*u**2 - u**2 + l*u**3 - 3*u**2.
u**2*(u - 1)
Let u(q) be the third derivative of -q**7/1260 + q**6/240 + q**5/72 - q**4/48 - q**3/9 + 5*q**2 + 11. What is y in u(y) = 0?
-1, 1, 4
Suppose -23 = -4*l + 3*x, 4*l = -13*x + 10*x - 7. Factor 0 + 1/8*h**l + 0*h + 1/8*h**4 + 1/4*h**3.
h**2*(h + 1)**2/8
Let j = -2/2379 - -21/793. Let p(h) be the first d