- 60*v**5 + 4170*v - 60*v**3 + 1 - 21 + 175*v**4 - 155*v**2 = 0. What is v?
-1, 1/4, 2/3, 1, 2
Let d(x) be the first derivative of -x**4/6 - 8*x**3/9 - x**2/3 + 4*x + 216. Factor d(s).
-2*(s - 1)*(s + 2)*(s + 3)/3
Let z(n) = 7*n**2 + 20*n + 17. Suppose -5*p + 9*p = 2*f + 10, 2*f + 3*p + 10 = 0. Let w(c) = -15*c**2 - 40*c - 35. Let m(a) = f*z(a) - 2*w(a). Factor m(y).
-5*(y + 1)*(y + 3)
Suppose -144 = -52*b + 16*b. Determine k, given that 4/9*k**b - 4/9*k**2 - 2/3*k**5 + 2/3*k**3 + 0*k + 0 = 0.
-1, 0, 2/3, 1
Let -30/7*h - 12/7*h**2 + 24/7*h**3 - 12/7 + 6/7*h**5 + 24/7*h**4 = 0. What is h?
-2, -1, 1
Let a(w) be the third derivative of -w**6/240 + w**5/24 - 1024*w**2. Determine f, given that a(f) = 0.
0, 5
Suppose 0 = 2*z + 3*i - 1, -2*i = -z - i + 3. Let d = 74 + -517/7. Factor d*a - 1/7*a**3 + 0 + 0*a**z.
-a*(a - 1)*(a + 1)/7
Let f(i) be the third derivative of 1/12*i**3 + 0 + 0*i**4 - 1/120*i**5 + 14*i**2 + 0*i. Factor f(x).
-(x - 1)*(x + 1)/2
Let x(m) = 24*m**4 - 146*m**3 - 14*m**2 - 28*m - 28. Let c(w) = 5*w**4 - 29*w**3 - 3*w**2 - 6*w - 6. Let v(k) = -14*c(k) + 3*x(k). Determine u so that v(u) = 0.
0, 16
Let a(p) be the second derivative of -5*p**4/12 - 5*p**3/3 + 175*p**2/2 - 376*p. Suppose a(w) = 0. Calculate w.
-7, 5
Suppose -4*j + j = -180. Let a be (6/(-12))/(j/(-16)). Solve a*b - 2/15*b**3 + 4/15 - 4/15*b**2 = 0.
-2, -1, 1
Let t be (-30*(-8)/48)/(5/2). Let m(k) be the second derivative of -7*k + 0 + 2/9*k**3 - 13/30*k**5 - 11/18*k**4 + 0*k**t. Factor m(o).
-2*o*(o + 1)*(13*o - 2)/3
Let q(t) = -t**3 - 19*t**2. Let z be q(-19). Let x(v) be the third derivative of 1/48*v**4 + 0*v - 1/24*v**3 + 1/240*v**5 + z - 1/240*v**6 - v**2. Factor x(m).
-(m - 1)*(m + 1)*(2*m - 1)/4
Let v(c) be the second derivative of 25*c**4/42 - 130*c**3/7 + 1521*c**2/7 - c + 20. Factor v(k).
2*(5*k - 39)**2/7
Let w(y) be the first derivative of y**5/50 - 16*y + 2. Let o(r) be the first derivative of w(r). Factor o(g).
2*g**3/5
Factor 5/2*u**2 + 0 - 1/2*u**5 - 1/2*u**4 + u + 3/2*u**3.
-u*(u - 2)*(u + 1)**3/2
Let p(l) = -4*l**3 - 197*l**2 - 725*l - 719. Let r(k) = -2*k**3 - 99*k**2 - 363*k - 361. Let z(q) = 3*p(q) - 5*r(q). Factor z(n).
-2*(n + 2)**2*(n + 44)
Let q(o) = 2*o**3 + o**2 - 2*o - 2. Let r be q(2). Let h be ((-2 - 0)/r)/(10/(-20)). Solve -6/7*v - h*v**2 + 0 = 0.
-3, 0
Let j be (3 - (-48)/(-10))*(-25)/15. Let g(a) be the second derivative of 0*a**2 - 1/110*a**5 + 0 + 0*a**3 - j*a + 1/66*a**4. Factor g(t).
-2*t**2*(t - 1)/11
Let c(r) be the second derivative of -r**5/180 + 2*r**4/9 + 25*r**3/54 - 18*r - 17. Factor c(b).
-b*(b - 25)*(b + 1)/9
Let z = 486 + -3378/7. Factor z*u + 10/7*u**2 + 8/7.
2*(u + 2)*(5*u + 2)/7
Let w(p) be the first derivative of -p**7/2100 - p**6/300 - p**5/150 - 9*p**3 + 22. Let h(r) be the third derivative of w(r). Factor h(j).
-2*j*(j + 1)*(j + 2)/5
Let s(f) be the second derivative of -5*f**4/36 + 5*f**3/18 - 46*f. Factor s(r).
-5*r*(r - 1)/3
Suppose -1 - 4 = -5*n, 9 = -a - 2*n. Let y = -11 - a. Factor 6*k**5 - k**2 - 3*k + y*k**2 - 5*k**2 - 3*k**5 + 6*k**4.
3*k*(k - 1)*(k + 1)**3
Let f(a) be the first derivative of a**6/11 - 102*a**5/55 + 93*a**4/22 - 30*a**3/11 - 198. Factor f(h).
6*h**2*(h - 15)*(h - 1)**2/11
Suppose 1/8*y**2 + 53/8 + 27/4*y = 0. What is y?
-53, -1
Let d(u) be the second derivative of 5/7*u**2 + 0 + 4*u - 2/7*u**3 + 1/42*u**4. Suppose d(y) = 0. What is y?
1, 5
Suppose -23/2*l**2 + 1/2*l**4 - 3/2*l**3 - 33/2*l - 7 = 0. What is l?
-2, -1, 7
Let x(l) = l**2 - 14*l + 48. Let z be x(9). Let y(o) be the second derivative of -5*o - 1/12*o**4 - 1/6*o**z + 0 - 1/6*o**2 - 1/60*o**5. Factor y(s).
-(s + 1)**3/3
Let i(w) be the second derivative of w**4/4 - 2*w**3 - 15*w**2/2 + 227*w. Let i(c) = 0. What is c?
-1, 5
Let c(d) be the second derivative of 1/4*d**3 + 1/24*d**4 - 6*d + 1/2*d**2 + 0 + 1/360*d**5. Let l(z) be the first derivative of c(z). Solve l(b) = 0 for b.
-3
Suppose -47*m - 56 = -51*m. Let p be 42/65 - (-3)/(273/m). Suppose 4/5*j**4 - p*j + 4/5 - 4/5*j**5 - 8/5*j**2 + 8/5*j**3 = 0. What is j?
-1, 1
Let v(h) be the first derivative of -2*h**3/21 - 4*h**2/7 + 77. Factor v(y).
-2*y*(y + 4)/7
Suppose -d = -8, -3*o = -5*o + 3*d - 14. Find r such that 2/3*r**4 + 2/9*r**3 + 0 + 2/9*r**o - 4/9*r - 2/3*r**2 = 0.
-2, -1, 0, 1
Let a be (4/14)/(3/42). Solve -2 + 0*p + 7*p**3 + 5*p - 2*p**3 - 4*p**3 - a*p**2 = 0.
1, 2
Let p(s) be the second derivative of 10*s**7/357 - 27*s**6/85 - 299*s**5/170 - 36*s**4/17 - 44*s**3/51 + s + 109. Suppose p(m) = 0. Calculate m.
-2, -1/2, -2/5, 0, 11
Let f(q) be the third derivative of -5/12*q**4 + 1/60*q**6 + 1/10*q**5 + 2/3*q**3 - 1/105*q**7 + 0*q + 10*q**2 + 0. Determine j so that f(j) = 0.
-2, 1
Let j = 702/115 + -426/115. Determine v, given that -j*v - 14/5 + 2/5*v**2 = 0.
-1, 7
Let f = 435/23 - 429/23. What is k in -18/23*k**3 - 42/23*k**2 - f + 34/23*k = 0?
-3, 1/3
Let a(x) be the first derivative of -2*x**5/5 + 528*x**4 - 278784*x**3 + 73598976*x**2 - 9715064832*x - 102. Solve a(w) = 0 for w.
264
Suppose -2*d + 105 - 84 = -3*x, -5*x - 13 = 4*d. Determine l so that -9/5 - 3/5*l + 21/5*l**2 + 3*l**d = 0.
-1, 3/5
Suppose 2*b + 3*o = 3*b - 24, 0 = 3*b + 4*o - 72. Let y = 26 - b. Factor 6*m - 4*m**2 - y*m**3 - 131 - 4*m**3 + 135.
-2*(m - 1)*(m + 1)*(3*m + 2)
Let y be (1/3)/(((-30)/(-36))/5). Let 3*m**3 - 3*m**4 - 3*m + 3*m**2 + 5*m**2 - 5*m**y = 0. What is m?
-1, 0, 1
Let f(h) be the third derivative of 0*h - 1/84*h**4 + 13/1470*h**7 - 13/420*h**5 + 0*h**3 - 3/280*h**6 + 11/2352*h**8 - 4*h**2 + 0. Find u such that f(u) = 0.
-1, -2/11, 0, 1
Let r(x) = 7*x**4 + 38*x**3 + 67*x**2 + 26*x. Let v(d) = -22*d**4 - 113*d**3 - 202*d**2 - 76*d. Let y(i) = -7*r(i) - 2*v(i). Let y(w) = 0. Calculate w.
-6, -1, 0
Suppose -c = 2*k - 4, 293*c - 299*c - 41 = -k. Solve 8/9 + 2/3*d**4 - 14/9*d**2 + 2/9*d**k + 0*d - 2/9*d**3 = 0.
-2, -1, 1
Let v(g) = -2*g**2 + 6*g + 17. Let s(h) = -8*h**2 + 22*h + 69. Let t(a) = 6*s(a) - 26*v(a). Factor t(n).
4*(n - 7)*(n + 1)
Let x(y) be the second derivative of y**6/180 - y**5/60 - 3*y**3 - 16*y. Let p(j) be the second derivative of x(j). Suppose p(v) = 0. Calculate v.
0, 1
Let v be 5940/(-300) + (0 - -25). Find r such that 12/5*r**4 + v*r**3 + 24/5*r**2 + 8/5*r + 0 + 2/5*r**5 = 0.
-2, -1, 0
Let f(y) = y + 2. Let w be f(-6). Let a be 7/(-14) + (-14)/w. Factor -8*u**2 + 8*u**2 - a*u**2 + 6*u.
-3*u*(u - 2)
Let c = 133/120 + -16/15. Let n(m) be the second derivative of c*m**6 - 1/16*m**4 + 0 - 7/80*m**5 - 9*m - 1/4*m**2 + 7/24*m**3. Factor n(k).
(k - 1)**2*(k + 1)*(5*k - 2)/4
Let n(z) be the third derivative of -z**9/90720 + z**7/2520 - z**6/540 + z**5/10 - 15*z**2. Let a(t) be the third derivative of n(t). Let a(d) = 0. Calculate d.
-2, 1
Let k(w) be the third derivative of -1/1620*w**6 + 0*w + 0 - 2*w**2 + 0*w**4 + 3/2*w**3 + 0*w**5. Let r(l) be the first derivative of k(l). Factor r(y).
-2*y**2/9
Let x = 7 - 5. Let o be 6*(x + 3/(-2)). Solve -r**3 + 7*r**2 + 3*r**o - 2 + 3*r**2 + 10 + 16*r = 0 for r.
-2, -1
Let v(o) = -9*o**2 - o + 7. Let y(q) = 3*q**2 - 2. Suppose t + 10 = -t - 4*u, -u - 34 = 5*t. Let z(j) = t*y(j) - 2*v(j). Factor z(g).
-g*(3*g - 2)
Let v be (7 - (-5031)/(-715))*(-7 + 2). Suppose -4/11 - v*d + 12/11*d**2 = 0. What is d?
-1/2, 2/3
Suppose 12 = -v - 2*r, -2*r = 2*v - 1 + 25. Let h be 4/v - (0 + -3). Let -2/3*n - 4/3*n**3 - 8/3*n**4 + 0 + 2*n**5 + h*n**2 = 0. Calculate n.
-1, 0, 1/3, 1
Suppose -5*v - 74 = -84. Suppose -7*o = -o + v*o. Find x, given that -1/4*x - 3/4*x**3 - 1/4*x**4 - 3/4*x**2 + o = 0.
-1, 0
Let j(q) = -q**3 - 6*q**2 - 11*q - 10. Let n be j(-5). Factor -n*x**3 + 17 - 117*x**2 - 67*x**3 - 18*x**3 - 5.
-3*(x + 1)*(5*x + 2)*(7*x - 2)
Let s(c) = 12*c**3 + 63*c**2 + 11*c - 19. Let b be s(-5). Let 7/4*f + 1/2*f**2 + b - 1/4*f**3 = 0. What is f?
-1, 4
Let f(r) = -r - 2. Let u be f(-1). Let m be (3 - u)/(16/8). Determine y, given that 7*y**m - 2*y + 0 + 0 + 5*y**2 = 0.
0, 1/6
Solve -1773*p - 15*p**2 - p**4 + 0*p**2 - 20*p**3 + 1773*p - 4*p**4 = 0 for p.
-3, -1, 0
Let l(o) be the second derivative of 1/24*o**6 + 0*o**4 - 2*o + 0 + 0*o**3 + o**2 - 1/30*o**5. Let c(r) be the first derivative of l(r). Solve c(d) = 0 for d.
0, 2/5
Let n(a) be the second derivative of -2*a**7/21 - 12*a**6/5 - 14*a**5/5 + 56*a**4/3 + 58*a**3 + 68*a**2 - 82*a - 1. Facto