 Let h*f + 3/8*f**2 + 0 = 0. What is f?
-3, 0
Factor -10/9 + 40/9*l**2 + 23/9*l + 7/9*l**3.
(l + 1)*(l + 5)*(7*l - 2)/9
Let w(l) = l**2 + 22*l - 20. Let z be w(-23). Factor -117*n + 28*n**4 + 37*n + 27*n**3 - 79*n**z - 16 + 20*n**5 - 124*n**2.
4*(n - 2)*(n + 1)**3*(5*n + 2)
Let w(z) be the second derivative of z**5/20 - 2427*z**4/2 + 11780658*z**3 - 57183313932*z**2 + 3*z + 3322. Factor w(m).
(m - 4854)**3
Let t(p) = 6*p**2 + p + 2. Let o be t(1). Let l be (-6)/24 - o/(-4). Factor -21*j**2 + 48*j**2 - 23*j**l - 8*j.
4*j*(j - 2)
Let a(g) be the third derivative of -8*g**2 + 1/8*g**4 + 3/10*g**5 + 16 + 0*g - 13*g**3. Suppose a(h) = 0. Calculate h.
-13/6, 2
Let d = 58208 - 116415/2. Find h such that -2916 + d*h**3 + 486*h - 27*h**2 = 0.
18
Suppose 3*w - 2 = -11, p - 72 = 4*w. Factor -225*c**2 + 0*c**4 - 5*c**4 - 217*c - p*c**3 - 53*c.
-5*c*(c + 3)**2*(c + 6)
Suppose -4*u + 47 = -4*q + 7, q = 5. Factor -5*d - d + 2*d + d**2 + d + 3*d**3 - 16*d**2 + u.
3*(d - 5)*(d - 1)*(d + 1)
Suppose -58*y - g = -55*y - 127, 0 = -2*g - 10. Factor -6384 + 12*a + 6280 + y*a - 2*a**2.
-2*(a - 26)*(a - 2)
Let v(n) be the second derivative of n**5/30 - 3*n**4/2 + 32*n**3/3 + 1280*n**2/3 + 3279*n. Factor v(s).
2*(s - 16)**2*(s + 5)/3
Let c(x) be the first derivative of -x**7/315 + 2*x**6/75 + 7*x**5/150 - 39*x + 46. Let y(i) be the first derivative of c(i). What is z in y(z) = 0?
-1, 0, 7
Determine i so that -608/5*i**2 + 2/5*i**3 - 1222/5*i - 612/5 = 0.
-1, 306
Let n(b) be the first derivative of 2/7*b - 3/14*b**2 - 1/35*b**5 + 3/28*b**4 + 14 - 1/21*b**3. Factor n(h).
-(h - 2)*(h - 1)**2*(h + 1)/7
Let c(g) be the third derivative of 0*g**3 + 0*g - 42*g**2 + 2/3*g**4 + 0 + 74/15*g**5 + 323/30*g**6 - 361/105*g**7. Factor c(h).
-2*h*(h - 2)*(19*h + 2)**2
Let c(n) be the third derivative of -1/480*n**6 - 1/720*n**5 - 12*n**2 + 1/96*n**4 + 1/36*n**3 - 1/2520*n**7 + 0*n + 0. Find u such that c(u) = 0.
-2, -1, 1
Let b(t) be the first derivative of t**6/48 + t**5/12 - 5*t**4/16 + t**2/2 + 8*t - 194. Let l(i) be the second derivative of b(i). Factor l(w).
5*w*(w - 1)*(w + 3)/2
Let l(m) be the third derivative of 16/15*m**3 + 0*m + 25 - m**2 - 11/75*m**5 - 7/5*m**4. Suppose l(f) = 0. Calculate f.
-4, 2/11
Suppose 7*w + 2 = 4*s + 5*w, 3*w - 3 = 4*s. Suppose -s*u = -9*u + 90. Determine o, given that u - 21*o - 33*o**2 - 27*o**2 - 34*o + 40*o**2 = 0.
-3, 1/4
Let a(w) be the third derivative of 9*w**7/70 - 5*w**6/8 - 3*w**5/10 + 9*w**4/2 + 4*w**3 - 28*w**2. Solve a(r) = 0.
-1, -2/9, 2
Let r = 876 - 870. Let q(s) be the first derivative of r*s**4 - 39/2*s**2 - 48/5*s**5 + 14 + 14*s**3 + 6*s + 5/2*s**6. Determine u so that q(u) = 0.
-1, 1/5, 1, 2
Suppose 3 = -t, -4*t + 0*t = 3*n + 6. Let z(c) be the second derivative of -1/33*c**4 + 0 + 6*c + 0*c**3 - 1/110*c**5 + 0*c**n. Factor z(u).
-2*u**2*(u + 2)/11
Let t(v) = 9*v**2 - 36*v + 39. Let d be t(2). Factor -21/8*y - d + 3/8*y**2.
3*(y - 8)*(y + 1)/8
Let w(s) = 1 - 8*s + 23 + s - 7*s**2 - 14. Let l be -2 + 5 + -1 + (-14 - -1). Let k(y) = -36*y**2 - 36*y + 50. Let x(a) = l*w(a) + 2*k(a). Factor x(j).
5*(j - 1)*(j + 2)
Let a be (-13 - -1)*14/(-56). Let w(h) = -h - 3. Let u(y) = -5*y**2 + 37*y + 156. Let n(m) = a*w(m) - u(m). What is r in n(r) = 0?
-3, 11
Let b be (-16)/(-2) + 98/(-7) + 7/((-42)/(-54)). Factor 2/5*d**b - 24/5*d**2 - 20 + 18*d.
2*(d - 5)**2*(d - 2)/5
Suppose -12 = 2*u - 3*f - 19, -u + 8 = 3*f. Factor -11 - m**5 + u + 23*m**2 - 10 - 7*m**4 - 7*m**3 + 0*m**4 + 8*m.
-(m - 1)**2*(m + 1)*(m + 4)**2
Suppose -3 + 9 = 3*g. Let r = 9343 + -9340. What is p in -10/9*p**r - 22/9*p**4 + 0*p + 4/9*p**g + 0 - 8/9*p**5 = 0?
-2, -1, 0, 1/4
Let -136/21*a + 10/21*a**4 - 82/21*a**3 + 166/21*a**2 + 40/21 + 2/21*a**5 = 0. Calculate a.
-10, 1, 2
Factor -67*h**3 - 61*h**3 - 100 + 0 - 90*h - 24*h**2 + 126*h**3.
-2*(h + 2)*(h + 5)**2
Let r(a) = -a**2 + 1389*a + 36794. Let q be r(-26). Factor -69/7*d**2 + 3*d**q + 9/7*d**3 + 3/7*d**5 - 96/7*d - 36/7.
3*(d - 2)*(d + 1)**3*(d + 6)/7
Let h(i) be the second derivative of 24*i**2 + 3/10*i**5 - 3 - 44/3*i**3 - 39*i - 7*i**4 + 1/3*i**6. Determine l, given that h(l) = 0.
-2, 2/5, 3
Let b(a) = 10679*a**2 + 27600*a + 18022. Let o(m) = 2134*m**2 + 5520*m + 3604. Let r(t) = -2*b(t) + 11*o(t). Determine k so that r(k) = 0.
-30/23
Let o = -30 - -30. Suppose -i + 19 = -o*v - 3*v, 2*i - 23 = 3*v. What is a in 4*a**i + 36*a**2 - 14*a**2 - 5 + 1 - 4 + 18*a**3 = 0?
-2, -1, 1/2
Let q(x) be the first derivative of 0*x**2 - 3/14*x**4 - 29*x + 19 + 3/140*x**5 + 0*x**3. Let n(l) be the first derivative of q(l). Find f, given that n(f) = 0.
0, 6
Let d(h) be the first derivative of -61 - 1/3*h**3 - 2*h**2 - 3*h. Factor d(x).
-(x + 1)*(x + 3)
Let b(d) be the first derivative of d**5/32 - 3*d**4/16 + 19*d**3/48 - 3*d**2/8 - 177*d - 154. Let g(z) be the first derivative of b(z). Factor g(l).
(l - 2)*(l - 1)*(5*l - 3)/8
Let g(b) = b**2 + 14*b + 33. Let x be (12 + -1)/(-69 + 68). Let c be g(x). What is f in -2/5*f**3 + 8/5*f + c + 6/5*f**2 = 0?
-1, 0, 4
Let n = 317 + -312. Suppose 0 = -4*f + c - 0*c + 8, -2*c = -n*f + 7. Suppose -1/4*v**f + 3/4*v**2 - 1 + 0*v = 0. Calculate v.
-1, 2
Let u = -6527 + 130481/20. Let n = u - -15/4. Determine b so that -4*b**2 - 12/5 + n*b**3 + 28/5*b = 0.
1, 3
Let t(k) be the first derivative of k**6/54 + 28*k**5/45 - 16*k**4/3 + 400*k**3/27 - 136*k**2/9 - 15. Solve t(a) = 0 for a.
-34, 0, 2
Let u be (2/(-10))/(11/(-110)). Let b(c) be the second derivative of -6*c**u + 0 + 2/3*c**3 - 18*c - 1/36*c**4. Solve b(q) = 0 for q.
6
Suppose 5*u = 4*f + 4*u + 1, 8*f + 4*u - 52 = 0. Factor -34/7 + 2/7*d**f + 32/7*d.
2*(d - 1)*(d + 17)/7
Let r(g) be the second derivative of 2*g**6/5 + 16*g**5/5 + 9*g**4 + 28*g**3/3 - 349*g. Solve r(z) = 0 for z.
-7/3, -2, -1, 0
Let y = 3193 - 3196. Let c = -28 + 13. Let k(m) = -m**3 + 4*m**2 + m + 1. Let j(n) = -n**2. Let f(h) = c*j(h) + y*k(h). Suppose f(q) = 0. Calculate q.
-1, 1
Let g = 11 - 21. Let s be (-15)/g + 2/4. Factor 9/4*q**s + 0*q + 0 - 3/4*q**3.
-3*q**2*(q - 3)/4
Let w(l) be the third derivative of -l**7/315 + l**6/30 - l**5/10 + l**4/9 + 1646*l**2. Suppose w(r) = 0. What is r?
0, 1, 4
Let i(x) be the third derivative of x**7/1260 + 7*x**6/180 - x**5/180 - 7*x**4/12 - 91*x**3/3 - 4*x**2. Let j(l) be the first derivative of i(l). Factor j(p).
2*(p - 1)*(p + 1)*(p + 21)/3
Let y(n) = -n**3 - n**2 + 25. Let d be y(8). Let q = d + 554. Determine p, given that 5/4*p**q + 1/4*p**4 + 0 + 3/4*p + 7/4*p**2 = 0.
-3, -1, 0
Let m(u) be the second derivative of -3*u**3 + 29/4*u**4 - 35*u - 9/2*u**5 + 7/10*u**6 + 0*u**2 + 0. Factor m(o).
3*o*(o - 3)*(o - 1)*(7*o - 2)
Solve -265 - 263/2*s + 1/2*s**2 = 0.
-2, 265
Suppose -2187/5 - 983/5*r**3 + 3807/5*r - 813/5*r**2 + 64/5*r**5 + 112/5*r**4 = 0. What is r?
-27/8, 1, 3
Factor -3*m**2 + 101010 + 2358*m + 6*m**2 + 362337.
3*(m + 393)**2
Let x(k) be the second derivative of -k**6/540 + k**5/90 - 4*k**3/27 + 138*k**2 + 2*k - 2. Let h(n) be the first derivative of x(n). Factor h(z).
-2*(z - 2)**2*(z + 1)/9
Let z(x) be the third derivative of 2*x**7/1785 - 19*x**6/1020 + 7*x**5/510 + 19*x**4/204 - 3*x**3/17 + 1506*x**2. Find y, given that z(y) = 0.
-1, 1/2, 1, 9
Let g(v) be the second derivative of -v**5/210 - v**4/42 + 5*v**3/7 - 27*v**2/2 + 60*v. Let z(n) be the first derivative of g(n). Let z(i) = 0. Calculate i.
-5, 3
Let t = 3333 - 39995/12. Let g(u) be the second derivative of 0 - t*u**5 - 5/6*u**2 + 15*u - 5/12*u**4 - 5/6*u**3. Factor g(x).
-5*(x + 1)**3/3
Let q = -121538/3 - -40514. Determine p, given that -q*p**2 + 8/3 + 4/3*p = 0.
-1, 2
Let u(d) = -15*d**3 - 282*d**2 - 1620*d - 2403. Let f(x) = -7*x**3 - 142*x**2 - 811*x - 1200. Let r(z) = 9*f(z) - 4*u(z). Solve r(s) = 0.
-44, -3
Let l = -506 + 353. Let w be l/17*3/(1 - 10). Determine d so that 1/7*d**4 + 15/7*d**5 - 17/7*d**w + 2/7*d + 0 - 1/7*d**2 = 0.
-1, -2/5, 0, 1/3, 1
Let x(n) be the first derivative of 2*n**6/9 + 38*n**5/15 + 15*n**4/2 + 20*n**3/9 - 52*n**2/3 - 16*n + 351. What is i in x(i) = 0?
-6, -2, -1/2, 1
Let 263/8*f + 195/8*f**2 - 11/8*f**3 + 57/8 = 0. Calculate f.
-1, -3/11, 19
Suppose -15/7*h**3 + 36/7*h**2 + 1/7*h**4 - 48/7 + 4/7*h = 0. What is h?
-1, 2, 12
Suppose 82 = q + 4*q - 2*z, -13 = -q - 3*z. Suppose -3*m + 2*x = -10, -3*m + 0 + 15 = -3*x. Factor -3