2 + 3*k - 11. Let n be l(4). Suppose -6*f**2 + 2*f**3 - 13*f - n*f - 4*f**3 + p*f = 0. Calculate f.
-2, -1, 0
Let c(h) be the second derivative of 3*h**5/5 - 351*h**4/4 + 3828*h**3 + 2904*h**2 + 3*h + 1165. Determine q so that c(q) = 0.
-1/4, 44
Find s, given that -15/4*s**2 - 21/2*s + 3/4*s**3 + 0 = 0.
-2, 0, 7
Let l = 53/2 - 26. Suppose 7*p = -7 + 21. Factor -1/2*x + l*x**p + 0.
x*(x - 1)/2
Suppose 32 = -11*f + 15*f + a, 2*f - 16 = -2*a. Factor -2*s**3 - 2*s - 4*s**2 - 11*s - 2*s - f*s**2 + 5*s.
-2*s*(s + 1)*(s + 5)
Let i be (3 + 2)/(5 - 4). Suppose -i*l = 5*q - 6*q - 18, 3*q + 6 = 3*l. Solve 0 - 7/6*p - 1/6*p**q = 0.
-7, 0
Let d(m) be the second derivative of -3*m**5/20 - 39*m**4/2 - 76*m**3 + 3*m + 54. Suppose d(w) = 0. Calculate w.
-76, -2, 0
Let y(i) = 12*i**2 - 112*i + 90. Let j(p) = 34*p**2 - 332*p + 270. Let n(l) = -5*j(l) + 14*y(l). What is x in n(x) = 0?
1, 45
Let d(h) be the first derivative of -h**3 - 51*h**2/2 - 156*h + 518. Solve d(b) = 0.
-13, -4
Determine r so that 0 + 6*r - 5/2*r**2 - 1/4*r**4 - 13/4*r**3 = 0.
-12, -2, 0, 1
Let l(x) = x**2 + x - 2. Suppose -5*r - u - 20 = 0, 7*u - 28 = r + 12*u. Let q(i) = -5*i**2 + 217*i - 6044. Let o(y) = r*l(y) - q(y). Factor o(v).
2*(v - 55)**2
Let c(r) be the first derivative of -57 - 57/4*r**2 + 1/8*r**3 + 1083/2*r. Factor c(v).
3*(v - 38)**2/8
Let n(b) be the first derivative of 3*b**5/35 - 453*b**4/2 + 1119361*b**3/7 - 478368*b**2 + 3345408*b/7 - 11457. Factor n(i).
3*(i - 1056)**2*(i - 1)**2/7
Let s(g) be the second derivative of 4*g**6/45 - 21*g**5/10 + 16*g**4 - 308*g**3/9 - 32*g**2 - 12*g - 61. Solve s(m) = 0.
-1/4, 2, 6, 8
Let f(i) be the second derivative of i**4/28 - 127*i**3/14 - 192*i**2/7 + 2*i + 1757. Factor f(s).
3*(s - 128)*(s + 1)/7
Let q = 11395 + -102553/9. Let l(z) be the third derivative of 1/180*z**6 + 0*z + 0 - 2/45*z**5 + 5/36*z**4 - 7*z**2 - q*z**3. What is h in l(h) = 0?
1, 2
Suppose 58/17*f**2 - 60/17*f**3 + 2/17*f**4 + 0 + 0*f = 0. Calculate f.
0, 1, 29
Factor 612*t - 219*t**2 - 212*t**2 + 728*t + 446 + 437*t**2.
2*(t + 223)*(3*t + 1)
Let y(m) be the first derivative of -20*m**2 - 4/3*m**3 - 64*m + 105. Factor y(g).
-4*(g + 2)*(g + 8)
Let m(r) be the third derivative of -r**7/630 + 7*r**6/15 - 294*r**5/5 + 9*r**4/4 + 263*r**2. Let k(y) be the second derivative of m(y). Solve k(j) = 0.
42
Let k(h) = -410*h - 13116. Let s be k(-32). Let w(i) be the third derivative of 35*i**2 + 6*i**3 + 0*i + 1/60*i**5 + 0 - 1/2*i**s. Find a such that w(a) = 0.
6
Let b be (64 - 82)*(-1 - 48/(-54)). Factor -64/25*t - 2/25*t**b - 512/25.
-2*(t + 16)**2/25
Let m(i) = -16*i**4 - 18*i**3 - 6*i**2 + 457*i. Let r(s) = 21*s**4 + 16*s**3 + 7*s**2 - 456*s. Let o(w) = -4*m(w) - 3*r(w). Solve o(h) = 0 for h.
-23, -5, 0, 4
Factor -3*l**2 - 47417 + 3*l**2 - 4*l**2 + 48073 + 320*l.
-4*(l - 82)*(l + 2)
Let s(j) = j**3 - 12*j**2 - 11*j - 23. Let k be s(13). Let h(f) = -f + 1. Let g(u) = u**2 + u + 4. Let x(w) = k*g(w) - 6*h(w). What is v in x(v) = 0?
-2, -1
Let u(w) be the second derivative of -5/72*w**4 - 19*w**2 + 1/72*w**6 + 0*w**5 + 0*w**3 - 16*w + 0. Let c(d) be the first derivative of u(d). Solve c(g) = 0.
-1, 0, 1
Let k(y) be the first derivative of 3/4*y**2 - 17*y + 3/4*y**4 + 3/10*y**5 + 1/20*y**6 + y**3 + 5. Let p(n) be the first derivative of k(n). Factor p(d).
3*(d + 1)**4/2
Let w = 15958 + -15958. Let j(r) be the third derivative of 1/15*r**3 + 0*r - 1/600*r**5 - 1/80*r**4 - 33*r**2 + w. Determine c so that j(c) = 0.
-4, 1
Factor 28*m**2 - 22/3*m**3 + 80/3 + 2/3*m**4 - 136/3*m.
2*(m - 5)*(m - 2)**3/3
Let u(n) = 40*n**4 - 45*n**3 - 212*n**2 - 127*n. Let f(s) = -22*s**4 + 22*s**3 + 106*s**2 + 62*s. Let g(c) = 11*f(c) + 6*u(c). Factor g(a).
-2*a*(a + 1)*(a + 5)*(a + 8)
Let r(u) be the third derivative of u**7/945 + u**6/180 - 7*u**5/27 + 31*u**2 - 26*u. Find a such that r(a) = 0.
-10, 0, 7
Suppose -134*m + 494*m = -505*m - 422*m. Solve m + 14/3*x - 1/3*x**2 = 0.
0, 14
Let c = -16 - -18. Factor -4*j**5 + 39*j + 40*j**3 + 5*j**5 - 24*j - 80*j**c - 32 - 10*j**4 + 65*j.
(j - 2)**5
Let r be (-1)/((-16)/(-18))*(-166)/249. Let v be (17 - 1162/70) + 3/(-120). Solve -v*b**2 - r - 9/8*b = 0 for b.
-2, -1
Let i(v) be the second derivative of 0*v**2 + 1/42*v**3 - 41*v - 1/84*v**4 + 0. Factor i(z).
-z*(z - 1)/7
Let u(r) be the third derivative of -1/6*r**4 - 1/90*r**5 + 0*r + 354*r**2 + 1/120*r**6 - 4/9*r**3 + 0 + 1/630*r**7. Factor u(a).
(a - 2)*(a + 1)*(a + 2)**2/3
Let w = 30477/11 + -274183/99. Factor 0 - w*g**2 - 4/9*g - 8/9*g**3 - 2/9*g**4.
-2*g*(g + 1)**2*(g + 2)/9
Let j(z) = -25*z**4 - 40*z**3 - 555*z**2 - 540*z - 120. Let n(v) = -v**4 - v**3 - 4. Let l(f) = -j(f) + 30*n(f). Factor l(g).
-5*g*(g - 12)*(g + 1)*(g + 9)
Suppose 0*i**3 + 2094*i - 20*i**3 + 16*i**3 + 1140*i**2 - 412*i**2 - 35218*i = 0. Calculate i.
0, 91
Let t(c) = -32*c - 734. Let m be t(-23). Let n be m + -2 - (-264)/484. Let -2/11*a**3 + 0 + n*a**2 + 0*a = 0. What is a?
0, 3
Let n(z) = z**3 + 26*z**2 + 58*z + 57. Let u be n(-24). Let g = u - -2023/11. Factor 0 + 2/11*y**3 + 2/11*y**4 - g*y**2 + 6/11*y.
2*y*(y - 1)**2*(y + 3)/11
Let c(g) be the second derivative of -169*g**5/60 + 481*g**4/36 + 77*g**3/18 + g**2/2 + 140*g. Factor c(s).
-(s - 3)*(13*s + 1)**2/3
Let x(o) = o**3 - 20*o**2 + 93*o - 13. Let y be x(7). Let r be y*(8 - 9 - -4). Factor -7/3*p**2 - 2/3*p**r - 8/3*p - 1.
-(p + 1)**2*(2*p + 3)/3
Let l(f) be the first derivative of 23 - 1/6*f**3 - f**2 + 1/10*f**5 + 1/2*f**4 + 0*f. Factor l(o).
o*(o - 1)*(o + 1)*(o + 4)/2
Let u(a) = a**2 + 22*a + 23. Let p be u(-21). Suppose -m - 9 - 1 = -p*i, -4*i - m = -14. Factor -3*d**i - 5*d**4 + 5*d**5 + 3*d**4.
5*d**4*(d - 1)
Suppose 0 = -16*i - 318 + 382. Let t(c) be the second derivative of 0 - 2/11*c**2 - 1/11*c**3 - 4*c + 1/110*c**5 + 0*c**i. Factor t(g).
2*(g - 2)*(g + 1)**2/11
Let z(t) be the third derivative of -1/5*t**5 + 0 - 1/8*t**4 + 1/40*t**6 + 39*t**2 + 0*t + 2*t**3. Find q such that z(q) = 0.
-1, 1, 4
Let i(k) be the first derivative of 41 + 4/35*k**5 + 0*k - 10/7*k**2 + 44/21*k**3 - k**4. Find r, given that i(r) = 0.
0, 1, 5
Let j(x) be the second derivative of x**4/18 - 25*x**3/3 + 1449*x. Factor j(n).
2*n*(n - 75)/3
Let i = -415203/2 + 207891. Suppose -216 - 3/2*o**4 + 39*o**3 + 468*o - i*o**2 = 0. Calculate o.
1, 12
Let k(b) be the third derivative of -7/72*b**4 + 228*b**2 + 0*b**3 - 1/360*b**5 + 0*b + 1. Suppose k(a) = 0. What is a?
-14, 0
Let f(q) = 9*q + 45. Let y be f(-4). Let m be 3/y - (-10)/6. Determine i so that -5*i**m - 13 + 29 - 11 = 0.
-1, 1
Let y be (8 + -7)/((-16)/(-12780)). Let t = y - 798. What is v in -3/2*v**2 + 15/8*v - t + 3/8*v**3 = 0?
1, 2
Suppose -54*q**2 - 3/2*q**4 - 33/2*q**3 - 54*q + 0 = 0. What is q?
-6, -3, -2, 0
Let v(c) = 7*c**3 - 142*c**2 - 456*c - 326. Let p(d) = 2*d**3 - 48*d**2 - 152*d - 108. Let a(b) = 19*p(b) - 6*v(b). Determine u, given that a(u) = 0.
-12, -2, -1
Let z = 363440 + -363437. Suppose 3*b = 2*k - 6, -3*k - 8 + 0 = 4*b. Factor 0 + 0*n**2 - 2/3*n**z - n**4 + k*n.
-n**3*(3*n + 2)/3
Let g = 555 + -560. Let z be 12/42*7 - (g - -4). Solve 0*c + 2/3*c**z - 4/3*c**2 + 2/3*c**4 + 0 = 0 for c.
-2, 0, 1
Let q(n) be the second derivative of n**8/280 - 13*n**7/420 + 2*n**6/45 + n**5/5 + 17*n**3/3 - 19*n + 2. Let f(u) be the second derivative of q(u). Factor f(y).
2*y*(y - 3)*(y - 2)*(3*y + 2)
Let a be (-34)/(-425) - (-196)/50. Factor 0 - 2/5*t**a + 0*t**3 + 0*t + 2/5*t**2.
-2*t**2*(t - 1)*(t + 1)/5
Factor -37520/3*x - 542/3*x**2 - 2/3*x**3 - 35912.
-2*(x + 3)*(x + 134)**2/3
Factor 13*j + 75*j + 24*j + 115353 - 115653 - 4*j**2.
-4*(j - 25)*(j - 3)
Let s(q) be the second derivative of -q**5/60 + 73*q**4/36 + 289*q**3/9 - 240*q**2 - 3*q - 36. What is z in s(z) = 0?
-9, 2, 80
Find t, given that 0 + 3/5*t**4 + 84*t**3 + 14271/5*t**2 - 30246/5*t = 0.
-71, 0, 2
Let z(c) = -c**2 + 20*c - 47. Let x be z(16). Suppose 0 = x*g - 29 - 5. Factor 0 + 0*u**3 + 9/2*u**g - 3/2*u**4 - 3*u.
-3*u*(u - 1)**2*(u + 2)/2
Let p(i) be the third derivative of -i**6/180 - 4*i**5/15 + i**3/2 + 260*i**2. Let q(m) be the first derivative of p(m). Factor q(z).
-2*z*(z + 16)
Factor -36*m**4 + 14*m**3 + 6*m**4 - 51*m**2 + 40*m + 32*m**4 - 5*m**2.
2*m*(m - 2)*(m - 1)*(m + 10)
Suppose 0 = -22*w - 2 - 42. Let g be 8/(-2)*w/14. Factor 0*p**3 + 0 + 0*p + 2/7*p**2 +