ivative of 0 + 1/40*f**5 - 3*f + 5/24*f**4 - 9/4*f**2 + t*f**3. Factor n(d).
(d - 1)*(d + 3)**2/2
Let f(k) be the third derivative of k**8/560 + 11*k**7/840 + k**6/45 - k**5/30 + 19*k**3/6 - 6*k**2. Let l(m) be the first derivative of f(m). Solve l(r) = 0.
-2, 0, 1/3
Let x(g) be the first derivative of -g**4/5 - 88*g**3/15 - 42*g**2 - 576*g/5 + 176. Factor x(m).
-4*(m + 3)**2*(m + 16)/5
Let a(x) be the third derivative of 135*x**8/56 + 183*x**7/35 - 233*x**6/30 + 18*x**5/5 - 2*x**4/3 - x**2 + 28*x. Suppose a(u) = 0. Calculate u.
-2, 0, 1/5, 2/9
Suppose 1/7*k**5 + 22/7*k**3 - 23/7*k + 0 + 24/7*k**2 - 24/7*k**4 = 0. Calculate k.
-1, 0, 1, 23
Let d(w) = 4*w**2 + 10*w + 6. Let u(r) = 3*r**2 + 9*r + 8. Let m(g) = -2*d(g) + 3*u(g). Let m(b) = 0. What is b?
-4, -3
Let o(k) = 34*k**2 + 435*k - 915. Let c(t) = 8*t**2 + 109*t - 229. Let d(z) = 26*c(z) - 6*o(z). Factor d(l).
4*(l - 2)*(l + 58)
Let f(m) = m**4 - m**3 + m + 1. Let p(b) = -b + 2. Let d be p(7). Let n(c) = 10*c**4 - 35*c**3 + 30*c**2 - 5*c - 10. Let s(g) = d*f(g) - n(g). Factor s(q).
-5*(q - 1)**3*(3*q + 1)
Let u(c) be the third derivative of c**8/336 + 2*c**7/35 + c**6/12 - c**5/5 - 11*c**4/24 - 7*c**2. Factor u(t).
t*(t - 1)*(t + 1)**2*(t + 11)
Let t(x) = 2*x**2 - x. Let h be t(-1). Let f = 6 + -4. Factor 5*v + 5 - 1 - v - 2 - f*v**4 - 4*v**h.
-2*(v - 1)*(v + 1)**3
Suppose -5*t + 7 = -4*v, -4*v + 3*t = -10*v + 21. Let 1/2*q**4 - 9/10*q**v - 2*q + 6/5 + 6/5*q**3 = 0. What is q?
-2, 3/5, 1
Let b(w) be the first derivative of 3*w**4/4 - 4*w**3 + 6*w**2 + 30. Determine z so that b(z) = 0.
0, 2
Suppose 38/11*y**3 + 0 - 100/11*y**2 + 64/11*y - 2/11*y**4 = 0. Calculate y.
0, 1, 2, 16
Let p(u) be the second derivative of -41*u**4/18 + 124*u**3/9 - u**2 - 793*u. Factor p(z).
-2*(z - 3)*(41*z - 1)/3
Suppose 4*x + 4 = 4*z, -4*z + 11 = x - 3. Let n(j) be the third derivative of -1/10*j**4 + 1/150*j**5 + 0*j - 4*j**2 + 3/5*j**z + 0. Solve n(s) = 0 for s.
3
Let r = -2042 - -2047. Suppose 0 + 0*h + 0*h**2 - 2/15*h**r - 2/15*h**3 + 4/15*h**4 = 0. Calculate h.
0, 1
Let n be 150/175 - (-12)/(-14). Let j(a) be the third derivative of 0 + 7*a**2 - 1/15*a**3 + 1/600*a**6 - 1/40*a**4 + 0*a + n*a**5. Factor j(x).
(x - 2)*(x + 1)**2/5
Let s = 11282/3 - 3760. Factor 0*v**3 - 4/3*v**4 - s*v + 2/3*v**5 + 0 + 4/3*v**2.
2*v*(v - 1)**3*(v + 1)/3
Suppose 4*t - 4*m = 44, -29 = 5*m - 19. Let l(w) be the second derivative of -1/18*w**3 - t*w - 1/18*w**4 - 2/45*w**6 + 7/60*w**5 + 0*w**2 + 0. Factor l(o).
-o*(o - 1)**2*(4*o + 1)/3
Let n(m) = m**3 + 4*m**2 - 7. Let z be n(-3). Factor 7*v + 0*v**2 + v**z - 6*v.
v*(v + 1)
Suppose -77 = 3*b - 86. Let p be ((-18)/(-105))/b*(8 + -1). Find y such that -2/5*y**3 + p*y + 4/5 - 4/5*y**2 = 0.
-2, -1, 1
Let b(u) = -2*u**2 - 26*u + 220. Let c(g) = 2*g**2 + 28*g - 222. Let y(p) = 4*b(p) + 5*c(p). Factor y(n).
2*(n - 5)*(n + 23)
Let h = -1851/5 + 371. Determine v, given that 0 + 2/5*v**2 - h*v = 0.
0, 2
Factor 1/7*d**2 - 20/7 - 1/7*d.
(d - 5)*(d + 4)/7
Let k(d) be the first derivative of -d**4/66 - 7*d**3/33 - 57*d + 18. Let b(a) be the first derivative of k(a). What is i in b(i) = 0?
-7, 0
Suppose 5*k - 4 = 3*v, -k - 2*k = 2*v - 10. Let i(n) = 1 + 1 - 1 - v*n + 3*n. Let a(t) = -2*t**3 - 2*t**2 - 4*t - 4. Let u(y) = -a(y) - 6*i(y). Factor u(z).
2*(z - 1)*(z + 1)**2
Let w(f) be the third derivative of f**9/574560 + f**8/95760 - 9*f**5/20 + 28*f**2. Let k(l) be the third derivative of w(l). Let k(u) = 0. What is u?
-2, 0
Let d(k) be the first derivative of -4*k + 2*k**2 + 21 - k**4 + 4/3*k**3. Suppose d(p) = 0. What is p?
-1, 1
Let r(m) be the second derivative of -2*m**4 + m**3/2 + 94*m. Factor r(w).
-3*w*(8*w - 1)
Factor 0 - 3/4*q**2 - 1/2*q**3 - 1/4*q.
-q*(q + 1)*(2*q + 1)/4
Let d(b) be the third derivative of -b**7/210 - 7*b**6/120 + 3*b**5/10 + 122*b**2 + b. What is m in d(m) = 0?
-9, 0, 2
Let z(c) = -1. Let j(o) = -3*o**2 - 14*o - 46. Let y(g) = j(g) + 3*z(g). Let b(l) = l**2. Let m(k) = -2*b(k) - y(k). Solve m(f) = 0.
-7
Let s(h) be the second derivative of -h**6/70 + 15*h**5/28 - 65*h**4/28 - 25*h**3/14 + 99*h**2/7 - h + 411. What is w in s(w) = 0?
-1, 1, 3, 22
Factor -3/5*x**2 + 9/5*x + 12/5.
-3*(x - 4)*(x + 1)/5
Let a = -1116 - -1118. Factor -5/2*t + a*t**2 + 1/2.
(t - 1)*(4*t - 1)/2
Let p(q) = q**3 + 4*q**2 - q - 1. Let l(c) = c. Let k(b) = -2*l(b) - p(b). Let t be k(-4). Factor s**3 + 2*s**2 - 8*s**4 + 6*s**t - s**5 + 0*s**3.
s**2*(s - 1)**2*(5*s + 2)
Suppose 2*d + 64 = 6*d - 2*x, -4*d - 4*x = -40. What is a in -78*a**3 + 72*a**2 - 9*a**5 - d*a + 59 + 42*a**4 - 53 - 19*a = 0?
2/3, 1
Suppose 2*s = 3*s - 8. Suppose 0 = 9*v - s*v - 5. Suppose -95*x**3 - 3*x**v + 87*x**3 + 2*x**5 - 5*x**4 - 4*x**2 = 0. Calculate x.
-2, -1, 0
Let w(d) be the third derivative of 0 - 16*d**2 + 0*d**3 - 5/6*d**4 + 1/24*d**6 + 0*d - 1/4*d**5. Factor w(a).
5*a*(a - 4)*(a + 1)
Suppose -9*z + 75 = 21. Suppose z = b + b. Factor -1/4*f**b + 0 + 0*f + 0*f**2.
-f**3/4
Let s(x) be the first derivative of 2/3*x + 1/3*x**2 - 4/9*x**3 + 2/15*x**5 + 1/9*x**6 + 7 - 1/3*x**4. Factor s(y).
2*(y - 1)**2*(y + 1)**3/3
Let d(c) be the first derivative of 0*c**2 - 7 + 0*c**3 + 1/8*c**4 + 0*c. Let d(g) = 0. Calculate g.
0
Suppose 7*i = -27 - 1. Let c be (i - (3 - 5))*(-27)/7. Factor -16/7*a**3 + 0*a - 36/7*a**2 + c - 2/7*a**4.
-2*(a - 1)*(a + 3)**3/7
Let i be (-52)/(-28) + (-18)/(-131 + 5). Find o, given that -7/8*o**i + 1/2 - 3/2*o = 0.
-2, 2/7
Suppose 2*k - 12 = 5*k. Let m = 6 + k. Factor 2*u**2 + 2*u + 6*u**m + 0*u - 8*u**4 - 2*u**3.
-2*u*(u - 1)*(u + 1)*(4*u + 1)
Let l be (((-224)/(-70))/(-4))/(-2). What is n in l*n**2 + 18/5 - 12/5*n = 0?
3
Let l(k) be the third derivative of -k**7/210 + 7*k**6/15 - 16*k**5 + 400*k**4/3 + 16000*k**3/3 - 73*k**2 + k. Factor l(i).
-(i - 20)**3*(i + 4)
Factor -15/7*b + 18/7*b**2 - 3/7*b**3 + 0.
-3*b*(b - 5)*(b - 1)/7
Factor -15*o**2 + 23*o**2 - 9*o**2 + 6*o + 21*o + 2*o - 28.
-(o - 28)*(o - 1)
Let b(q) be the first derivative of 3*q + 15 + 21/2*q**2 + 6*q**3. Suppose b(j) = 0. Calculate j.
-1, -1/6
Let y(r) be the second derivative of r**6/150 - 3*r**5/20 + 27*r**4/20 - 63*r**3/10 + 81*r**2/5 + 4*r + 22. Solve y(g) = 0 for g.
3, 6
Let x(z) be the first derivative of 33/14*z**2 - 24/5*z**5 - 43/7*z**3 + 21 + 8/7*z**6 - 3/7*z + 219/28*z**4. Suppose x(r) = 0. Calculate r.
1/4, 1
Let t(y) = 7 - y**3 - y**2 + 5*y**3 - 1170*y - y**3 + 1163*y. Let p be t(1). Factor 9/7*l**p + 0 + 2/7*l + l**3.
l*(l + 1)*(7*l + 2)/7
Let n be (16/6)/4 + 105/45. Let j(p) be the first derivative of 6/5*p**5 + 0*p**2 + 0*p - 2*p**3 - 1/2*p**4 - n + 1/3*p**6. What is t in j(t) = 0?
-3, -1, 0, 1
Let y = 12 + -13. Let a be 3 + y + -3 - -4. Factor p + 1 + 2*p + p**a + 4 - 4 + 3*p**2.
(p + 1)**3
Suppose 4*w = 3*v - 26, 0*w - w + 1 = 0. Suppose -2*p - 2 = -v. Suppose 24/7*t**p + 4/7 - 6/7*t - 18/7*t**2 + 16/7*t**3 = 0. What is t?
-1, -2/3, 1/2
Let z = 81 - 78. Factor 96*s + 16*s**2 + s**3 - 55 - 60*s**2 + 199 + 3*s**z.
4*(s - 6)**2*(s + 1)
Let a(n) be the third derivative of -1/8*n**6 + 0*n**3 + 2/21*n**7 - 2*n + 0*n**4 + 0*n**5 + 5*n**2 - 5/252*n**8 + 0. Factor a(m).
-5*m**3*(2*m - 3)**2/3
Let j(p) be the first derivative of -2*p**3/45 + 2*p**2/3 + 112*p/15 + 108. Factor j(q).
-2*(q - 14)*(q + 4)/15
Factor 10*b**3 - 1/3*b**5 + 50/3*b**2 + 5/3*b**4 + 35/3*b + 3.
-(b - 9)*(b + 1)**4/3
Let i(n) be the first derivative of n**4 - 16*n**3/3 + 2*n**2 + 24*n + 237. Factor i(c).
4*(c - 3)*(c - 2)*(c + 1)
Let d(o) = -o + 6. Let t be d(4). Suppose 13*b = 12*b. Find h such that 0*h**3 + 10/11*h**5 - 4/11*h**4 + 0*h + 0*h**t + b = 0.
0, 2/5
Let q = 17831/89105 + -2/17821. Solve q*a**2 - 4/5 - 3/5*a = 0.
-1, 4
Let 10 + 26*n - 41*n**2 + 40*n**2 + 17 = 0. What is n?
-1, 27
Factor 1125*n + 52*n**2 + 83*n**2 + 4145 + 44 + 3*n**3 + 576*n - 220.
3*(n + 3)*(n + 21)**2
Let w(o) = 8*o**2 + 25*o + 3. Let s(g) = -2*g**2 + 3*g + 6. Let y(a) = a**2 - 4*a - 5. Let n(h) = -4*s(h) - 5*y(h). Let q(f) = 7*n(f) - 2*w(f). Factor q(u).
(u + 1)*(5*u + 1)
Let n(z) = -5*z**4 + 30*z**2 - 15. Let i(v) = -v**3 - v**2 + v. Let k(t) = -10*i(t) - n(t). Factor k(s).
5*(s - 1)**2*(s + 1)*(s + 3)
Let l be ((-26688)/924)/(-8) + 2/(-11). Let m(n) be the second derivative of -11*n + 0 + 1/28*n**4 + 4/7*n**3 + l*n**2. Factor m(k).
3*(k + 4)**2/7
Let i = -260679/11 + 23