- 75*i. Let a(b) = 4*g(b) - 15*y(b). Factor a(q).
-3*q*(q + 21)
Suppose -141*h + 221 = -141 - 61. Factor -1 + 3/2*p**h + 3*p - 1/4*p**4 - 13/4*p**2.
-(p - 2)**2*(p - 1)**2/4
Let t(l) be the first derivative of -21*l**5/50 + 8*l**4/5 - 11*l**3/5 + 6*l**2/5 - l/10 + 518. What is f in t(f) = 0?
1/21, 1
Let u(n) be the third derivative of -1/60*n**5 + 2/3*n**3 + 0*n**4 + 11*n**2 + 0 + 0*n. Solve u(z) = 0 for z.
-2, 2
Let f be (-10)/(-6)*(-21)/(-5). Let t(n) be the second derivative of 0 + 0*n**2 + f*n + 1/60*n**4 + 1/10*n**3. Factor t(h).
h*(h + 3)/5
Let j(k) = -2*k**2 + 26*k + 33. Let z be j(14). Let x(p) be the third derivative of 2/15*p**3 + 6*p**2 - 1/150*p**z + 0 + 0*p - 1/60*p**4. Factor x(b).
-2*(b - 1)*(b + 2)/5
Let x be (-2460)/(-1440) + (-6)/16. Let v(d) be the second derivative of 2/9*d**4 - 9*d - x*d**2 - 2/9*d**3 + 0 + 1/15*d**5. Factor v(m).
4*(m - 1)*(m + 1)*(m + 2)/3
Solve -1156/9 - 128/9*r**3 - 4/9*r**4 + 2176/9*r - 296/3*r**2 = 0.
-17, 1
Let i(z) = -10*z**3 - 25*z**2 + 10*z + 117. Let j(t) = t**3 + t**2 + 2*t + 1. Let n(h) = -2*i(h) - 22*j(h). What is x in n(x) = 0?
-2, 8
Let z(l) be the second derivative of l**4/18 - 6*l**3 - 55*l**2/3 - 4*l + 22. Factor z(p).
2*(p - 55)*(p + 1)/3
Let n(y) be the first derivative of 3*y**4/4 - 17*y**3 - 243*y**2/2 - 189*y + 343. Determine r, given that n(r) = 0.
-3, -1, 21
Solve -1/6*s**2 + 5/3 - 1/2*s = 0.
-5, 2
Let b be 1 - (1 - (9 - 5)/2). Let n(y) be the first derivative of -25/12*y**3 - b*y**2 - 19/16*y**4 - 1/24*y**6 - 7/20*y**5 - y - 2. Factor n(x).
-(x + 1)**3*(x + 2)**2/4
Let x be 264229/819 - (-6)/27. Let u = 323 - x. Suppose -4/13*m**3 + 30/13*m**4 - 14/13*m - 28/13*m**2 + 18/13*m**5 - u = 0. Calculate m.
-1, -1/3, 1
Suppose -2*n = -3*b + 30, 2*n + 2*n = -2*b + 4. Suppose -4*g + 28 - b = 0, -4*z + g + 7 = 0. Factor 2/5 + 21/5*v**2 + v**4 - 17/5*v**z - 11/5*v.
(v - 1)**3*(5*v - 2)/5
Suppose 2*o - 19 = y - 6, 3*y + 9 = 0. Let t(x) be the third derivative of 0*x**3 - 1/20*x**5 + 0*x - o*x**2 + 1/4*x**4 + 0. Factor t(a).
-3*a*(a - 2)
Suppose 0 = -5*k - 150 + 680. Let f = k + -528/5. Factor 0*p + 0 + f*p**2.
2*p**2/5
Let t(d) be the second derivative of d**8/112 + d**7/42 + d**6/72 + 8*d**3/3 + 6*d. Let p(g) be the second derivative of t(g). Factor p(w).
5*w**2*(w + 1)*(3*w + 1)
Suppose 0*g - 5*g = -5. Suppose 0 = -0*a - a - 2*r - g, -5*a = 5*r - 5. Factor 2/3*o**a + 4/3*o**2 + 2/3*o + 0.
2*o*(o + 1)**2/3
Suppose 1/4*d**2 - 1/8*d - 1/4 + 1/8*d**3 = 0. What is d?
-2, -1, 1
Let q = -101 - -71. Let x be (6/(-10))/(6/q). Factor 16*y**x + 6*y**2 + 2*y + 2*y**2 + 7*y**4 + 3*y**2.
y*(y + 1)**2*(7*y + 2)
Let g(m) be the second derivative of -1/9*m**4 + 0 + 8/3*m**3 - 22/3*m**2 - 31*m. Factor g(c).
-4*(c - 11)*(c - 1)/3
Let 4*d + 5*d - 3*d**2 + 5*d + 10*d - 21 - 27 = 0. Calculate d.
4
Let f(p) be the second derivative of 5*p**5 - 215*p**4/3 + 592*p**3/3 - 224*p**2 - 283*p. Suppose f(u) = 0. What is u?
4/5, 7
Let d(o) be the third derivative of o**8/1680 - o**6/180 + o**4/24 + 8*o**3/3 + 18*o**2. Let g(f) be the first derivative of d(f). Factor g(w).
(w - 1)**2*(w + 1)**2
Let p be (-11)/(22/(-12)) + -4. Suppose 10*t + 0*t**3 - t**3 - 2 - 9*t + 2*t**p = 0. Calculate t.
-1, 1, 2
Factor 58/9 - 2/9*j**2 - 56/9*j.
-2*(j - 1)*(j + 29)/9
Let m(k) be the first derivative of -3 - 1/18*k**4 + 0*k**2 - k - 2/9*k**3. Let p(u) be the first derivative of m(u). Suppose p(v) = 0. What is v?
-2, 0
Suppose -61 = -3*l - 7. Let p = -15 + l. Factor -4 + 4*k**5 + 8*k**p + 2*k**4 - 5*k - 8*k**2 + 13*k**4 - 7*k - 3*k**4.
4*(k - 1)*(k + 1)**4
Let q(r) be the third derivative of 0 - 1/20*r**6 - 4/3*r**3 - 7*r**2 + 7/30*r**5 + 0*r + 0*r**4. Factor q(i).
-2*(i - 2)*(i - 1)*(3*i + 2)
Let h = 9 - 5. Let d be h/(-6) + 84/18. Suppose 4/3*p**5 - 4/3*p**3 + 4/3*p**2 + 0*p + 0 - 4/3*p**d = 0. What is p?
-1, 0, 1
Let b(i) be the first derivative of -38 + i**5 - 35/4*i**4 - 5/3*i**3 + 0*i + 35/2*i**2. Find j such that b(j) = 0.
-1, 0, 1, 7
Let g be 2 + -1 + (3 - 1) + -1. Determine p so that 51*p**4 - 3*p**3 + 47*p**4 + 3*p**2 - 100*p**4 + p**g - 2 + 3*p = 0.
-2, -1, 1/2, 1
Let r(w) = -3*w**2. Let g(b) = -23*b**2 - 16*b. Let z(f) = 3*g(f) - 24*r(f). Factor z(l).
3*l*(l - 16)
Let d(g) be the third derivative of -g**6/720 + g**5/240 + g**4/24 + 7*g**3/3 - 7*g**2. Let t(b) be the first derivative of d(b). Suppose t(x) = 0. Calculate x.
-1, 2
Factor 108*b + 4/3*b**3 + 0 - 24*b**2.
4*b*(b - 9)**2/3
Determine h so that 6*h**4 - 361*h**3 + 4*h**4 - 1326*h**2 - 224 - 11*h - 175*h**3 - 993*h = 0.
-1, -2/5, 56
Let y be 45/(-27)*(-464)/145. Factor -12*j + 10/3*j**2 - y.
2*(j - 4)*(5*j + 2)/3
Let a(d) be the first derivative of -d**3/3 - 13*d**2/2 + 14*d + 498. Solve a(i) = 0.
-14, 1
Let b(n) be the first derivative of n**7/1960 + n**6/420 - n**5/280 - n**4/28 - 13*n**3/3 - 11. Let a(i) be the third derivative of b(i). Factor a(k).
3*(k - 1)*(k + 1)*(k + 2)/7
Let b = -8257/10 + 1661/2. Let 4/5*m**2 - b + 4/5*m = 0. Calculate m.
-3, 2
Let u(w) be the second derivative of 1/8*w**4 + 3*w**2 - w**3 - 18*w + 0. Factor u(c).
3*(c - 2)**2/2
Suppose 8*b + 3 - 19 = 0. Let q(j) be the second derivative of 1/50*j**5 + 0 - 1/15*j**3 - 1/30*j**4 + 0*j**b + 1/75*j**6 + 6*j. Factor q(t).
2*t*(t - 1)*(t + 1)**2/5
Let f(n) = -6*n**3 - 30*n**2 + 11*n + 35. Let h(v) = 21*v**3 + 105*v**2 - 39*v - 123. Let d(y) = 18*f(y) + 5*h(y). Factor d(z).
-3*(z - 1)*(z + 1)*(z + 5)
Let j(h) = -2*h**4 + 14*h**3 + 85*h**2 + 106*h + 51. Let n(g) = -g**4 + 7*g**3 + 42*g**2 + 53*g + 25. Let z(p) = -3*j(p) + 7*n(p). Factor z(y).
-(y - 11)*(y + 1)**2*(y + 2)
Let b(x) be the first derivative of x**4/36 + 14*x**3/9 - 29*x**2/6 + 44*x/9 + 279. What is n in b(n) = 0?
-44, 1
Let q(z) be the second derivative of 3*z + 2/15*z**6 + 0*z**5 - 1/3*z**3 - 1/3*z**4 + 1/21*z**7 + 0 + 0*z**2. Let q(b) = 0. Calculate b.
-1, 0, 1
Factor 4*b**2 - 14*b**3 + 62*b**2 - 8077 - 64*b + 8053.
-2*(b - 3)*(b - 2)*(7*b + 2)
Let b = -10 + 4. Let c(t) = -7*t**3 - 8*t**2 - t + 6. Let f(x) = 6*x**3 + 7*x**2 + x - 5. Let z(p) = b*f(p) - 5*c(p). Suppose z(r) = 0. Calculate r.
-1, 0
Suppose 0*h - 3*h**5 - 20/3*h**4 - 2/3*h**2 + 0 - 13/3*h**3 = 0. What is h?
-1, -2/9, 0
Let n(k) be the second derivative of -k**4/3 - 72*k**3 - 5832*k**2 + 67*k. Factor n(q).
-4*(q + 54)**2
Let l = -29 - -23. Let b(z) = -5*z - 28. Let k be b(l). Factor 2/7*t**k - 4/7*t + 2/7.
2*(t - 1)**2/7
Let r(w) = 86*w - 167. Let v be r(2). Let y(c) be the first derivative of 3/4*c**4 - 6 + 6/5*c**v + 0*c**3 + 1/2*c**6 + 0*c + 0*c**2. Solve y(t) = 0.
-1, 0
Solve -2/7*q**2 - 96/7 + 52/7*q = 0 for q.
2, 24
Let m(n) be the second derivative of 28*n + 0 - 3/20*n**4 + 6/5*n**2 + 2/5*n**3 - 1/50*n**6 - 3/25*n**5. Find g such that m(g) = 0.
-2, -1, 1
Determine f so that -63/4 + 3/4*f**2 + 15*f = 0.
-21, 1
Let d be (-22)/44 - 9/45*5/(-2). Factor 3/11*y**3 - 1/11*y**5 + 2/11*y**2 + d + 0*y**4 + 0*y.
-y**2*(y - 2)*(y + 1)**2/11
Let j(v) = 36*v**3 + 2*v - 2. Let d be j(1). Let z = d - 71/2. Determine m, given that -z*m**3 - 3/2*m**2 - 1/2 - 3/2*m = 0.
-1
Let n(a) be the second derivative of a**7/210 - 4*a**6/45 + 8*a**5/15 - 11*a**3/6 + a. Let c(p) be the second derivative of n(p). Solve c(h) = 0 for h.
0, 4
Let g(d) be the second derivative of d**7/168 - d**6/24 + 5*d**4/6 - 10*d**3/3 + 6*d**2 - 19*d + 5. Factor g(j).
(j - 2)**4*(j + 3)/4
Suppose x = -1 + 6. Suppose 5*j + 4*r - 11 = 0, -5*j + 1 + 11 = 3*r. Find t such that -6 - 2*t**3 + 2*t**j + 6*t**4 + 4 - 4*t**2 - 2*t**x + 6*t - 4*t**3 = 0.
-1, 1
Let h(z) = -8*z**3 - 9*z**2 - 4*z + 16. Let u(p) = 7*p**3 + 10*p**2 + 4*p - 15. Let j(d) = 3*h(d) + 4*u(d). Factor j(n).
(n + 2)**2*(4*n - 3)
Let k(p) be the second derivative of -15*p + 0*p**3 + 0 + 0*p**4 + 0*p**2 - 1/30*p**5 - 2/9*p**6 - 25/63*p**7. Determine r so that k(r) = 0.
-1/5, 0
Let h(l) be the third derivative of l**6/24 - l**5/3 - 55*l**4/24 - 5*l**3 - l**2 - 9*l. Factor h(y).
5*(y - 6)*(y + 1)**2
Let m(p) be the second derivative of 0*p**2 + 0 - 2/3*p**3 + 1/10*p**5 - 24*p - 1/6*p**4. Factor m(n).
2*n*(n - 2)*(n + 1)
Factor 44/9*m + 8 + 4/9*m**2.
4*(m + 2)*(m + 9)/9
Let w(n) = 26*n**3 + 71*n**2 - 64*n + 22. Let a(u) = 5*u**3 + 14*u**2 - 13*u + 4. Let t(s) = 11*a(s) - 2*w(s). Factor t(g).
3*g*(g - 1)*(g + 5)
Let q(d) be the third derivative of d**7/70 