/30. Factor 0 - 2/5*a**2 + 0*a**3 - 1/5*a**5 + v*a**4 + 1/5*a.
-a*(a - 1)**3*(a + 1)/5
Let s(t) be the third derivative of t**8/1344 - t**7/280 + t**5/60 - 26*t**2. Factor s(h).
h**2*(h - 2)**2*(h + 1)/4
Let d(b) = b**2 - 1. Let t(v) = -v**2 + 3. Let x(n) = -2*d(n) - t(n). Let p(z) = -2*z**3 - 6*z**2 + 2*z - 6. Let i(s) = p(s) - 6*x(s). Solve i(f) = 0.
-1, 0, 1
Suppose 45/4*i**2 + 5/4*i**4 + 0 + 15/2*i**3 + 0*i = 0. What is i?
-3, 0
Let k(u) be the third derivative of -u**6/180 - u**5/15 - u**4/3 - u**3/2 - u**2. Let a(r) be the first derivative of k(r). Find x, given that a(x) = 0.
-2
Let k(l) = -l**2 - 1. Let q(i) = -i**2 - 5*i + 2. Let p(n) = 6*k(n) - 3*q(n). Factor p(x).
-3*(x - 4)*(x - 1)
Let a(v) be the third derivative of 0*v**3 - 1/60*v**6 - v**2 + 0 + 1/12*v**4 + 0*v**5 + 0*v. Factor a(b).
-2*b*(b - 1)*(b + 1)
Let r = 5 + -1. Suppose 5*x + 5*f - 24 = -9, x - r = -2*f. Factor -2*v**2 - 2*v + 2*v**2 + v - v**x.
-v*(v + 1)
Let s = -907 - -8167/9. Factor 10/9*q**4 + 14/3*q**2 + 34/9*q**3 + s + 22/9*q.
2*(q + 1)**3*(5*q + 2)/9
Let q(t) = -2*t**2 - 30*t + 40. Let s(p) = -p**2 - 10*p + 14. Let o(j) = 3*q(j) - 8*s(j). Factor o(i).
2*(i - 4)*(i - 1)
Let l = -869 - -871. Find c such that 0*c - 2/3*c**5 + 0 + l*c**4 + 2/3*c**2 - 2*c**3 = 0.
0, 1
Solve 3*y**3 + 12*y + 9*y**2 + 6*y - 12*y = 0.
-2, -1, 0
Let l(h) be the third derivative of 0*h + 0 - 1/150*h**5 - h**2 + 0*h**3 - 1/60*h**4. Suppose l(u) = 0. What is u?
-1, 0
Let p = 3/28 - -135/308. Let h(c) = c**2 + 3*c. Let t be h(-3). What is x in -2/11*x**2 + t - 4/11*x**4 + 0*x + p*x**3 = 0?
0, 1/2, 1
Let m(v) be the first derivative of -2*v**4 - 26*v**3/3 - 11*v**2 - 4*v - 16. Determine l, given that m(l) = 0.
-2, -1, -1/4
Suppose -h - 48 = 3*h. Let g(u) = -u**2 - 11*u + 14. Let z be g(h). Factor -4*q**z + q + 1/2.
-(2*q - 1)*(4*q + 1)/2
Let l = -2 + 4. Let p(v) be the first derivative of 0*v**l + 0*v + 2 + 0*v**4 + 1/20*v**5 + 0*v**3. Solve p(n) = 0 for n.
0
Let i(k) be the second derivative of k**7/21 + k**6/30 - 3*k**5/10 + k**4/12 + k**3/3 - 2*k. Factor i(p).
p*(p - 1)**2*(p + 2)*(2*p + 1)
Let w = 52 + -46. Let o(c) be the second derivative of c - 1/24*c**4 + 0*c**2 + 0*c**3 - 1/120*c**w + 3/80*c**5 + 0. Determine z so that o(z) = 0.
0, 1, 2
Suppose -6*t + 16 = -2*t. Let a(h) = h - 2. Let c be a(t). Factor -2/3*k**c + 0 + 0*k.
-2*k**2/3
Let n(d) = -d**2 - 55*d + 9. Let a(k) = -28*k + 4. Let g(x) = -9*a(x) + 4*n(x). Factor g(p).
-4*p*(p - 8)
Let h(s) be the third derivative of 0*s**3 + 0*s**4 + 0*s - 1/840*s**7 + 1/240*s**5 + 4*s**2 + 0 + 0*s**6. Suppose h(z) = 0. What is z?
-1, 0, 1
Let j(x) be the first derivative of 3/20*x**5 + 1/16*x**4 + 1/24*x**6 - 1/4*x**3 - 1 + 0*x - 1/4*x**2. Solve j(p) = 0 for p.
-2, -1, 0, 1
Let k(c) be the third derivative of c**6/12 - 13*c**5/60 + 7*c**4/30 - 2*c**3/15 - 2*c**2. Suppose k(a) = 0. Calculate a.
2/5, 1/2
Let u(n) = -4*n + 47. Let d be u(11). Let h(t) be the first derivative of 2 + 1/15*t**d + 0*t + 0*t**2. Find y, given that h(y) = 0.
0
Let n(m) = m**2 + 2. Let i be n(0). Let t(b) be the first derivative of -1/3*b**i - 1/9*b**6 + 4/9*b**3 - 2/3*b - 2/15*b**5 - 1 + 1/3*b**4. Factor t(s).
-2*(s - 1)**2*(s + 1)**3/3
Let h(w) be the third derivative of w**6/60 + w**5/15 - w**4/4 + 10*w**2. Let h(b) = 0. Calculate b.
-3, 0, 1
Let b(g) be the first derivative of -g**6/60 + g**5/60 + g**4/12 - g**3/6 - 2*g**2 + 9. Let f(m) be the second derivative of b(m). Determine u so that f(u) = 0.
-1, 1/2, 1
Let v(b) = b**3 - 4*b**2 - b + 2. Let j be v(4). Let x be (-2)/((3 + 9)/j). Determine y so that 0 + 2/3*y**2 + x*y + 1/3*y**3 = 0.
-1, 0
Let s = 103/287 + -3/41. Factor -s*w**2 - 2/7*w**3 + 0 + 4/7*w.
-2*w*(w - 1)*(w + 2)/7
Let k(h) be the second derivative of -h**5/30 - h**4/3 - 4*h**3/3 - 8*h**2/3 - 2*h. Let k(n) = 0. Calculate n.
-2
Let m(p) be the second derivative of -1/70*p**5 + 1/42*p**4 + 0*p**3 + 0 + 0*p**2 - 3*p. Factor m(t).
-2*t**2*(t - 1)/7
Let h(o) be the third derivative of -o**5/100 - o**4/4 - 5*o**3/2 + o**2. Factor h(b).
-3*(b + 5)**2/5
Let f(v) = 7*v**4 - 4*v**2 + 5*v - 3. Let h(y) = -1 + y**4 + 5*y + 0 + 0*y**4 - 4*y. Let j(d) = -f(d) + 5*h(d). Let j(s) = 0. What is s?
-1, 1
Factor 0 - 1/3*z**2 + 2/9*z + 1/9*z**3.
z*(z - 2)*(z - 1)/9
Let s = -2 + 6. Suppose 6*n + 6*n**3 - 2*n**3 + s*n**2 - 2*n**3 - 4*n = 0. What is n?
-1, 0
Let i be 10/(-2)*(-8 - (-333)/45). Determine c, given that -1/2*c**4 + 0 + 0*c + 0*c**2 + c**i = 0.
0, 2
Let g(v) be the second derivative of v**6/90 - 7*v**5/60 + 4*v**4/9 - 2*v**3/3 - 9*v. Factor g(q).
q*(q - 3)*(q - 2)**2/3
Let b(w) be the first derivative of -w**6/90 + w**5/30 - w**3/3 + 3. Let j(u) be the third derivative of b(u). Suppose j(z) = 0. What is z?
0, 1
Let a(h) = h + 15. Let n be a(-11). Suppose -4*x + 3*y = 7, -x + n + 3 = y. Determine k so that 0*k + 2*k**3 - 6*k**2 + x - 4 + 0*k**3 + 6*k = 0.
1
Let s(m) = -12*m**2 - 45*m - 24. Let n(a) be the second derivative of a**4/4 + 11*a**3/6 + 3*a**2 + 3*a. Let u(y) = -9*n(y) - 2*s(y). Factor u(l).
-3*(l + 1)*(l + 2)
Let z(l) be the second derivative of l**5/20 + 5*l**4/36 + l**3/18 - l**2/6 + 4*l. Determine y, given that z(y) = 0.
-1, 1/3
Let u(y) = 6*y**2 + 9*y - 9. Let z(t) = -4*t + 4. Let d(x) = x**2 + 8*x - 8. Let o(i) = -3*d(i) - 5*z(i). Let j(g) = -9*o(g) - 4*u(g). What is n in j(n) = 0?
0
Suppose 3*t = 2*s - s + 14, 5*t - 3*s = 30. Let c(y) be the first derivative of -11/6*y**2 - 2/3*y + 1 - y**t. Determine o so that c(o) = 0.
-1, -2/9
Let t = -2 - -4. Let w = t - 0. Find s such that 7*s + 14*s**2 - s - w*s = 0.
-2/7, 0
Let l(t) be the third derivative of -t**7/1365 + t**6/780 + t**5/195 + 20*t**2. Factor l(f).
-2*f**2*(f - 2)*(f + 1)/13
Suppose 2*j + 2 = 4*j. Let f be 1 + (2 - 0 - j). Factor -z**4 + 2*z**4 + f*z**5 - 3*z**4.
2*z**4*(z - 1)
Let i(g) be the first derivative of -1 + 2/3*g**3 - 2*g**2 + 2*g. Factor i(j).
2*(j - 1)**2
What is x in -2*x**2 + 0*x**2 - x**3 + x**2 + 2*x = 0?
-2, 0, 1
Let p = -1 + 1. Let y be (-1)/(-2)*(7 - 1). Find a such that 0*a**4 + 2/3*a + 0*a**2 + p - 4/3*a**y + 2/3*a**5 = 0.
-1, 0, 1
Solve 0 + 1/6*b**5 + 3/2*b**3 + 1/3*b - 7/6*b**2 - 5/6*b**4 = 0 for b.
0, 1, 2
Let m(b) be the first derivative of -b**6/33 + 6*b**5/11 - 37*b**4/11 + 20*b**3/3 + 75*b**2/11 - 250*b/11 + 11. Find u, given that m(u) = 0.
-1, 1, 5
Let i(c) be the second derivative of c**5/5 - c**4 - 2*c**3/3 + 6*c**2 - 6*c + 1. Factor i(l).
4*(l - 3)*(l - 1)*(l + 1)
Let d(k) be the third derivative of -k**5/60 + k**4/24 + k**3 - 17*k**2. Factor d(q).
-(q - 3)*(q + 2)
Let t(u) be the first derivative of u**7/105 - u**6/60 + u**2 - 5. Let q(c) be the second derivative of t(c). Find n, given that q(n) = 0.
0, 1
Let y(j) = -j**2 - 7*j - 4. Let w be y(-6). Suppose -1 + 2*m**2 - m + 0 + m**3 + 0*m**w - m**2 = 0. Calculate m.
-1, 1
Let y(z) = z**2 + 1. Let f(s) = -2*s**2 - 4*s + 1. Let d(x) = 2*f(x) + 6*y(x). Determine n, given that d(n) = 0.
2
Let t = 709/7 + -101. Let g be (4/3)/(7/3). Factor t*c**2 + 2/7 + g*c.
2*(c + 1)**2/7
Let j(b) be the second derivative of 1/6*b**4 + 0*b**3 + 0 + 0*b**2 - 1/4*b**5 - 2*b. Find w, given that j(w) = 0.
0, 2/5
Let t = -1 - -4. Find x such that -6*x**4 + 2*x**t + 4*x**4 + 3*x**5 - 4*x**4 + x**3 = 0.
0, 1
Let g(h) = -h**3 + h**2 - h. Let n(c) = 5*c**3 - 13*c**2 + 12*c. Let y(b) = -4*g(b) - n(b). Factor y(f).
-f*(f - 8)*(f - 1)
Let k(q) be the third derivative of -q**5/45 - 2*q**4/9 + 8*q**3/3 - 10*q**2. Factor k(b).
-4*(b - 2)*(b + 6)/3
Let o(z) be the third derivative of z**8/3360 - z**7/560 + z**6/360 - z**3/2 + 7*z**2. Let t(k) be the first derivative of o(k). Solve t(q) = 0.
0, 1, 2
Let d(g) = g**3 + g**2 + 1. Let p(t) = 2*t**3 - 24*t**2 + 8*t + 12. Let u(v) = 4*d(v) + p(v). Factor u(o).
2*(o - 2)**2*(3*o + 2)
Let p(h) be the first derivative of -h**5/40 - h**4/8 - h**3/4 - h**2/4 - h/8 + 42. Suppose p(l) = 0. Calculate l.
-1
Factor -3*n**3 - 5/3*n**2 + 0 + 1/3*n**5 - n**4 + 0*n.
n**2*(n - 5)*(n + 1)**2/3
Factor 0 + 13/6*j**2 + 1/2*j + 2/3*j**4 + 8/3*j**3.
j*(j + 3)*(2*j + 1)**2/6
Let o(x) be the first derivative of x**6/90 + x**5/15 - x**4/2 + 2*x**3 - 5. Let z(u) be the third derivative of o(u). Let z(m) = 0. Calculate m.
-3, 1
Let c be ((-24)/(-9))/(34/(-6)). Let n = c + 138/221. Determine z so that -n*z**4 + 4/13*z**2 - 