3 + 24*v**2 - 11*v. Find s, given that a(s) = 0.
-4
Let o(j) be the first derivative of j**9/12096 + j**8/1680 + j**7/840 - j**3/3 + 5. Let x(k) be the third derivative of o(k). Find d, given that x(d) = 0.
-2, 0
Determine w so that 64/7*w - 8/7 - 18*w**2 - 16/7*w**3 + 32/7*w**4 = 0.
-2, 1/4, 2
Let p(m) = -7*m**3 - m**2 + 13*m + 4. Let h(u) = -15*u**3 - 3*u**2 + 25*u + 8. Let z be (10/(-2))/(-1)*-1. Let c(x) = z*p(x) + 3*h(x). Factor c(j).
-2*(j - 1)*(j + 1)*(5*j + 2)
Let r(g) = -2*g - g - 4 + 9 - 5*g**2 - 7*g**3. Let s(a) = -4*a + 1 - 9*a + 12*a. Let i(f) = -r(f) + 5*s(f). Factor i(d).
d*(d + 1)*(7*d - 2)
Let h(r) = 6*r - 23 + 11 - 4*r. Let l be h(7). Find v such that 2/3 + 2/3*v**l + 4/3*v = 0.
-1
Determine x so that 2*x**2 - 6*x**2 + 3*x**2 - 5*x + 6*x + x**4 - x**3 = 0.
-1, 0, 1
Let k = 4 - 119/30. Let b(v) be the second derivative of 3*v - k*v**4 - 2/5*v**2 + 1/5*v**3 + 0. Let b(x) = 0. Calculate x.
1, 2
Let f(v) be the third derivative of v**8/224 - v**7/630 - 3*v**6/80 - v**5/30 + v**4/36 - 31*v**2. Suppose f(y) = 0. What is y?
-1, 0, 2/9, 2
Let h(t) = -3*t**2 - 12*t - 7. Let b(r) = r**2 + r - 1. Let m(l) = 2*b(l) + h(l). Factor m(w).
-(w + 1)*(w + 9)
Let g = 132 - 127. Find l such that -44/9*l**2 - 56/9*l + 2*l**g + 20/3*l**4 - 16/9 + 38/9*l**3 = 0.
-2, -1, -2/3, 1
Let x(m) = -2*m**3 - 4*m**2 + 4*m. Let g(f) = f**2. Suppose 2 = -5*y + 2*y - 5*u, -3*u = -5*y + 8. Let l(q) = y*x(q) + 2*g(q). Factor l(t).
-2*t*(t - 1)*(t + 2)
Suppose 5*b - 22 = -3*n, -4*n - 2 = -4*b - 10. Let -4*t**5 - t**4 + 4*t**2 + 6*t**2 - 7*t**4 + 4*t**3 - 2*t**b = 0. Calculate t.
-2, -1, 0, 1
Let x(i) be the second derivative of i**4/60 - i**3/15 - 3*i**2/10 - 15*i. Let x(w) = 0. What is w?
-1, 3
Let n(a) be the second derivative of -a**8/1176 - 4*a**7/735 - a**6/105 - a**2 + 4*a. Let o(h) be the first derivative of n(h). Factor o(t).
-2*t**3*(t + 2)**2/7
Factor -7*o + 4*o + 9*o - 3*o**2.
-3*o*(o - 2)
Let a(w) = 6*w**3 + 12*w**2 - 4*w - 14. Let g(n) = 19*n**3 + 36*n**2 - 12*n - 43. Let b(m) = -7*a(m) + 2*g(m). Factor b(j).
-4*(j - 1)*(j + 1)*(j + 3)
Factor 0 + 0*i + 3/5*i**4 + 48/5*i**2 - 24/5*i**3.
3*i**2*(i - 4)**2/5
Let r(c) = 4*c**3 - 2*c + 0*c**3 + 0*c**2 - 8*c**4 - 2*c + 2*c**2. Let d(z) = 7*z**4 - 4*z**3 - 2*z**2 + 4*z. Let s(x) = 6*d(x) + 5*r(x). Factor s(m).
2*m*(m - 2)*(m - 1)*(m + 1)
Let n(m) be the first derivative of -m**7/1050 - m**6/300 - m**5/300 + 2*m**2 + 1. Let c(r) be the second derivative of n(r). Let c(b) = 0. Calculate b.
-1, 0
Let f(d) be the first derivative of -d**6/3 + 4*d**5/5 - 4*d**3/3 + d**2 - 15. Let f(u) = 0. What is u?
-1, 0, 1
Factor 15*z**3 + 27*z**4 + 4*z - 14*z**3 + 26*z**2 + 19*z**4 + 53*z**3 + 14*z**5.
2*z*(z + 1)**3*(7*z + 2)
Let p be (4/(-18))/((-4)/6). Let v(l) be the first derivative of -1/2*l**2 - p*l**3 - 2 + l + 1/4*l**4. What is s in v(s) = 0?
-1, 1
Let i(a) be the third derivative of 1/60*a**6 - a**2 - 1/3*a**3 + 1/4*a**4 - 1/10*a**5 + 0*a + 0. Determine d, given that i(d) = 0.
1
Let t(m) = 3*m**5 + 3*m**4 + 2*m**3 - 3*m**2 - 5. Let h(v) = -2*v**5 - 2*v**4 - v**3 + 2*v**2 + 3. Let o(g) = 10*h(g) + 6*t(g). Factor o(b).
-2*b**2*(b - 1)*(b + 1)**2
Let g(l) = -2*l - 15. Let x be g(-10). Let v(s) be the second derivative of 0 - 1/20*s**x + 1/6*s**3 + 0*s**2 + 3*s + 0*s**4. Factor v(y).
-y*(y - 1)*(y + 1)
Let o(y) = -y**3 - 3*y**2 - 18*y + 18. Let a(q) = -9*q**3 - 26*q**2 - 145*q + 143. Let p(u) = 6*a(u) - 51*o(u). Factor p(i).
-3*(i - 2)**2*(i + 5)
Solve -4*c + 8 + 1/2*c**2 = 0.
4
Let t(d) be the second derivative of d**5/210 + d**4/84 - 5*d**2/2 + d. Let m(n) be the first derivative of t(n). Factor m(b).
2*b*(b + 1)/7
Suppose 3*l - 5*g - 29 = 0, -2*l = l + 4*g + 7. Let w be 4 - (24/l)/4. Let -1/3*v + 0 + 1/3*v**3 + 4/3*v**4 - 4/3*v**w = 0. Calculate v.
-1, -1/4, 0, 1
Let u = 79/345 + -2/69. Let m = -11 - -15. Factor 0 - 1/5*b + u*b**2 - 1/5*b**m + 1/5*b**3.
-b*(b - 1)**2*(b + 1)/5
Let i(f) be the second derivative of 1/5*f**2 - 1/30*f**4 + 1/50*f**5 + f + 0 - 1/15*f**3. Let i(n) = 0. Calculate n.
-1, 1
Let u(w) = w**5 - w**4 - w**3 - w**2 - w. Suppose 5*s = -5 + 20. Let m(t) = -7*t**5 + 10*t**4 + t**3 + 2*t. Let d(g) = s*m(g) + 6*u(g). What is o in d(o) = 0?
-2/5, 0, 1
Let w(v) = -5. Let c(b) = -1. Let h(l) = -9*c(l) + 2*w(l). Let x(d) = -d**2 + 3. Let t(g) = 2*h(g) + x(g). Factor t(z).
-(z - 1)*(z + 1)
Suppose -2*f + 3 - 1 = -4*j, j = 2*f - 5. Let v be (-2 - 0 - 0) + 7. What is o in o**f - v*o + 5*o - 2*o**4 + o**5 = 0?
0, 1
Solve -2/3*b**2 + 16/3 + 4/3*b = 0.
-2, 4
Let p(u) be the first derivative of 8*u**6/9 - 8*u**5/5 + 3*u**4/4 - u**3/9 - 10. Determine s so that p(s) = 0.
0, 1/4, 1
Let v(o) be the second derivative of -o**6/40 + o**5/10 + o**4/8 - o**3 - 3*o**2 - 6*o. Let d(p) be the first derivative of v(p). What is t in d(t) = 0?
-1, 1, 2
Let o(x) = x**3 - 6*x**2 + 11*x - 10. Let i be o(4). Factor i + 2/3*m**2 - 8/3*m.
2*(m - 3)*(m - 1)/3
Let i = 17/15 - 4/5. Let t(n) be the first derivative of 1 + i*n**2 + 0*n + 2/9*n**3. Factor t(f).
2*f*(f + 1)/3
Let q(s) be the second derivative of s**6/105 - s**4/42 + 3*s. Suppose q(h) = 0. Calculate h.
-1, 0, 1
Determine m so that -1/4*m**3 + 0*m + 0 + 1/4*m**2 = 0.
0, 1
Let z be 3 - 3 - (0 - 10). Let c(b) = b - 10. Let p be c(z). Solve 0*x + p + 0*x**2 + 1/2*x**3 + 1/2*x**4 = 0.
-1, 0
Let l(h) = h**2 - 24*h - 31. Let y(i) = -8*i - 10. Let t(u) = -2*l(u) + 7*y(u). Factor t(w).
-2*(w + 2)**2
Let w(h) = h + 5. Let k be w(-7). Let p be -2 + 4/5 - k. What is v in 2/5*v - p*v**4 + 2*v**3 + 0 - 8/5*v**2 = 0?
0, 1/2, 1
Let i(y) be the third derivative of y**8/112 - y**7/35 + y**5/10 - y**4/8 - 16*y**2. Factor i(a).
3*a*(a - 1)**3*(a + 1)
Let f be (-36)/8 - (-2)/4. Let u be (2/f)/(-4 - -2). Factor 0 + 1/2*i**4 + 0*i + 1/4*i**3 + 0*i**2 + u*i**5.
i**3*(i + 1)**2/4
Suppose 4 = 5*r - 6. Let -3*u - 3*u**r + 2*u + 3*u**2 + u**2 = 0. Calculate u.
0, 1
Suppose 5*k - 24 = 36. Factor t + 0*t - 2*t**4 + 11*t - t**4 + 12 - 9*t**2 - k*t**3.
-3*(t - 1)*(t + 1)*(t + 2)**2
Let s(t) = -5*t**5 + t**4 + 3*t - 3. Let l(y) = -6*y**5 + 2*y**4 + 4*y - 4. Let v be -2 + 0 - (0 - -1). Let q(u) = v*l(u) + 4*s(u). Factor q(i).
-2*i**4*(i + 1)
Let k(u) = 0 + 1 + 0 + u + 0*u. Let w be k(2). Factor 0 - 2/3*b**4 + 0*b**w + 2/3*b**2 + 0*b.
-2*b**2*(b - 1)*(b + 1)/3
Suppose -1/2 + 0*t**2 - 3/4*t**5 + 5/2*t**4 - 5/2*t**3 + 5/4*t = 0. What is t?
-2/3, 1
Let v = -4 + 14. Let c = v + -7. Suppose 0*y + 0 - 2/9*y**2 - 2/9*y**c = 0. What is y?
-1, 0
Let m(r) be the third derivative of r**7/210 + r**6/40 - r**4/6 - 14*r**2. Determine g so that m(g) = 0.
-2, 0, 1
Let f(h) be the second derivative of -h**5/4 + 5*h**4/12 + 15*h**3/2 - 45*h**2/2 - 7*h + 6. Factor f(p).
-5*(p - 3)*(p - 1)*(p + 3)
Suppose -2*n - d - 1 = 4, 10 = 5*n - 2*d. Let i be (-272)/(-102) + (-1)/(-3). Factor -1/4*g - 1/4*g**i + n + 1/2*g**2.
-g*(g - 1)**2/4
Let s(a) be the first derivative of -a**6/40 - a**5/20 + a**4/8 + a**3/2 - 2*a**2 + 4. Let g(l) be the second derivative of s(l). Find n, given that g(n) = 0.
-1, 1
Let p(u) be the second derivative of u**5/45 + u**4/9 + 4*u**3/27 + 21*u. Suppose p(f) = 0. Calculate f.
-2, -1, 0
Let r = 458 + -867/2. Suppose -4*g = -68 - 84. Find q such that -4 + r*q**3 + g*q - 105*q**2 + 343/2*q**4 = 0.
-1, 2/7
Let v(p) = 2*p**2 + 2*p - 18. Let d(a) = -10*a**2 - 10*a + 92. Let s(u) = -3*d(u) - 16*v(u). Factor s(y).
-2*(y - 2)*(y + 3)
Let m(i) = i. Let h be m(3). Let f be -3 - (1 - (5 - -2)). Factor -f*q**3 - q**h + 5*q**3.
q**3
Let r = -595/4 + 149. Factor -r*i**3 - 1/4*i**2 + 0*i + 0.
-i**2*(i + 1)/4
Let i(j) be the second derivative of 1/147*j**7 + 0*j**2 + 0 + 1/105*j**6 + j - 3/70*j**5 - 5/42*j**4 - 2/21*j**3. Determine t so that i(t) = 0.
-1, 0, 2
Let i(y) be the first derivative of -y**3/9 - y**2/2 - 11. Suppose i(f) = 0. What is f?
-3, 0
Factor 2*o + 5*o + 5 - 13 + o - 2*o**2.
-2*(o - 2)**2
Let k(r) = 9*r**5 - 2*r**3 + 2*r. Let w(s) = 72*s**5 + s**4 - 17*s**3 + 17*s. Let u(c) = -51*k(c) + 6*w(c). Suppose u(y) = 0. What is y?
0, 2/9
Let b(u) = -14*u**5 - 20*u**4 - 23*u**3 + 17*u**2 + 17*u. Let n(x) = -5*x**5 - 7*x**4 - 8*x**3 + 6*x**2 + 6*x. Let w(o) = 6*b(o) - 17*n(o). Factor w(y).
y**3*(y - 2)*(y + 1)
Factor -3*x**3 - 19*x**2 + 17*x**2 - 5*x**4 - 4*x**3 + 0*x**3.
-x**2*(x + 1)*(5*x + 2)
Let x(h) = h**3 + h*