. Let a(g) be the second derivative of -2*g - 1/30*g**6 + y + 1/10*g**5 + 0*g**3 - 1/12*g**4 + 0*g**2. Suppose a(c) = 0. What is c?
0, 1
Let o be (-4)/(-144) - 2/(-9). Factor 0 + 1/4*n**3 - o*n + 0*n**2.
n*(n - 1)*(n + 1)/4
Suppose 0*y + 27*y = 135. Factor 0 + 1/2*l**y + l**2 - l**4 + 0*l**3 - 1/2*l.
l*(l - 1)**3*(l + 1)/2
Suppose 5*c - 10 = -2*i, -2*c - 3*c = 3*i - 5. Suppose 7 + 5 = c*u. What is m in -10/3*m**2 + 2/3 - 2*m**u + 2*m + 8/3*m**4 = 0?
-1, -1/4, 1
Let g(r) be the second derivative of 3*r**4/4 + 7*r**3/6 - r. Let c(b) = 5*b**2 + 4*b. Let s(t) = 7*c(t) - 4*g(t). Determine n so that s(n) = 0.
0
Let j = -5 + 7. Factor 0*b**3 + 3*b**2 + b**4 - 2*b**3 + b**j - 3*b**2.
b**2*(b - 1)**2
Let d be 1/(56/12) + 4/14. Determine i, given that 1/4*i**3 + 0 + 1/2*i**2 - d*i**4 - 1/4*i = 0.
-1, 0, 1/2, 1
Find c such that 14*c**2 + 0 - c**5 + 13/2*c**4 - 4*c - 15*c**3 = 0.
0, 1/2, 2
Let h = -1 + 5. Let s = h - 0. Factor 0 + u + 3*u**3 + 3*u**2 + 2*u**4 + 0 - u**s.
u*(u + 1)**3
Suppose -3*p + 2*p = 1. Let y = p + 7. Factor -2*f**3 + y*f**2 + f**5 - 6*f**2 + f + 0*f**5.
f*(f - 1)**2*(f + 1)**2
Let v(n) be the first derivative of n**6/51 - 2*n**5/17 + 4*n**4/17 - 8*n**3/51 - 1. Factor v(b).
2*b**2*(b - 2)**2*(b - 1)/17
Let n = -9/46 - -873/230. Let 6*w**2 + 64/5*w + 24/5 - n*w**3 = 0. What is w?
-2/3, 3
Let k(i) be the third derivative of i**8/21 + 74*i**7/315 + 19*i**6/45 + 4*i**5/15 - i**4/9 - 2*i**3/9 - i**2. Find x, given that k(x) = 0.
-1, -1/3, 1/4
Let n(j) = -j**3 + 7*j**2 - 4*j - 6. Let b be n(6). Let v be 9/(-42)*(-8)/b. Factor 0 + 6/7*w**3 + v*w**5 - 2/7*w**2 + 0*w - 6/7*w**4.
2*w**2*(w - 1)**3/7
Let y(d) be the first derivative of -2*d**3/15 + 6*d**2/5 - 18*d/5 - 5. Find a, given that y(a) = 0.
3
Suppose 0*k - 40 = -4*k. Let a = 13 - k. Factor -11*o**3 + 6*o**2 - 15*o**4 - o**3 + 3*o**a + 0*o**2.
-3*o**2*(o + 1)*(5*o - 2)
Let u(c) = -5*c**2 - c. Let m be u(1). Let o = -6 - m. Factor -2/3*g**4 + o*g**2 + 0 + 0*g + 0*g**3 - 2/3*g**5.
-2*g**4*(g + 1)/3
Suppose 2*c = 10 - 0. Let f(q) be the third derivative of 1/3*q**3 + q**2 + 1/15*q**c - 1/120*q**6 - 5/24*q**4 + 0*q + 0. Factor f(j).
-(j - 2)*(j - 1)**2
Let c(a) be the third derivative of -a**8/6720 + a**7/2520 - 7*a**5/60 - 5*a**2. Let k(g) be the third derivative of c(g). Determine o so that k(o) = 0.
0, 2/3
Suppose 3*a = -2*u + 10, 2*a + u - 6 = -0*u. Let j(t) be the second derivative of 0 - 3*t - 1/4*t**a - 1/4*t**3 - 1/8*t**4 - 1/40*t**5. Factor j(o).
-(o + 1)**3/2
Factor 0*i - 18/7*i**2 - 12/7*i**3 + 0 - 2/7*i**4.
-2*i**2*(i + 3)**2/7
Suppose 4*h - 2 = 14. Determine r, given that -2*r**2 + 17 - 2*r + h*r - 3*r - 15 + r**3 = 0.
-1, 1, 2
Let h(w) be the first derivative of w**4 + 4*w**3 - 8*w**2 - 29. Factor h(v).
4*v*(v - 1)*(v + 4)
Let z(h) = h**2. Let m be z(-2). Factor m*v**4 - 3*v**4 + v**2 - 3*v**2 + 1.
(v - 1)**2*(v + 1)**2
Let b(w) be the third derivative of w**5/60 - w**4/6 + 2*w**3/3 - 39*w**2. Determine z, given that b(z) = 0.
2
Let x(p) be the second derivative of 0 - 1/60*p**5 - p + 0*p**3 - p**2 - 1/24*p**4. Let a(l) be the first derivative of x(l). Factor a(s).
-s*(s + 1)
Let z(t) be the first derivative of t**4/2 - 10*t**3/21 - 2*t**2/7 + 1. Factor z(h).
2*h*(h - 1)*(7*h + 2)/7
Let k(l) be the second derivative of 0 - l + l**2 + 1/30*l**5 - 1/3*l**3 + 0*l**4. Let i(o) be the first derivative of k(o). Let i(q) = 0. Calculate q.
-1, 1
Let g be (-5)/105*(-7)/(-6)*-3. Let v(j) be the second derivative of -g*j**3 + 0*j**2 + 0 - 1/6*j**4 - 1/20*j**5 - 3*j. Let v(s) = 0. What is s?
-1, 0
Find q such that -2/3*q**2 + 2/3 + 0*q = 0.
-1, 1
Let f(r) = 37*r**2 - 371*r - 108. Let b(l) = 55*l**2 - 557*l - 162. Let d(u) = 5*b(u) - 8*f(u). Find a such that d(a) = 0.
-2/7, 9
Let n be (27 - 31)/(-2 - 8). Find y, given that 2/5*y**3 - n*y - 2/5*y**4 + 0 + 2/5*y**2 = 0.
-1, 0, 1
Let j(h) be the second derivative of h**5/60 - 2*h**3/9 - 14*h. Suppose j(t) = 0. Calculate t.
-2, 0, 2
Suppose 0*m = 5*m. Suppose -3*t = 3*y - 2*y - 44, 3*t - y - 52 = m. Suppose 7*i**2 - 8 - i**2 + 4*i**2 - t*i = 0. What is i?
-2/5, 2
Let f(y) be the third derivative of -y**9/120960 + y**8/20160 - y**7/10080 + y**5/10 + 2*y**2. Let w(b) be the third derivative of f(b). Factor w(h).
-h*(h - 1)**2/2
Let i be (-2)/6 + -5 - -6. Suppose -2/3*a + 0*a**2 - 1/3 + 1/3*a**4 + i*a**3 = 0. Calculate a.
-1, 1
Let f(c) be the third derivative of -c**8/336 - c**7/105 + c**6/24 + c**5/10 + 39*c**2. Determine o so that f(o) = 0.
-3, -1, 0, 2
Factor -2/3 - 4/3*q**3 + 5/3*q**2 + 7/3*q.
-(q - 2)*(q + 1)*(4*q - 1)/3
Solve -1/4*g**2 + 2 - 7/4*g = 0.
-8, 1
Let u = -3 - -5. Suppose -3*w - u = -5. What is d in -w - 2 - 2*d**2 - 1 + 6*d = 0?
1, 2
Suppose -5*d = -15*d. Let a(h) be the first derivative of -1/6*h**2 + 1/9*h**3 + d*h - 3. Solve a(p) = 0 for p.
0, 1
Let q be (3 + (-15)/6)*12/11. Factor -2/11*r**3 - 6/11*r**2 - 2/11 - q*r.
-2*(r + 1)**3/11
Suppose -16/7*h - 16/7*h**2 + 0 - 4/7*h**3 = 0. Calculate h.
-2, 0
Let r = -139 - -1253/9. Suppose 0 + r*n**2 + 2/9*n = 0. Calculate n.
-1, 0
Factor 2/5 - 2/5*w**3 - 6/5*w + 6/5*w**2.
-2*(w - 1)**3/5
Let p be (2/10)/(1/2). Let d be 3 + -1 - (-4 - (-9 - -5)). Factor -8/5 - d*i**2 + p*i**3 + 16/5*i.
2*(i - 2)**2*(i - 1)/5
Let l(h) = 18*h**4 + 12*h**3 - 5*h**2 - 5*h + 5. Let u(k) = -27*k**4 - 18*k**3 + 7*k**2 + 7*k - 7. Let r(d) = -7*l(d) - 5*u(d). Find t, given that r(t) = 0.
-2/3, 0
Let a(d) be the first derivative of 10*d**2 - 1 + d**4 - 8*d - 16/3*d**3. Factor a(i).
4*(i - 2)*(i - 1)**2
Let n(j) be the second derivative of -j**6/480 + j**4/32 - 5*j**3/6 - 3*j. Let s(k) be the second derivative of n(k). Factor s(d).
-3*(d - 1)*(d + 1)/4
Let c(h) = -5*h**5 + 13*h**4 - 17*h**3 + 3*h**2 + 2. Let s(w) = -25*w**5 + 64*w**4 - 86*w**3 + 14*w**2 + 11. Let t(k) = 11*c(k) - 2*s(k). Solve t(f) = 0.
0, 1
Suppose f = 3*f - 8. Suppose -2*y - y - 33 = -3*z, 3*z = -2*y + 8. Factor -z*x + x + 9*x + x**2 + f.
(x + 2)**2
Let i(z) = -2*z - 3. Let h be i(-3). Suppose -2*p + 5*p = 6. Factor -5*l**h + p*l**3 + 2*l + 4*l**2 + 5*l**3.
2*l*(l + 1)**2
Let c be (-11)/(88/(-40))*(-4)/(-10). Determine t so that 2*t**3 + 1/2 + 1/2*t**4 + 3*t**2 + c*t = 0.
-1
Let u = -6 + 9. Suppose 0 = -u*c + 8*c. Solve 0*l**2 - 5*l**3 - 4*l**4 + 6*l**3 + c*l**2 = 0 for l.
0, 1/4
Suppose 4*i = -5*b - 5, 5*i + 3*b - b = -2. Factor 1/5*y**4 + 2/5*y**3 + i*y**2 + 0*y + 0 - 1/5*y**5.
-y**3*(y - 2)*(y + 1)/5
Let t be (-2)/5 - (-4)/10. Let q(r) be the third derivative of 0*r**4 + 2*r**2 + 0 + t*r + 0*r**3 + 1/180*r**6 + 1/90*r**5. Solve q(a) = 0.
-1, 0
Let o(d) be the first derivative of 1/10*d**4 + 2 + 0*d**2 + 0*d + 2/15*d**3. Factor o(j).
2*j**2*(j + 1)/5
Let z(v) be the second derivative of -1/30*v**4 - 4/5*v**2 - 3*v + 0 + 4/15*v**3. Suppose z(s) = 0. What is s?
2
Let s(z) be the second derivative of z**6/30 + z**5/5 + z**4/3 - 13*z. Solve s(b) = 0.
-2, 0
Let k be (-6)/(-2) + (7 - 6). Solve -3*l - 4*l**2 - k*l**2 + l + 6*l**2 = 0 for l.
-1, 0
Let i(l) = -4*l**3 - 15*l**2. Let g(m) = 4*m**3 + 16*m**2. Let u(r) = 3*g(r) + 4*i(r). Determine w so that u(w) = 0.
-3, 0
Let m = -4 + 8. Factor -2*f**m - 2*f**2 - f**4 + 0*f**4 + 5*f**2.
-3*f**2*(f - 1)*(f + 1)
Let k(f) = -3*f**2 - 8*f - 16. Let m(x) = 4*x**2 + 8*x + 16. Let t(u) = -3*k(u) - 2*m(u). Let t(z) = 0. Calculate z.
-4
Let g(o) be the second derivative of o**7/147 + 4*o**6/105 + 2*o**5/35 - 9*o. Factor g(i).
2*i**3*(i + 2)**2/7
Let b(w) be the third derivative of 0 - 1/15*w**5 - 2/3*w**3 - 9*w**2 + 0*w + 1/3*w**4. Factor b(f).
-4*(f - 1)**2
Let z(p) be the second derivative of -p**6/120 + p**5/60 + p**4/24 - p**3/6 - p**2/2 + 2*p. Let m(t) be the first derivative of z(t). Solve m(h) = 0 for h.
-1, 1
Let w(n) be the first derivative of 1/13*n**2 + 1/26*n**4 - 4/39*n**3 + 1 + 0*n. Factor w(l).
2*l*(l - 1)**2/13
Let h(k) = -k - 4. Let i be h(0). Let r = 6 + i. Determine l, given that -1 + 1 - r*l**4 + 2*l**2 = 0.
-1, 0, 1
Let b(t) = 4*t**2 + 3*t**3 - 2*t**3 + 0*t**3 + 3*t. Let o be b(-3). Suppose -h**3 + o*h**3 - 3*h + 4*h = 0. What is h?
-1, 0, 1
Let q(l) = -6*l + 3. Let x be q(2). Let u be (-78)/x*(-9)/(-12). Factor 9*d**2 + 11*d**3 + 7/2*d + 1/2 + u*d**4 + 3/2*d**5.
(d + 1)**4*(3*d + 1)/2
Let p(d) = d. Let z be p(3). Suppose -z = q - 6. Suppose 1/2 - 19/4*t**q + 7/4*t - 5/4*t**2 + 15/4*t*