79/2. Find q such that -1/2 + 1/4*q + c*q**2 - 1/4*q**3 = 0.
-1, 1, 2
Let g(n) be the second derivative of -125*n**4/12 - 25*n**3/3 - 5*n**2/2 - 2*n. Find p, given that g(p) = 0.
-1/5
Let a = -1142 - -1145. Suppose 0*m + 1/7*m**4 - 1/7*m**a + 1/7*m**5 + 0 - 1/7*m**2 = 0. Calculate m.
-1, 0, 1
Suppose -7*j + 2*j - 1080 = 0. Let v = j + 2378/11. Factor 4/11*c**4 - v*c**3 + 0 + 0*c + 0*c**2 - 2/11*c**5.
-2*c**3*(c - 1)**2/11
Let y(h) = -4*h**3 + 12*h + 8. Let p(r) = r**3 - 3*r - 2. Let u(s) = -18*p(s) - 4*y(s). Determine q, given that u(q) = 0.
-1, 2
Let j(c) be the first derivative of -4*c - 11/3*c**3 - 1 - 5/8*c**4 - 7*c**2. Suppose j(b) = 0. Calculate b.
-2, -2/5
Let m(v) be the third derivative of v**8/168 + v**7/105 - v**6/30 - v**5/15 + v**4/12 + v**3/3 + 5*v**2. Determine k so that m(k) = 0.
-1, 1
Let w = -10 + 12. Let x be (0 - 0 - 0) + 6. Factor 2 + 4*t**w - t**2 + 3*t**2 + 2*t**3 + x*t.
2*(t + 1)**3
Let l be 91/56*((0 - 0) + 2). Find k such that -9/4*k**3 + 6*k**2 - l*k + 1/2 = 0.
1/3, 2
Factor 4/7*c + 4/7*c**2 - 4/7*c**3 - 4/7*c**4 + 0.
-4*c*(c - 1)*(c + 1)**2/7
Factor -3*c**5 - 2*c**5 + 3*c**5 - 2*c + 4*c**3.
-2*c*(c - 1)**2*(c + 1)**2
Let q = -12 + 8. Let s = 6 + q. Determine f, given that 4*f**5 - s*f**5 + 2*f**3 - 6*f**3 + 2*f = 0.
-1, 0, 1
Let f(t) be the second derivative of 2*t**7/105 - 2*t**5/15 + 2*t**3/3 + 4*t**2 + t. Let s(n) be the first derivative of f(n). Let s(y) = 0. What is y?
-1, 1
Let -7*f**5 - 13 - 10*f**4 + 13 + 2*f**5 + 15*f**3 = 0. What is f?
-3, 0, 1
Factor 2/3*b - 1/6*b**3 + 0 + 0*b**2.
-b*(b - 2)*(b + 2)/6
Let a(m) be the second derivative of m**6/6 + m**5/4 - 5*m**4/3 - 10*m**3/3 - 35*m. What is o in a(o) = 0?
-2, -1, 0, 2
Let g = -3 + 8. Let a = -3 + g. Factor -28*h**a + 28*h**2 + 3*h**3.
3*h**3
Let f(u) = -u**2 - u - 1. Let n(g) = -4*g**2 - g + 4. Let l(z) = f(z) + n(z). Let w(v) = -6*v**2 - 2*v + 4. Let p(r) = -5*l(r) + 4*w(r). Factor p(d).
(d + 1)**2
Let j(p) be the third derivative of p**7/42 - p**6/8 + 5*p**4/6 - 13*p**2. Solve j(g) = 0 for g.
-1, 0, 2
Let z be -3*((-109)/3 + 0). Let h = z + -319/3. Determine s so that 10/3*s**2 + 2/3 + h*s + 4/3*s**3 = 0.
-1, -1/2
Let g(l) be the third derivative of 0*l**3 + 0 + 0*l + 1/60*l**5 + 0*l**4 + l**2. Let g(x) = 0. Calculate x.
0
Let l(p) be the third derivative of -2*p**7/105 - p**6/15 + p**5/5 + 2*p**4/3 - 8*p**3/3 - 17*p**2. Factor l(h).
-4*(h - 1)**2*(h + 2)**2
Suppose 4*q + 20 = 5*m, -16 = 4*q + m - 5*m. Factor q*b + 0 - 4/3*b**3 + 2/3*b**4 + 2/3*b**2.
2*b**2*(b - 1)**2/3
Let t(b) be the first derivative of b**7/315 + b**6/90 - b**4/18 - b**3/9 + 2*b**2 + 9. Let s(f) be the second derivative of t(f). Factor s(u).
2*(u - 1)*(u + 1)**3/3
Factor 3*k**2 - 3 + 3/2*k - 3/2*k**3.
-3*(k - 2)*(k - 1)*(k + 1)/2
Let z(i) be the third derivative of -1/40*i**6 - 1/4*i**4 + 2*i**2 + 0 + 0*i + 0*i**3 - 3/20*i**5. Find d such that z(d) = 0.
-2, -1, 0
Let q = 71 + -1064/15. Let j(o) be the first derivative of -6/25*o**5 + 1 + 3/10*o**4 + q*o**6 - 2/15*o**3 + 0*o + 0*o**2. Find s such that j(s) = 0.
0, 1
Let h(t) be the second derivative of 0 - 4*t - 1/36*t**3 - 1/72*t**4 + 0*t**2 + 1/120*t**5 + 1/180*t**6. Let h(q) = 0. Calculate q.
-1, 0, 1
Let z(j) be the third derivative of -j**8/5040 - j**7/630 - j**6/180 - j**5/90 - j**4/72 + j**3/2 - j**2. Let t(i) be the first derivative of z(i). Factor t(y).
-(y + 1)**4/3
Let q(x) be the third derivative of -2/3*x**4 - x**2 + 2/35*x**7 + 0*x**3 - 1/30*x**6 - 8/15*x**5 + 0*x + 0. Factor q(b).
4*b*(b - 2)*(b + 1)*(3*b + 2)
Let 4 + 26*b**3 - 5*b**5 - 5*b**2 + 5*b**2 - 3*b**5 - 18*b + 2*b**2 - 6*b**4 = 0. What is b?
-2, -1, 1/4, 1
Let a = -2 + 4. Factor -a*z**3 + 4*z**3 - 6*z**3 - 32*z**4 - 64*z**5.
-4*z**3*(4*z + 1)**2
Let j = -3 - -6. Let g(w) be the second derivative of -1/15*w**j + 0*w**2 + 0 - 3*w + 0*w**4 + 1/50*w**5. Solve g(y) = 0 for y.
-1, 0, 1
Suppose -w - 1 = 3. Let k be ((-5)/w)/(10/12). Find n, given that k*n**2 - 3/2*n + 0 = 0.
0, 1
Let w = -3 - -33. Suppose -k = 4*k - w. Find m, given that -4*m**2 + 3*m**2 + 1 + k*m - m**3 - 5*m = 0.
-1, 1
Let r(z) be the first derivative of -3*z**4/2 - 5*z**3/2 - 3*z**2/4 + 6. Factor r(q).
-3*q*(q + 1)*(4*q + 1)/2
Solve 0 + 0*m + 0*m**3 - 4/5*m**2 + 4/5*m**4 = 0.
-1, 0, 1
Suppose -2 + 22 = 10*t. Solve -1/2*w - t*w**3 + 0 - 5/2*w**2 = 0 for w.
-1, -1/4, 0
Let z(b) = 10*b**4 - 4*b**3 + 16*b**2 + 4*b + 6. Let x(o) = -2*o**4 + o**3 - 3*o**2 - o - 1. Let l(j) = 16*x(j) + 3*z(j). Factor l(c).
-2*(c - 1)**3*(c + 1)
Let g(k) be the second derivative of k**4/84 + 5*k**3/42 + 2*k**2/7 + 12*k. Let g(c) = 0. What is c?
-4, -1
Factor 6/5*c**2 + 2*c - 2/5*c**4 - 2/5*c**3 + 4/5.
-2*(c - 2)*(c + 1)**3/5
Let a(p) = -p**3 - p**2. Let n(b) = -b**5 + b**4 + 3*b**3 + b**2. Let k(c) = -2*a(c) - n(c). Solve k(h) = 0.
-1, 0, 1
Let s(v) be the second derivative of v**7/56 + 3*v**6/40 + 3*v**5/40 - v**4/8 - 3*v**3/8 - 3*v**2/8 - v. Determine r, given that s(r) = 0.
-1, 1
Let r(y) be the second derivative of 1/2*y**3 + 0*y**2 + 0 + 1/60*y**5 - 3*y - 1/60*y**6 + 1/6*y**4. Let n(a) be the second derivative of r(a). Solve n(c) = 0.
-2/3, 1
Let l = 22/3 + -7. Suppose l*o**3 + 1/3*o**2 - 1/3 - 1/3*o = 0. What is o?
-1, 1
Let u(x) be the third derivative of x**5/40 + 2*x**2. Factor u(g).
3*g**2/2
Let -3/11*w**3 + 3/11*w - 2/11 + 1/11*w**2 + 1/11*w**4 = 0. What is w?
-1, 1, 2
Let j(x) be the first derivative of 3*x**5/5 - 3*x**4/2 + 3*x**2 - 3*x - 3. Suppose j(m) = 0. Calculate m.
-1, 1
Let m(l) = -4*l**3 + 51*l**2 - 196*l + 5. Let n(h) = -2*h**3 + 26*h**2 - 98*h + 2. Let r(q) = -4*m(q) + 10*n(q). Factor r(z).
-4*z*(z - 7)**2
Let y(o) be the first derivative of o + 2 - 2/11*o**2 - 5/33*o**3 - 1/110*o**5 - 2/33*o**4. Let a(f) be the first derivative of y(f). Factor a(h).
-2*(h + 1)**2*(h + 2)/11
Let z(a) be the first derivative of -5*a**3/12 - a**2 + a - 1. Let z(y) = 0. What is y?
-2, 2/5
Let m(r) be the third derivative of -r**8/144 + r**7/315 + 5*r**2. Solve m(w) = 0 for w.
0, 2/7
Let q(t) = -2*t**2 - 12*t - 7. Let o be q(-5). Let y(v) be the first derivative of -3/4*v**4 - 9/2*v**2 - o*v - 3*v**3 - 3. Let y(w) = 0. Calculate w.
-1
Determine t, given that -5 + 2*t**2 - 5 - 1 + 9 = 0.
-1, 1
Factor -2/7*t**5 - 4/7*t**2 + 0*t**3 + 2/7*t + 0 + 4/7*t**4.
-2*t*(t - 1)**3*(t + 1)/7
Let g(i) = 6*i**5 + 27*i**4 + 54*i**3 + 9*i + 9. Let t(z) = 3*z**5 + 13*z**4 + 27*z**3 + 5*z + 5. Let w(o) = -5*g(o) + 9*t(o). Factor w(p).
-3*p**3*(p + 3)**2
Let w = -12 - -12. Let r(j) be the first derivative of 0*j**2 + 0*j**5 + 0*j**3 + 0*j**4 + 1/12*j**6 + w*j - 3. Factor r(h).
h**5/2
Let q be ((-3)/(-2))/(2/12). Factor 7*i**2 - 4*i**2 - 4*i**3 - 4*i**4 + 20*i + 8 + q*i**2.
-4*(i - 2)*(i + 1)**3
Let g = -44 + 47. Let b(q) be the first derivative of -q - 1/3*q**g + 2 + q**2. Suppose b(t) = 0. What is t?
1
Let d be (9 - 5) + (-8)/4. Let z(k) be the second derivative of k + 1/3*k**d - 1/60*k**5 + 1/9*k**4 - 5/18*k**3 + 0. Factor z(o).
-(o - 2)*(o - 1)**2/3
Let i(f) = -18*f**2 + 10*f + 6. Let l be 2/3*(-8 + -1). Let o(a) = 35*a**2 - 19*a - 11. Let w(d) = l*o(d) - 11*i(d). Factor w(n).
-4*n*(3*n - 1)
Find j such that 0*j**3 - 18/5 - 12/5*j**4 - 3/5*j + 3/5*j**5 + 6*j**2 = 0.
-1, 1, 2, 3
Let o be (-2 - 21/(-6))/((-6)/(-12)). Let w(p) be the first derivative of 1/2*p**2 + 0*p - 1/4*p**4 + 1/3*p**o - 1/5*p**5 + 3. Determine l so that w(l) = 0.
-1, 0, 1
Let k = -3973/15 - -265. Let s(p) be the first derivative of -1/10*p**4 - 2 + 0*p + 2/5*p**2 + k*p**3. Factor s(h).
-2*h*(h - 2)*(h + 1)/5
Let k(z) be the first derivative of -z**3 - 3*z**2/2 - 4. Factor k(f).
-3*f*(f + 1)
Let m(d) be the third derivative of d**5/100 + 11*d**4/20 + 121*d**3/10 + 9*d**2. Factor m(q).
3*(q + 11)**2/5
Let m(u) be the third derivative of 1/12*u**4 + 0*u**5 + u**2 - 1/210*u**7 - 1/60*u**6 + 0*u + 1/6*u**3 + 0. Factor m(p).
-(p - 1)*(p + 1)**3
Suppose 0 = z - 3 + 1. Factor -25 + 3*m**3 - 2 + 15*m**z + 5*m + 4*m.
3*(m - 1)*(m + 3)**2
Suppose 0 = -8*l + 6*l + 2. Let f(n) be the first derivative of -l - 1/7*n**2 + 0*n**3 + 0*n + 1/14*n**4. Let f(w) = 0. Calculate w.
-1, 0, 1
Let q(j) be the first derivative of -1/5*j**5 + j**4 + 2*j**2 - 2 - 2*j**3 - j. Find z such that q(z) = 0.
1
Suppose -z + s - 6*s - 8 = 0, -z - s = 0. Suppose -z*n - 12 = -4*p, 0*p - 4*p = 5*n - 26.