t?
1, 2
Let c(r) be the first derivative of 9*r**5/25 + 3*r**4/10 - 9*r**3/5 - 18*r**2/5 - 12*r/5 + 2. Suppose c(d) = 0. What is d?
-1, -2/3, 2
Let q(c) be the second derivative of -c**6/20 + 3*c**4/8 - c**3/2 - 38*c. Solve q(m) = 0.
-2, 0, 1
Let c(y) be the third derivative of y**9/181440 + y**8/30240 + y**7/15120 - y**5/12 - 5*y**2. Let k(o) be the third derivative of c(o). Factor k(t).
t*(t + 1)**2/3
Let s = -3695 + 155215/42. Let x = s + 1/14. Suppose -10/3*p**4 - 20/3*p**2 - 10/3*p - 2/3 - x*p**5 - 20/3*p**3 = 0. What is p?
-1
Let x(d) be the second derivative of 2/9*d**4 + 3*d + 0 + 1/9*d**6 + 0*d**3 - 1/63*d**7 - 4/15*d**5 + 0*d**2. Let x(q) = 0. What is q?
0, 1, 2
Let x(a) = a**3 - a**2 - 2*a + 3. Let j(y) = y**2 - 6*y - 5. Let u be j(7). Let n be x(u). Find r such that -1/3*r + 1/3 + 1/3*r**n - 1/3*r**2 = 0.
-1, 1
Let y = -14 - -14. Let s(p) be the second derivative of y + 2*p + 0*p**2 - 1/36*p**4 - 1/60*p**5 + 1/9*p**3. Factor s(h).
-h*(h - 1)*(h + 2)/3
Let n(z) be the third derivative of 2*z**5/75 - z**4/20 + 3*z**2. Factor n(m).
2*m*(4*m - 3)/5
Let x(z) be the first derivative of z**6/45 + 4*z**5/75 + z**4/30 + 4. Solve x(t) = 0 for t.
-1, 0
Let k be 0/((-9)/(36/(-8))). Let y(d) be the first derivative of 1/2*d**2 - 1/3*d**3 + k*d + 1. Factor y(n).
-n*(n - 1)
Let j(n) be the second derivative of -n**5/50 + n**4/12 - n**3/15 - 15*n. Suppose j(g) = 0. Calculate g.
0, 1/2, 2
Let k(m) = -m + 2. Let w be k(-8). Factor 3 + w*j - 12*j + 1 - 2*j**2.
-2*(j - 1)*(j + 2)
Let f(s) = 2*s**4 + 2*s. Let h = 11 - 9. Let c(o) = -o**5 + o**4 + o**3 + o. Let r(z) = h*c(z) - f(z). Factor r(i).
-2*i**3*(i - 1)*(i + 1)
Let b(w) be the first derivative of 2*w**6/3 - 24*w**5/5 + 13*w**4 - 16*w**3 + 8*w**2 + 24. Let b(q) = 0. Calculate q.
0, 1, 2
Let s(r) = r**2 - 2. Let m(d) be the second derivative of -d**4/4 + 7*d**2/2 - 3*d. Let f(b) = 6*m(b) + 21*s(b). Factor f(c).
3*c**2
Let d = 154 - 150. Factor 0*t + 4/3*t**2 + 0 + 2*t**3 + 2/3*t**d.
2*t**2*(t + 1)*(t + 2)/3
Let s(a) = -4*a**4 + 7*a**3 - 9*a**2 + 13*a + 7. Let r(w) = w**4 - 2*w**3 + 3*w**2 - 4*w - 2. Let c(t) = -7*r(t) - 2*s(t). Determine i so that c(i) = 0.
-2, 0, 1
Suppose z + 2*d = d + 4, 13 = 2*z - 3*d. Let g(w) be the second derivative of 1/60*w**z + 0*w**3 + 0*w**2 - 1/36*w**4 + 0 - w. Factor g(h).
h**2*(h - 1)/3
Suppose 13 = 22*g - 75. Let c(t) = -t - 8. Let x be c(-8). Factor 0*m + x - 2/3*m**g - 2/3*m**3 + 4/3*m**2.
-2*m**2*(m - 1)*(m + 2)/3
Let m(v) be the second derivative of -v**7/168 - v**6/40 + v**4/12 - 8*v. What is g in m(g) = 0?
-2, 0, 1
Let q(t) be the first derivative of -4*t**3/9 - 4*t**2/3 - 4*t/3 - 7. Factor q(f).
-4*(f + 1)**2/3
Let u(g) = 10*g**3 + 13*g**2 + 10*g + 7. Let q(v) = -7*v**3 - 9*v**2 - 7*v - 5. Let z(j) = 7*q(j) + 5*u(j). Find a, given that z(a) = 0.
-1, 0
Let j(t) be the third derivative of -t**10/60480 + t**9/7560 - t**8/3360 - t**4/6 - 2*t**2. Let d(y) be the second derivative of j(y). Factor d(c).
-c**3*(c - 2)**2/2
Suppose -9*w + 29 = 2. Let q(h) be the second derivative of 0*h**3 + 0*h**2 - w*h + 0 + 1/54*h**4. Find c such that q(c) = 0.
0
Let k(g) be the second derivative of g**4/28 + g**3/14 + 2*g. Determine o so that k(o) = 0.
-1, 0
Suppose -n + 2*n - 33 = -3*y, -5*y = -20. Factor 7 - 6*h**3 + 24*h + 9 + n*h**4 - 24*h**3 - 3*h**4 - 28*h**2.
2*(h - 2)*(h - 1)*(3*h + 2)**2
Solve 8/15*o**2 - 2/3*o - 2/15*o**3 + 4/15 = 0 for o.
1, 2
Let m = -20 - -25. Suppose -m*v = -3*v. Solve 0*b**2 + 1/2*b**3 - 1/4*b**5 + 0 + v*b**4 - 1/4*b = 0 for b.
-1, 0, 1
Factor 1/2*i - 1/4 - 1/4*i**2.
-(i - 1)**2/4
Let v(w) be the second derivative of -3/80*w**5 + 0 + 0*w**2 - 1/40*w**6 + 0*w**3 + 1/56*w**7 + 1/16*w**4 - 10*w. Find r such that v(r) = 0.
-1, 0, 1
Let d(v) be the second derivative of -3*v + 4*v**2 + 0*v**3 - 1/10*v**5 + 0 - 1/2*v**4. Find c, given that d(c) = 0.
-2, 1
Let -6 - 3*s**2 - s**2 - s**2 - 8*s + 3*s**2 = 0. What is s?
-3, -1
Let v(c) = 49*c**3 + 82*c**2 + 32*c + 13. Let q(u) = 33*u**3 + 55*u**2 + 21*u + 9. Let j(s) = 7*q(s) - 5*v(s). Suppose j(w) = 0. Calculate w.
-1, -1/2, -2/7
Determine n so that 0*n + 33/8*n**3 + 3/2*n**5 - 39/8*n**4 + 0 - 3/4*n**2 = 0.
0, 1/4, 1, 2
Let i = 56 - 56. Factor -2/3*n**5 + 0 + 0*n + i*n**2 + 2/3*n**4 + 0*n**3.
-2*n**4*(n - 1)/3
Let h(u) = 5*u**5 + 5*u**4 - 3*u**3 - u**2 + 2*u - 4. Let p(t) = 6*t**5 + 6*t**4 - 3*t**3 - t**2 + 2*t - 5. Let l(s) = -5*h(s) + 4*p(s). Factor l(g).
-g*(g - 1)**2*(g + 1)*(g + 2)
Let p(b) be the first derivative of 4*b**5/5 + 4*b**4 - 4*b**3/3 - 8*b**2 + 8. Find k, given that p(k) = 0.
-4, -1, 0, 1
Factor -4/11*c**3 + 0*c + 0 + 2/11*c**5 - 2/11*c**4 + 0*c**2.
2*c**3*(c - 2)*(c + 1)/11
Suppose -5*k = h - 15 - 1, -3 = -2*k + 3*h. Suppose 4/3*z**2 - 2*z + 2/3 - 2*z**4 + 2/3*z**5 + 4/3*z**k = 0. Calculate z.
-1, 1
Let d(a) be the first derivative of -a**6/15 + a**4/2 - 2*a**3/3 - 4*a - 5. Let o(l) be the first derivative of d(l). Find x such that o(x) = 0.
-2, 0, 1
Factor -8/7*v**2 + 8/7 - 12/7*v.
-4*(v + 2)*(2*v - 1)/7
Factor -4/11*i - 2/11*i**2 + 0 + 2/11*i**3.
2*i*(i - 2)*(i + 1)/11
Let a = -5 + 7. Suppose 4*o - 5*n = 7, -o - a*o - 3*n = -12. Factor 0*v - v**4 + 0*v + o*v**5 - 2*v**3.
v**3*(v - 1)*(3*v + 2)
Let h = -1/5 - -7/10. Let s(b) be the first derivative of -1/3*b**3 + 0*b + h*b**2 - 3 - 1/2*b**4. Suppose s(x) = 0. What is x?
-1, 0, 1/2
Let r be (20/(-12))/((-2)/6). Factor -4*m**3 - 6*m**2 + m**4 + 2*m**2 - 2*m**r + 6*m - 1 - 1 + 5*m**4.
-2*(m - 1)**4*(m + 1)
Let f(a) be the second derivative of -a**6/210 - a**5/140 + a**4/28 + 5*a**3/42 + a**2/7 - 3*a - 6. Suppose f(n) = 0. Calculate n.
-1, 2
Suppose 4 = 2*u, -u - 10 = -2*v + u. Suppose -g = 2 - 7. Factor -v*x**3 + 29*x**3 + 10*x**g + 4*x**2 + 4*x**5 + 32*x**4.
2*x**2*(x + 1)**2*(7*x + 2)
Suppose 2*s - 9 + 3 = 0. Solve -3*v**2 + v**3 - s*v**5 - 2*v**3 - 9*v**4 - 8*v**3 = 0 for v.
-1, 0
Let l(i) be the third derivative of -i**8/70560 + i**7/5880 - i**6/1260 + i**5/10 + 3*i**2. Let u(k) be the third derivative of l(k). Solve u(a) = 0 for a.
1, 2
Let u = -192 - -385/2. Factor 0*v - u*v**5 + 1/6*v**4 + 1/3*v**3 + 0*v**2 + 0.
-v**3*(v - 1)*(3*v + 2)/6
Let p(r) = -6*r**2 - 79*r - 73. Let a(x) = x**2 + 20*x + 18. Let d(n) = -9*a(n) - 2*p(n). Factor d(f).
(f - 8)*(3*f + 2)
Let u(m) be the third derivative of -m**7/525 - 11*m**6/300 - 3*m**5/10 - 27*m**4/20 - 18*m**3/5 + 22*m**2. Suppose u(v) = 0. What is v?
-3, -2
Let c(n) be the first derivative of n**8/168 - n**7/45 + n**6/36 - n**5/90 + 2*n**2 - 4. Let i(b) be the second derivative of c(b). Factor i(o).
2*o**2*(o - 1)**2*(3*o - 1)/3
Let i(w) = -4*w**2 + 20*w - 16. Let c(j) = 4*j**2 - 19*j + 15. Let r(t) = -4*c(t) - 3*i(t). Suppose r(z) = 0. Calculate z.
1, 3
Factor -14*i**2 - 26*i + 5 + 16*i - 1.
-2*(i + 1)*(7*i - 2)
Factor -q - 3*q - 4*q**2 - 4*q.
-4*q*(q + 2)
Let t(q) be the third derivative of -q**8/10080 + q**7/420 - q**6/40 - 2*q**5/15 + q**2. Let k(g) be the third derivative of t(g). Factor k(c).
-2*(c - 3)**2
Factor 2*l**4 + 28/3*l**2 - 46/3*l**3 + 0*l + 0.
2*l**2*(l - 7)*(3*l - 2)/3
Let w(g) = -g**3 + 5*g**2 + 2*g - 3. Let c be w(5). Let h be ((-1)/c)/((-12)/42). Factor 0*v**3 + 0*v + 0 + 1/2*v**4 - h*v**2.
v**2*(v - 1)*(v + 1)/2
Let c be 3 + -2*(0 + 1). Let b = c + -1. Find v, given that b*v + 0 + 1/4*v**2 = 0.
0
Let o(y) = 84*y**2 + 124*y + 136. Let l(d) = 13*d**2 + 19*d + 21. Let w(s) = 32*l(s) - 5*o(s). Factor w(c).
-4*(c + 1)*(c + 2)
Let m(n) = n**3 + 1. Let i(s) = s**3 + s**2 - s + 2. Let r(h) = 3*i(h) - 4*m(h). Let d(z) be the first derivative of r(z). Factor d(f).
-3*(f - 1)**2
Let k(l) be the second derivative of 11*l**4/3 - 32*l**3/3 - 40*l**2 - 6*l. Let s(h) = 5*h**2 - 7*h - 9. Let u(w) = -3*k(w) + 28*s(w). Factor u(d).
4*(d + 1)*(2*d - 3)
Let p(t) be the third derivative of -t**6/360 + t**5/180 + t**4/36 + 2*t**2. Factor p(c).
-c*(c - 2)*(c + 1)/3
Factor 8/3*w**2 - 7/3*w + 2/3 - 2/3*w**3 - 2/3*w**4 + 1/3*w**5.
(w - 1)**4*(w + 2)/3
Let f(w) = 2*w**5 - 2*w**4 + 8*w**3 + 4*w. Let o(c) = 3*c**5 - 3*c**4 + 15*c**3 + 7*c. Let x(q) = 7*f(q) - 4*o(q). Factor x(t).
2*t**3*(t - 2)*(t + 1)
Let m(v) = -3*v**4 + 10*v**3 + 8*v**2 + 8*v + 4. Let j(a) = -4*a**4 + 11*a**3 + 7*a**2 + 8*a + 5. Let k(w) = 4*j(w) - 5*m(w). Find z, given that k(z) = 0.
-2, 0
Let g(m) be the third derivative of -m*