 s*t = 0. What is t?
0, 4
Let i(d) be the second derivative of 49*d**6/720 + 77*d**5/360 + 2*d**4/9 + d**3/9 + 3*d**2/2 - d. Let v(h) be the first derivative of i(h). Solve v(j) = 0.
-1, -2/7
Let l(x) = -x**3 + 4*x**2 - 105*x + 422. Let b be l(4). Solve -1/4*d - 3/4*d**3 - 1/4*d**4 - 3/4*d**b + 0 = 0 for d.
-1, 0
Let t(d) = 4*d**4 + 13*d**3 + d**2 + 9*d - 9. Let o(w) = 2*w**4 + 6*w**3 + 4*w - 4. Let z(x) = 9*o(x) - 4*t(x). Factor z(h).
2*h**2*(h - 1)*(h + 2)
Let l(w) be the second derivative of -w**6/15 + w**5/4 - 17*w**4/96 + w**3/24 + 32*w. Factor l(i).
-i*(i - 2)*(4*i - 1)**2/8
Let s(y) be the third derivative of y**7/735 - y**6/420 - y**5/70 + y**4/84 + 2*y**3/21 + 9*y**2. Factor s(p).
2*(p - 2)*(p - 1)*(p + 1)**2/7
Determine a so that -a + 1 - 3*a - 4*a - 5 - 4*a**2 = 0.
-1
Let a(r) = 13*r**4 + 79*r**3 + 245*r**2 + 105*r + 5. Let p(m) = -7*m**4 - 39*m**3 - 123*m**2 - 53*m - 3. Let t(q) = -3*a(q) - 5*p(q). Let t(o) = 0. What is o?
-5, -1/2, 0
Let a(u) be the first derivative of 2*u**6/3 + 8*u**5/5 - 8*u**3/3 - 2*u**2 - 4. Factor a(l).
4*l*(l - 1)*(l + 1)**3
Factor -t**2 + 0*t - 8 - 2*t + 6*t + 5*t**2.
4*(t - 1)*(t + 2)
Let j(x) be the first derivative of 7*x**6/9 - 2*x**5/3 - x**4/3 - 10. Find l, given that j(l) = 0.
-2/7, 0, 1
Suppose 3*h = -h - 4. Let f be h - (2 + -2) - -3. Let 8/3*j**f - 2*j - 3*j**4 + 1/3 + 4/3*j**5 + 2/3*j**3 = 0. What is j?
-1, 1/4, 1
Let y be (-1)/((5*-3)/5). Let n(d) be the third derivative of 0 + 0*d**3 + d**2 + 8/15*d**5 + 0*d + 1/4*d**6 + y*d**4. Let n(q) = 0. What is q?
-2/3, -2/5, 0
Let p = -104 - -106. Let i(a) be the second derivative of -3/2*a**3 + a**2 + 5/12*a**4 - 7/30*a**6 + p*a + 0 + 9/20*a**5. Factor i(b).
-(b - 1)**2*(b + 1)*(7*b - 2)
Let q(n) = -n**2 + 12*n + 3. Let m be q(12). Suppose 3*k = 3*h + 6, -3*h - 9 + m = 4*k. Factor 2/3*d**5 + 0*d**4 + 0*d**2 - 2/3*d**3 + 0 + k*d.
2*d**3*(d - 1)*(d + 1)/3
Factor -1/2*i**2 + 1/4*i**3 - 5/4*i + 3/2.
(i - 3)*(i - 1)*(i + 2)/4
Let n(f) be the third derivative of f**5/360 - f**4/72 + f**3/36 + 6*f**2. Factor n(a).
(a - 1)**2/6
Let p(b) = 3*b - 10. Let t be p(5). Let d(c) be the third derivative of 0 + 0*c - 3*c**2 - 1/270*c**t - 1/108*c**4 + 0*c**3. Factor d(k).
-2*k*(k + 1)/9
Let u(c) be the third derivative of 1/5*c**5 + 0*c - 3/20*c**6 + 2/35*c**7 - 1/8*c**4 + 0 + 6*c**2 - 1/112*c**8 + 0*c**3. Find p such that u(p) = 0.
0, 1
Let 5/4*r - 1/4*r**3 - r**5 - 7/4*r**2 - 1/4 + 2*r**4 = 0. Calculate r.
-1, 1/2, 1
Let z(w) be the first derivative of 2 + 0*w**2 + 2*w - 2/21*w**4 - 1/21*w**3. Let b(d) be the first derivative of z(d). Find v such that b(v) = 0.
-1/4, 0
Let l be (68/(-10) - -4)/(18/(-15)). Determine w so that 4/3*w**3 - 2/3 + 5/3*w**2 - l*w = 0.
-2, -1/4, 1
Suppose -5*h + 2 = 2*t, 0*t + 8 = -t + 2*h. Let u = t + 7. Let -2*r**u - 4*r**2 + r**2 + r**2 = 0. What is r?
-1, 0
Let a(p) be the first derivative of -p**4/20 + p**3/15 - 17. Find d such that a(d) = 0.
0, 1
Let c(w) be the first derivative of w**6/15 + w**5/5 - 2*w**3/3 - w**2 - 2*w + 5. Let n(x) be the first derivative of c(x). Solve n(m) = 0.
-1, 1
Factor 8*t - 6*t**2 - 3 + 3*t**3 + t - 3*t**2.
3*(t - 1)**3
Let k(c) = -2*c - 7. Let g be k(-6). Let f be (-12)/(-66) - (-31)/11. Factor 0*n**f - n**3 + 0*n**3 + n**g.
n**3*(n - 1)*(n + 1)
Suppose i + 11 = 4*y, -5*i = -2*y + 4*y - 33. Let d(v) = 4*v - 13. Let c be d(y). Factor 3/2*z**5 + 0*z + 3*z**4 + 3/2*z**c + 0*z**2 + 0.
3*z**3*(z + 1)**2/2
Let g = -3/139 + -801/1529. Let t = g + 40/33. Suppose -4/3 + 10/3*n - 8/3*n**2 + t*n**3 = 0. Calculate n.
1, 2
Factor -2*a**2 - 5*a**3 + a**2 + 8*a**3.
a**2*(3*a - 1)
Let k = 23/14 + -8/7. Find j, given that 3/2*j**3 + 3/2*j**4 + 1/2*j**5 + 0 + k*j**2 + 0*j = 0.
-1, 0
Let v(b) be the second derivative of b**4/36 + b**3/9 - 4*b. Let v(l) = 0. What is l?
-2, 0
Let x(y) = 13*y. Let n be x(6). Suppose -3*r + n = 24. Solve 4 - 13*c + 3*c - 4*c - r*c**2 = 0 for c.
-1, 2/9
Let y(a) be the third derivative of 11*a**8/672 - 31*a**7/420 + 9*a**6/80 - a**5/24 - a**4/24 + 18*a**2 - 2*a. Factor y(d).
d*(d - 1)**3*(11*d + 2)/2
Let z(b) = 7*b - 42. Let i be z(6). Solve d**2 - 1/2*d**3 - 1/2*d + i = 0 for d.
0, 1
Suppose -6*c = -2*c - 20. Suppose -6*p + c*p = 0. Factor 1/2*h**4 + 3/2*h**2 + p - 3/2*h**3 - 1/2*h.
h*(h - 1)**3/2
Let v(i) be the third derivative of -i**8/3528 - 2*i**7/2205 + i**6/420 + 4*i**5/315 + i**4/63 - 8*i**2. Solve v(l) = 0.
-2, -1, 0, 2
Let b(h) be the third derivative of 3*h**8/112 + 11*h**7/70 + h**6/8 - 3*h**5/20 + 12*h**2. Determine a, given that b(a) = 0.
-3, -1, 0, 1/3
Let w(v) be the second derivative of -2*v**7/147 + 2*v**6/21 - 8*v**5/35 + 4*v**4/21 - 6*v. Factor w(s).
-4*s**2*(s - 2)**2*(s - 1)/7
Factor 16/13*m**2 + 2/13*m**4 + 0 + 10/13*m**3 + 8/13*m.
2*m*(m + 1)*(m + 2)**2/13
Let a(t) be the second derivative of t**7/84 - t**5/20 + t**3/12 + 22*t. Factor a(u).
u*(u - 1)**2*(u + 1)**2/2
Let v(d) be the third derivative of 0*d**3 - 15/448*d**8 - 1/40*d**6 + 0 + 6*d**2 - 1/8*d**5 + 0*d + 13/140*d**7 + 3/32*d**4. Determine f so that v(f) = 0.
-3/5, 0, 1/3, 1
Let y(d) be the third derivative of -7*d**2 + 1/105*d**7 + 1/6*d**4 - 1/30*d**6 + 0*d - 1/30*d**5 + 0 + 0*d**3. Determine v, given that y(v) = 0.
-1, 0, 1, 2
Let g(o) be the first derivative of -2/5*o**5 - 4 + 0*o**2 + 0*o**3 + 1/2*o**4 + 0*o. Factor g(l).
-2*l**3*(l - 1)
Let s(t) = -3*t + 3. Let g be s(-4). Suppose -5*r - 3 + g = -4*i, 2*r = i + 3. Find y, given that 2/7*y - 2/7*y**4 + r + 2/7*y**2 - 2/7*y**3 = 0.
-1, 0, 1
Let k(b) = -b**2 + b - 2. Suppose -2 = -o - 5*x - 14, 0 = 5*o - 5*x. Let z(j) = -j - 1. Let t(u) = o*k(u) + 2*z(u). Suppose t(i) = 0. Calculate i.
1
Let j = 4 - 2. Determine t so that -t + 3*t - 4 - 4*t**4 + 2*t**3 + 27*t**j - 15*t**2 = 0.
-1, 1/2, 2
Let g = 194 + -1742/9. Suppose -4/9*n + 0 + g*n**3 + 2/9*n**2 - 2/9*n**4 = 0. Calculate n.
-1, 0, 1, 2
Let k = 53 + -158/3. Factor 1/6 + 1/6*a**2 - k*a.
(a - 1)**2/6
Let y be ((-1)/(-2))/((-14)/(-1296)). Let f = y - 46. Factor -f*a + 0 - 2/7*a**2.
-2*a*(a + 1)/7
Suppose -j - 2*j - 18 = 0. Let f = -3 - j. Factor 3*p**3 + 4*p**4 - p**f + 5*p**5 - 3*p**5.
2*p**3*(p + 1)**2
Let n = -3/44 + -107/44. Let h = n - -11/4. Factor -h*p**3 + 1/4 + 1/4*p - 1/4*p**2.
-(p - 1)*(p + 1)**2/4
Let l = 39 - 24. Suppose 8*a - 3*a - l = 0. Let x(i) = i**4 + i**3 - 3*i + 3. Let f(p) = p**4 + p**3 - p + 1. Let n(r) = a*f(r) - x(r). Factor n(s).
2*s**3*(s + 1)
Let o = 1 + -1. Suppose -5*t = 4*w - 8, w - 2*t + 5 - 7 = 0. Let 0 - 1/2*a**4 + 0*a**3 + 1/2*a**w + o*a = 0. Calculate a.
-1, 0, 1
Let a(z) be the first derivative of 4*z**5/5 + 8*z**4 + 64*z**3/3 - 6. What is h in a(h) = 0?
-4, 0
Let b(z) be the first derivative of -5 + 2/13*z - 2/39*z**3 + 0*z**2. Suppose b(t) = 0. Calculate t.
-1, 1
Find s such that 11*s + 8*s - 9*s**3 + 6*s**2 - 15*s - s**3 = 0.
-2/5, 0, 1
Let z = 3932/5 - 784. Factor -1/5*a**4 - 6/5*a**3 - 13/5*a**2 - 4/5 - z*a.
-(a + 1)**2*(a + 2)**2/5
Suppose -5*q + 48 + 12 = 0. Factor 5*g + 7*g + g**3 - q*g.
g**3
Let y(z) be the third derivative of z**5/30 + z**4/8 + 3*z**2. Let h be y(-2). Suppose 2/9*s**3 + 2/9*s + 0 - 4/9*s**h = 0. Calculate s.
0, 1
Let d(h) be the second derivative of h**5/70 - h**4/14 + h**3/7 - h**2/7 + 9*h. Suppose d(r) = 0. What is r?
1
Let i(y) = -y**2 - 5*y - 4. Let n be i(-4). Let t be n/2 - 10/(-45). Let t*s**3 + 0 - 2/3*s**4 + 0*s + 4/9*s**2 = 0. Calculate s.
-2/3, 0, 1
Let a(n) be the first derivative of 5 - 2*n + 2/3*n**6 + 0*n**2 - n**4 - 6/5*n**5 + 8/3*n**3. Factor a(d).
2*(d - 1)**3*(d + 1)*(2*d + 1)
Let a(p) be the second derivative of p**4/24 + p**3/3 - 5*p**2/4 - 10*p. Suppose a(n) = 0. What is n?
-5, 1
Let s = -374 - -5612/15. Find g, given that 2/15*g**4 + 0*g - 2/15*g**3 - s*g**2 + 0 + 2/15*g**5 = 0.
-1, 0, 1
Let k(x) be the third derivative of 2*x**7/525 - x**6/75 - 4*x**5/75 + 4*x**4/15 - 15*x**2. Factor k(w).
4*w*(w - 2)**2*(w + 2)/5
Let a(l) be the third derivative of l**7/8820 + l**6/2520 - l**4/24 - 2*l**2. Let i(c) be the second derivative of a(c). Factor i(h).
2*h*(h + 1)/7
Let m(v) = v - 6. Let s be m(12). Let t(p) = -5*p**2 - 5*p. Let k(l) = -l**2 - l. Let y(b) = s*t(b) - 33*k(b). Find i, given that y(i) = 0.
-1, 0
Let a(g) be the third derivative of -25*g**8/504 + 17*g**7/63 - 31*g**6/180 + g**5/30 + 35*g**2. Factor a(b).
-2*b**2*