f x**5/15 - 2*x**4/3 + 2*x**3 + 10*x**2 - 2*x. Suppose i(d) = 0. What is d?
1, 3
Let z(y) = -y**2 - 15*y + 36. Let k be z(-17). Factor q + 5*q - 2*q**2 - k*q.
-2*q*(q - 2)
Let y(n) be the second derivative of 1/2*n**3 - 14*n - 3/2*n**2 - 1/16*n**4 + 0. Let y(x) = 0. What is x?
2
Let g(u) be the first derivative of 0*u - 23 - 1/18*u**6 - 2/15*u**5 + 8/9*u**3 + 2/3*u**2 + 1/4*u**4. Determine r so that g(r) = 0.
-2, -1, 0, 2
Let h(u) be the second derivative of u**6/165 - 9*u**5/55 + 39*u**4/22 - 108*u**3/11 + 324*u**2/11 - 146*u - 2. Determine y so that h(y) = 0.
3, 6
Suppose 18/5*y**4 - 4/5*y**3 - 18/5*y**2 + 8/5*y**5 + 0 - 4/5*y = 0. What is y?
-2, -1, -1/4, 0, 1
Let f(r) be the third derivative of r**7/13860 + r**6/3960 + 7*r**4/12 - 4*r**2. Let p(u) be the second derivative of f(u). Factor p(c).
2*c*(c + 1)/11
Let s(v) be the first derivative of v**6/36 + v**5/6 - 3*v**4/8 - 17*v**3/18 + 2*v**2/3 + 2*v - 28. Let s(b) = 0. Calculate b.
-6, -1, 1, 2
Let y(f) be the first derivative of 25*f**6/9 + 4*f**5/15 - 25*f**4/3 - 8*f**3/9 + 25*f**2/3 + 4*f/3 + 253. Find d such that y(d) = 0.
-1, -2/25, 1
Let b(q) be the third derivative of -q**7/70 - q**6/5 - 21*q**5/20 - 9*q**4/4 + 2*q**2 - 287*q. Factor b(j).
-3*j*(j + 2)*(j + 3)**2
Let u = 11872 - 83080/7. Suppose 5*h + 0 = 15, 2*v - 13 = -3*h. Factor 2/7*n**3 + u*n + 12/7*n**v + 16/7.
2*(n + 2)**3/7
Let i be ((-144)/30)/(6/(-140)). Factor 2*n**5 + 96*n + 11*n**4 + 0 + 7*n**4 + 47*n**3 + 32 + i*n**2 + 17*n**3.
2*(n + 1)*(n + 2)**4
Let a(o) be the first derivative of -2/5*o**5 + 0*o**3 - o**4 + 2*o**2 + 2*o - 13. Factor a(n).
-2*(n - 1)*(n + 1)**3
Let l(v) be the first derivative of 5*v**4/4 - 5*v**3/3 - 185*v**2/2 - 175*v - 328. Factor l(b).
5*(b - 7)*(b + 1)*(b + 5)
Let z(a) be the second derivative of -a**7/700 - a**6/120 - a**5/50 - a**4/40 + 4*a**3/3 - 5*a. Let r(y) be the second derivative of z(y). Factor r(g).
-3*(g + 1)**2*(2*g + 1)/5
Factor 2/9*m**2 - 4/3 + 10/9*m.
2*(m - 1)*(m + 6)/9
Let g(n) be the third derivative of -1/5*n**3 - 1/150*n**5 + 0 + 0*n - 5*n**2 + 1/15*n**4. Let g(m) = 0. Calculate m.
1, 3
Factor 0 + 3/4*b**2 + 153/4*b.
3*b*(b + 51)/4
Let h = -6 + 11. Suppose h = -5*f + 20. Factor s**5 + 0*s**2 - 3*s**2 - 3*s**3 + f*s**2 - 2*s**2.
s**2*(s - 2)*(s + 1)**2
Let n be (4 - (-208)/(-64)) + 17/4. Let f(m) be the first derivative of -2*m**2 + n - 2/3*m**3 - 2*m. Factor f(j).
-2*(j + 1)**2
Suppose -3*w = j - 29, 4*j + 20 = 8*w - 3*w. Let b be (-1)/(-2)*w/10. Factor 4/5*d - 2/5 - b*d**2.
-2*(d - 1)**2/5
Let n(h) = -h**2 + 2*h + 6. Let d be n(0). Let u be (-4)/(d/(-3 + 0)). Let 6/7 - 3/7*k**u - 3/7*k = 0. What is k?
-2, 1
Suppose -140*m = -275 - 5. Factor 18/5*f - 27/5 - 3/5*f**m.
-3*(f - 3)**2/5
Let b = -31 - -35. Factor -b - m**2 + 2*m**2 - 4 + 4*m + 3*m**2.
4*(m - 1)*(m + 2)
Let v(l) = 8*l + 140. Let p be v(-17). Let r be 1 + p - ((-6)/2 - -3). Factor 1/2 + 5*q**2 - 5/2*q - 1/2*q**5 + 5/2*q**4 - r*q**3.
-(q - 1)**5/2
Let y = -28257/5 + 5657. Factor -2/5*b**2 - y*b - 98/5.
-2*(b + 7)**2/5
Let n = 1858/5 - 371. Let o = -12/17 + 111/85. Factor -3/5*g**3 + n*g + o - 3/5*g**2.
-3*(g - 1)*(g + 1)**2/5
Solve 4/3*d - 14/9*d**3 + 2/9*d**5 + 0 - 10/9*d**2 + 10/9*d**4 = 0.
-6, -1, 0, 1
Let f(s) = -s**5 - s**3 - s**2 - s. Let c(o) = o - 6. Let b be c(4). Let n(l) = 2*l**4 - l**3 - 3*l**2 - 2*l. Let u(t) = b*n(t) + 2*f(t). Factor u(m).
-2*m*(m - 1)*(m + 1)**3
Let a = -1720 - -5165/3. What is p in -2/3 - p**2 - a*p = 0?
-1, -2/3
Let w(l) be the first derivative of -12 - 8/7*l**3 - 30/7*l - 3/28*l**4 - 51/14*l**2. Find z such that w(z) = 0.
-5, -2, -1
Let q(l) be the second derivative of l**6/80 + 3*l**5/32 + l**4/32 - 21*l**3/16 - 27*l**2/8 - 41*l - 4. Suppose q(z) = 0. Calculate z.
-3, -1, 2
Let w be 6 - (3 - 144/(-30)) - -2. Factor -6*l + 72*l**2 + 1296*l**4 + w - 7776/5*l**5 - 432*l**3.
-(6*l - 1)**5/5
Let h(b) be the second derivative of b**6/30 + 13*b**5/20 + 31*b**4/6 + 64*b**3/3 + 48*b**2 + 88*b. Factor h(w).
(w + 2)*(w + 3)*(w + 4)**2
Determine m so that 2/9*m - 94/9*m**2 + 94/9 - 2/9*m**3 = 0.
-47, -1, 1
Let v(x) be the first derivative of 5*x**6/12 - 11*x**5/2 + 55*x**4/4 + 50*x**3 - 90*x**2 + 311. Determine o so that v(o) = 0.
-2, 0, 1, 6
Let f = 20703 - 20701. Factor 0 - 4/3*z**f + 0*z.
-4*z**2/3
Suppose 0 = -2*n - 78 - 22. Let j be (12/(-21))/(n/35). Factor -2/5*z**4 + 0 + 2/5*z**2 - j*z**3 + 2/5*z.
-2*z*(z - 1)*(z + 1)**2/5
Suppose 2*v - 150 = -142. Let i(y) = -y + 6. Let q be i(6). Factor q*t**2 + 4*t - 3*t + 5*t**2 - v*t**2.
t*(t + 1)
Let f be 10/(-4) + (-12)/8. Let v = 6 + f. Factor 63 - 63 - 3*r**v - 9*r.
-3*r*(r + 3)
Suppose 21*z + 19*z - 3 = 39*z. Solve -a + 3 - 1/3*a**z - 5/3*a**2 = 0 for a.
-3, 1
Factor 192*s**2 + 10 - 49*s**2 + 15*s - 46*s**2 - 47*s**2 - 45*s**2.
5*(s + 1)*(s + 2)
Let o(v) = -2*v. Let s(w) = 3*w**2 + 6*w - 9. Let f(l) = -6*o(l) - s(l). Find g such that f(g) = 0.
-1, 3
Let f(v) = 7*v**2 - 371*v + 4. Let l be f(53). Factor 0*r + 9/7*r**l + 0*r**2 + 3/7*r**5 + 0 + 6/7*r**3.
3*r**3*(r + 1)*(r + 2)/7
Let k(t) be the first derivative of 5*t**3/3 + 190*t**2 - 385*t + 860. Suppose k(z) = 0. Calculate z.
-77, 1
Suppose 27 = 3*r - 3*h, 0 = 2*r + 4*h + 6 - 0. Let y(k) be the first derivative of -1/9*k**2 - 9 + 1/18*k**4 + 2/45*k**r + 0*k - 2/27*k**3. Factor y(z).
2*z*(z - 1)*(z + 1)**2/9
Let z(n) be the third derivative of n**7/490 - n**6/280 - 18*n**2. Factor z(a).
3*a**3*(a - 1)/7
Let s = 1755 + -1752. Factor -1/4*p**5 + 0 - 7/4*p**2 - 1/2*p - 5/4*p**4 - 9/4*p**s.
-p*(p + 1)**3*(p + 2)/4
Let c(n) be the first derivative of 3 - 5/4*n**4 + 0*n**2 + 0*n - 10/3*n**3. Factor c(w).
-5*w**2*(w + 2)
Let m = -71/30 - -43/15. Suppose -1/2*j**4 + m*j**2 + 0*j**3 + 0 + 0*j = 0. What is j?
-1, 0, 1
Let g(q) = q**3 - 2*q**2 + 2*q - 5. Let m be g(3). Suppose -m = -2*h - t - 3, -3*h = 3*t - 12. What is u in 42/5*u**2 + 18/5*u**4 - 10*u**h - 4/5 - 6/5*u = 0?
-2/9, 1
Let x(w) = -22*w**3 + 46*w**2 - 38*w + 7. Let u(c) = -15*c**3 + 30*c**2 - 25*c + 5. Let s(m) = -7*u(m) + 5*x(m). Suppose s(r) = 0. What is r?
0, 1, 3
Let q(t) be the second derivative of 0*t**2 - 18*t - 3/40*t**5 + 0 + 1/84*t**7 + 0*t**3 + 0*t**4 + 1/30*t**6. Solve q(h) = 0.
-3, 0, 1
Suppose 17 = j + 13. Let b be (-27)/(-3) - (0 - -1). Solve -18*w**3 - j*w - 5*w**5 + b*w**4 + 2*w**4 + 21*w**2 + 3*w**5 - 7*w**2 = 0.
0, 1, 2
Let k(o) be the first derivative of -32 + 55*o**3 + 9*o + 2*o**2 + o**2 - 56*o**3. Factor k(u).
-3*(u - 3)*(u + 1)
Let n(w) = w - 3. Let c be n(10). Suppose -4*k + 12 = 4*u, 3*u - c*u - 2*k + 12 = 0. Factor 2/11 - 2/11*a**u - 2/11*a**2 + 2/11*a.
-2*(a - 1)*(a + 1)**2/11
Factor 366*t**5 - 362*t**5 - 129*t**4 + 16*t - 12*t**3 + 16*t**2 + 121*t**4.
4*t*(t - 2)**2*(t + 1)**2
Let h = 43 - 29. Factor -h*a + 4 - 7*a + 7*a + 10*a**2.
2*(a - 1)*(5*a - 2)
Suppose -v = 3*k + v - 14, -8 = 2*k - 3*v. Suppose 0 = -3*d - k*y, -6*y = -5*d - y. Suppose 0*m**3 + 0*m**4 - 4/7*m**5 + 0*m + d*m**2 + 0 = 0. Calculate m.
0
Suppose v = 6*v - 2*g - 28, 12 = 4*v + g. Suppose -t + 2*w + 12 = 3*t, -5*t + v*w = -18. Factor -2/5*f**3 + 0 + 0*f - 2/5*f**t.
-2*f**2*(f + 1)/5
Find w, given that 40 + 2*w + 3*w**2 + 2*w**2 + 57*w - 14*w = 0.
-8, -1
Let m(f) be the second derivative of -2*f**6/15 - 3*f**5/5 - f**4 - 2*f**3/3 + 145*f. Factor m(o).
-4*o*(o + 1)**3
Let u be -13 - -15 - 6/12. Factor -3*v**2 + 0 - u*v**3 + 9/2*v.
-3*v*(v - 1)*(v + 3)/2
Let t(g) be the third derivative of g**7/735 + 19*g**6/35 + 2166*g**5/35 - 794*g**2. Factor t(x).
2*x**2*(x + 114)**2/7
Let g be 3/(18/2)*0. Let k(d) be the first derivative of -1 + 0*d**3 + 0*d**2 + 0*d + g*d**5 + 0*d**4 - 1/21*d**6. Factor k(z).
-2*z**5/7
Let m be 9*1/27 + (-79)/(-6). What is u in 12*u + 3/2 - m*u**2 = 0?
-1/9, 1
Suppose -w - 5*m = 0, 0 = -0*w + 4*w + 4*m. Suppose 66*t = 69*t + 4*a + 15, -4*t - 18 = 5*a. Find r such that w*r + 2/3*r**2 + r**t + 0 + 1/3*r**4 = 0.
-2, -1, 0
Let r(p) be the first derivative of -p**7/210 - 2*p**6/45 - p**5/10 - 7*p**3 - 25. Let u(j) be the third derivative of r(j). Factor u(g).
-4*g*(g + 1)*(g + 3)
Let k(z) be the third derivative of z**5/40 + 3*z**4/8 + 5*z**3/4 - z**2 - 25*z. Factor k(p).
3*(p + 1)*(p + 5)/2
Let a(d) be the first derivative of -1/4*d**4 - 2/3*d**3 - d + 10 + 3/2*d**2. Let z(c) = 1. Let f(w) = -3*a(w) - 3*z(w). Find j, given 