, 1
Factor 3*r**5 + 280*r**3 + 147*r**2 + 0*r + 0*r**5 + 45*r**4 - 91*r**3 + 0*r.
3*r**2*(r + 1)*(r + 7)**2
Let c(l) = -l + 0*l + 1 - l + 3*l. Let j(q) = -3*q**2 + 13*q - 11. Let z = -10 + 11. Let i(r) = z*j(r) - c(r). Determine n, given that i(n) = 0.
2
Let u = 929/765 + 2/255. Let k = u + -7/9. Suppose 2/9*f + 2/9*f**3 + k*f**2 + 0 = 0. What is f?
-1, 0
Let o(i) be the first derivative of -i**5/80 - i**4/8 - 3*i**3/8 - i**2/2 + 20*i + 45. Let b(t) be the first derivative of o(t). Let b(f) = 0. Calculate f.
-4, -1
Factor -3/4*t**2 + 15/4*t + 18.
-3*(t - 8)*(t + 3)/4
Let j(p) be the first derivative of 1/2*p**3 + 0*p**2 + 0*p - 12 - 3/16*p**4. Solve j(g) = 0.
0, 2
Let u = 3955/52 - 979/13. Factor -u*d**3 - 9/4 + 3/4*d + 9/4*d**2.
-3*(d - 3)*(d - 1)*(d + 1)/4
Let f(x) be the second derivative of 0 - 8*x - 7/4*x**4 + 5/2*x**3 + 3*x**2. Factor f(j).
-3*(j - 1)*(7*j + 2)
Let x(b) = 510*b + 3. Let q be x(0). Factor 1/5*g**4 + 0 + 1/5*g - 1/5*g**2 - 1/5*g**q.
g*(g - 1)**2*(g + 1)/5
Let w(o) = 3*o**2 + 14*o - 12. Let z(c) = -c**2 - 2*c + 1. Let f(t) = -w(t) - 4*z(t). Factor f(b).
(b - 4)*(b - 2)
Let u(v) be the first derivative of 4/7*v + 1/7*v**2 + 22 - 2/21*v**3. What is g in u(g) = 0?
-1, 2
Suppose y - 2*i = 11, 3*i + 27 = 3*y - i. Let a(t) be the first derivative of -1/15*t**5 + y - 1/12*t**4 + 1/9*t**3 + 1/6*t**2 + 0*t. Factor a(s).
-s*(s - 1)*(s + 1)**2/3
Let b(u) = u**2 + 7*u - 1. Let x be b(-6). Let s be ((-16)/x)/(-7 - -9). What is h in s + 2/7*h**2 + 8/7*h = 0?
-2
Let s(b) be the second derivative of b**5/10 + 3*b**4/2 - 4*b**3/3 - 36*b**2 + 68*b + 2. Factor s(h).
2*(h - 2)*(h + 2)*(h + 9)
Factor 2*o + 2*o**2 - o**2 + 0*o + 5*o**2.
2*o*(3*o + 1)
Let t(s) be the second derivative of s**7/420 + s**6/60 + s**5/30 - s**2 - 7*s. Let k(j) be the first derivative of t(j). Find q such that k(q) = 0.
-2, 0
Let p(q) be the first derivative of 5*q**3/3 + 115*q**2 + 2645*q - 2. Suppose p(m) = 0. What is m?
-23
Find r such that -14*r**4 + 10*r**2 - 36*r**3 - 4*r**2 - 3 - 29*r**4 + 12*r + 16*r**4 = 0.
-1, 1/3
Determine b so that -1/3*b**2 + 2 - 5/3*b = 0.
-6, 1
Factor 48/11*i + 2/11*i**3 - 18/11*i**2 - 32/11.
2*(i - 4)**2*(i - 1)/11
Let f = -35 - 38. Let c = -71 - f. Find p, given that 6/5*p**3 - 2/5*p**4 - 4/5*p**c + 0*p + 0 = 0.
0, 1, 2
Let m(g) be the third derivative of 1/336*g**8 + 1/24*g**4 + 1/20*g**6 + 0*g**3 - 2/105*g**7 + 2*g**2 + 0 - 1/15*g**5 + 0*g. Factor m(i).
i*(i - 1)**4
Suppose 3*c + 3*c = -42. Let n be (c/(28/24))/((-20)/6). Solve 3/5*f + n*f**4 - 3/5*f**3 + 0 - 9/5*f**2 = 0.
-1, 0, 1/3, 1
Let k = 50 + -8. Let v be 540/k + (-2)/(-14). Let -v*z**3 + 9*z**2 - 3*z**3 + z**3 + 6*z = 0. What is z?
-2/5, 0, 1
Let m(t) be the third derivative of t**6/24 + 7*t**5/4 + 245*t**4/8 + 1715*t**3/6 + 4*t**2 - 69*t. Suppose m(i) = 0. What is i?
-7
Let y be 462/30 - 9/(-15). Suppose -y = k - 18. Factor 3/2*t**3 - 1/2*t**4 + 0*t**2 + 0 - k*t.
-t*(t - 2)**2*(t + 1)/2
Let s(w) be the first derivative of -2*w**5/65 + 3*w**4/26 + 12*w**3/13 + 4*w**2/13 - 48*w/13 - 147. Solve s(y) = 0.
-2, 1, 6
Let h(l) be the third derivative of -11*l**5/3 - 445*l**4/24 - 5*l**3/3 + 407*l**2. Let h(u) = 0. What is u?
-2, -1/44
Let -3*v**3 + 3*v**2 + 0*v + 0 - 4/3*v**4 = 0. What is v?
-3, 0, 3/4
Let m(u) be the third derivative of u**6/660 - u**5/44 + 31*u**4/264 - 2*u**3/11 + 3*u**2 - 12*u. Find k, given that m(k) = 0.
1/2, 3, 4
Suppose -2*i - 15 = -3*h, h - 9 = -7*i + 9*i. Let s(v) be the third derivative of -1/90*v**5 + 0 + 0*v + 2*v**2 + 0*v**4 + 1/9*v**h. Factor s(z).
-2*(z - 1)*(z + 1)/3
Let a be -3 + (4/(-18) - 282/(-54)). Suppose -5*l - 25 = -a*o, -o + 11 = -l - l. Factor -9/2*s**3 - 6*s**4 - 5/2*s**o + 0*s + 0 - s**2.
-s**2*(s + 1)**2*(5*s + 2)/2
Let c(o) be the first derivative of -13 + 7/20*o**5 + 0*o - o**4 + 11/12*o**3 - 1/4*o**2. Factor c(l).
l*(l - 1)**2*(7*l - 2)/4
Let g = -524693/8 + 65414. Let r = g - -173. Suppose 0 - 3/4*b**2 + r*b - 3/2*b**3 + 9/8*b**5 + 3/4*b**4 = 0. Calculate b.
-1, 0, 1/3, 1
Suppose -8/15*x**4 + 8/15*x - 22/15*x**2 + 0 - 38/15*x**3 = 0. What is x?
-4, -1, 0, 1/4
Let z = 4188 + -62812/15. Factor 2/15*v**2 + 8/15 - z*v.
2*(v - 2)**2/15
Factor -82944/5 + 1152/5*d - 4/5*d**2.
-4*(d - 144)**2/5
Let p(g) be the first derivative of 15 + 0*g**2 + 0*g - 5/3*g**3. Factor p(a).
-5*a**2
Let c(w) be the first derivative of -3*w**4 - 28*w**3/3 - 32*w**2/3 - 16*w/3 + 180. Determine d so that c(d) = 0.
-1, -2/3
Let r = -6299 - -6303. Factor 32/5*q**3 - 16/5 + 64/5*q - 72/5*q**2 - q**r.
-(q - 2)**3*(5*q - 2)/5
Let r(m) be the first derivative of -10*m**6/3 + 29*m**5 - 45*m**4 - 385*m**3/3 + 100*m**2 + 240*m - 70. Suppose r(y) = 0. Calculate y.
-1, -3/4, 1, 4
Let m(v) be the second derivative of -v**9/2646 - 3*v**8/1960 - v**7/1470 - 3*v**3/2 - 35*v. Let o(s) be the second derivative of m(s). Factor o(p).
-2*p**3*(p + 2)*(4*p + 1)/7
Factor -66/13*c**2 + 80/13*c - 32/13 - 2/13*c**4 + 20/13*c**3.
-2*(c - 4)**2*(c - 1)**2/13
Let j(x) = -x + 1. Let v = -1 - -41. Let m(z) = 3*z**2 + 9*z - 8. Let n(y) = v*j(y) + 5*m(y). Let n(t) = 0. What is t?
-1/3, 0
Let g(s) = -2*s + 9. Let q(j) = -j + 4. Let n(f) = 3*g(f) - 7*q(f). Let x(r) = -5*r**2 - 20*r + 25. Let v(o) = 30*n(o) + x(o). Factor v(h).
-5*(h - 1)**2
Suppose 0 = 5*h - 10 - 10. Suppose h*s - 5*c = 31, 2*c = -4*s - c + 7. What is z in 25*z**5 + 12*z**3 - 16*z**s + 7*z**2 + 9*z**2 - 2*z + 7*z**5 - 42*z**3 = 0?
-1, 0, 1/4, 1
Let n be ((-42)/(-9))/(1 + 2/(-6)). Suppose -n = 7*y - 21. Find q, given that 2/5*q**3 - 2/5*q + 1/5 + 0*q**y - 1/5*q**4 = 0.
-1, 1
Let q = 627 - 623. Let a(z) be the first derivative of -1 + 0*z + 3/5*z**5 - 3/4*z**q + 3/2*z**2 - z**3. Factor a(m).
3*m*(m - 1)**2*(m + 1)
Let s(c) be the third derivative of -c**5/12 - 20*c**4 - 1920*c**3 - 2*c**2 + 1. Factor s(p).
-5*(p + 48)**2
Let -5/2*c**3 + 16*c + 39*c**2 + 0 = 0. Calculate c.
-2/5, 0, 16
Factor -6*t - 2*t - 15*t + 4*t**2 + 11*t.
4*t*(t - 3)
Suppose -2*x + m + 3 = 0, -5*x + 9 = 2*m - 3. Let 48*l**2 - 46*l**x + 0 + 8*l + 0 = 0. What is l?
-4, 0
Let h(p) = 5*p**4 - 2*p**3 - p**2 + 6*p + 6. Let c(z) = z**4 - z**2 + 1. Let y(a) = -6*c(a) + h(a). Factor y(u).
-u*(u - 2)*(u + 1)*(u + 3)
Factor 300 + 3/5*y**4 + 81*y**2 - 57/5*y**3 - 255*y.
3*(y - 5)**3*(y - 4)/5
Let i(b) be the first derivative of b**6/24 - b**5/10 - 5*b**4/16 + 5*b**3/6 + b**2/2 - 2*b - 170. Suppose i(p) = 0. Calculate p.
-2, -1, 1, 2
Let y(n) be the second derivative of n**4/30 + n**3/15 - 12*n**2/5 - 211*n. Factor y(r).
2*(r - 3)*(r + 4)/5
Let k(g) be the third derivative of g**8/2016 - g**7/210 + 11*g**6/720 - g**5/180 - g**4/12 + 2*g**3/9 + 84*g**2. Factor k(o).
(o - 2)**3*(o - 1)*(o + 1)/6
Let b(l) be the third derivative of 2*l**7/105 - 3*l**6/40 + l**5/10 - l**4/24 - 17*l**2. Factor b(s).
s*(s - 1)**2*(4*s - 1)
Let r(k) be the second derivative of k**6/15 - 3*k**5/5 - 7*k. Factor r(m).
2*m**3*(m - 6)
Let g(l) = 6*l**2 - 4*l + 5. Let h be g(2). Suppose 2*s - h = -15. Factor 1/6*z**4 - 1/2*z**s + 1/3*z**2 + 0 + 0*z.
z**2*(z - 2)*(z - 1)/6
Let o(x) be the first derivative of -2*x**5/85 - x**4/17 - 2*x**3/51 - 643. Suppose o(n) = 0. What is n?
-1, 0
Suppose 4*k - 48 = 4*b, 2*b = k - 0*k - 15. Factor -2 - 3*n**2 - 3*n**5 - 6*n**4 - k*n**3 + 2 - 3*n**4.
-3*n**2*(n + 1)**3
Solve 3/4*s**5 - 9/2*s + 21/4*s**4 + 0 - 21/4*s**2 + 15/4*s**3 = 0.
-6, -1, 0, 1
Let c = -893 - -8931/10. Let i(y) be the first derivative of 7 + 0*y + 0*y**2 - 3/4*y**4 + 3/2*y**3 + c*y**5. Suppose i(o) = 0. What is o?
0, 3
Factor -2/11*l**2 - 10/11*l - 12/11.
-2*(l + 2)*(l + 3)/11
Let p(r) = -2*r**2 + 31*r - 117. Let s be p(7). Let -4/7*j**4 + 4/7*j**s + 0*j + 0 + 0*j**3 = 0. Calculate j.
-1, 0, 1
Let t(z) = 13*z + 121. Let p be t(-9). Let u(n) be the first derivative of 0*n**p + 1/10*n**5 - 11 + 0*n**3 + 1/24*n**6 + 0*n + 0*n**2. Factor u(f).
f**4*(f + 2)/4
Suppose 5*r + 230 - 915 = 0. Let h = r - 1779/13. Factor 0 - h*b**5 + 0*b - 2/13*b**4 + 0*b**2 + 0*b**3.
-2*b**4*(b + 1)/13
Let i = -57 + 56. Let k(x) = -6*x - 6. Let y be k(i). Factor 0 - 4/3*o**3 - 2/3*o**2 + y*o - 2/3*o**4.
-2*o**2*(o + 1)**2/3
Let i(o) = -12*o**2 + 392*o - 2716. Let y(x) = -4*x**2 + 130*x - 905. Let p(m) = -5*i(m) + 16*y(m). Let p(z) = 0. What is z?
15
Let g(i) be the first derivative of i**3/3 - 2*i**2 + 3*i - 2. Let f be g