8/5*b + 2*b**3 + 2/5*b**4 + t.
2*b*(b + 1)*(b + 2)**2/5
Factor -2/7*s**2 - 8/7*s - 6/7.
-2*(s + 1)*(s + 3)/7
Let k(f) be the second derivative of -f**4/28 + f**3/14 + 9*f. Factor k(w).
-3*w*(w - 1)/7
Suppose 2*u - 3*o - 4 = -2*o, -3*u - 4*o = 5. Suppose 0 = t - 3 + u. Determine m, given that 8 + m**3 + 6*m**t + 3*m**3 - 3*m**3 + 12*m = 0.
-2
Let h(j) be the third derivative of -j**8/2184 + 2*j**7/1365 - 8*j**2. Factor h(r).
-2*r**4*(r - 2)/13
Factor 2/11*j + 2/11*j**3 + 0 + 4/11*j**2.
2*j*(j + 1)**2/11
Suppose -2*v + 2*l = -3*v, 0 = -3*v - l. Find x, given that v - 1/4*x - 1/4*x**2 = 0.
-1, 0
Let u(p) be the third derivative of p**9/52920 - p**8/5880 + p**7/1764 - p**6/1260 - p**4/6 - 2*p**2. Let b(k) be the second derivative of u(k). Factor b(h).
2*h*(h - 2)*(h - 1)**2/7
Let d(b) be the second derivative of b**6/10 + 3*b**5/5 + b**4 + 6*b. Determine i, given that d(i) = 0.
-2, 0
Let m(b) be the second derivative of -1/18*b**4 - 1/45*b**6 + 1/15*b**5 + 0*b**3 - 4*b + 0 + 0*b**2. Factor m(o).
-2*o**2*(o - 1)**2/3
Let z(r) be the third derivative of -r**9/40320 - r**8/40320 + r**7/5040 + r**5/20 - 2*r**2. Let p(y) be the third derivative of z(y). Factor p(o).
-o*(o + 1)*(3*o - 2)/2
Let w(m) be the first derivative of m**7/5040 - m**6/2160 - 7*m**3/3 - 6. Let s(o) be the third derivative of w(o). Factor s(t).
t**2*(t - 1)/6
Let n be (1 - 9/6)*-12. Factor 24*t**2 + 3 - 19*t - 18*t**3 + 4*t + n*t**3.
-3*(t - 1)*(2*t - 1)**2
Let y(z) = -z**2 + 4*z + 9. Let l(j) = 5*j**2 - 15*j - 35. Let s(f) = 4*l(f) + 15*y(f). Suppose s(q) = 0. What is q?
-1, 1
Factor 10/3*k**3 + 625/6 + 250/3*k + 25*k**2 + 1/6*k**4.
(k + 5)**4/6
Factor 19 - 4*m**4 + 16*m**3 - 16*m + 4 - 11 - 8*m**2.
-4*(m - 3)*(m - 1)**2*(m + 1)
Let s(h) = -3*h**2 + 16*h - 7. Let w(z) = 3*z**2 - 15*z + 6. Let r(l) = 6*s(l) + 7*w(l). Find k, given that r(k) = 0.
0, 3
Let c be 24 + (3 - -3)/(-3). Let h be c/99 + (-10)/126. Factor h*a**2 - 1/7*a - 2/7.
(a - 2)*(a + 1)/7
Factor 7*w**3 - 2*w**5 + 4*w**2 - 2*w**2 - 5*w**3 - 2*w**4.
-2*w**2*(w - 1)*(w + 1)**2
Factor -1/9*u**2 - 2/9 + 1/3*u.
-(u - 2)*(u - 1)/9
Let o(j) be the first derivative of j**6/27 + 2*j**5/45 - j**4/18 - 2*j**3/27 - 23. Determine u, given that o(u) = 0.
-1, 0, 1
Let z = -35 - -106/3. Let n(q) be the third derivative of 0 - 2/15*q**5 - 1/3*q**4 - z*q**3 + 2*q**2 + 0*q. Suppose n(x) = 0. What is x?
-1/2
Let c(h) be the second derivative of -4*h + 1/3*h**3 + 1/3*h**4 - h**2 + 1/21*h**7 - 1/5*h**5 - 1/15*h**6 + 0. Factor c(u).
2*(u - 1)**3*(u + 1)**2
Let o(g) = g**2 + 1. Let i(z) = 3*z**2 + 6*z + 11. Let m = -13 + 12. Let a(x) = m*i(x) + 2*o(x). Factor a(n).
-(n + 3)**2
Let s = -1 + 4. Factor x**2 + 0*x**2 + x**2 - s*x**3 + 2*x**3.
-x**2*(x - 2)
Let n(x) = -10*x**5 + 14*x**4 - 4*x**3 + 2*x. Let i(l) = 51*l**5 - 71*l**4 + 20*l**3 - 11*l. Let p(b) = 2*i(b) + 11*n(b). Factor p(t).
-4*t**3*(t - 1)*(2*t - 1)
Let u(y) be the third derivative of -y**5/15 - 4*y**4/3 - 32*y**3/3 - 25*y**2. Let u(d) = 0. Calculate d.
-4
Suppose -5*s - 1 = -21. Let q(k) be the second derivative of -1/3*k**3 + 0*k**2 - 7/20*k**5 + 3/4*k**s + 0 - k. What is t in q(t) = 0?
0, 2/7, 1
Let b(r) be the first derivative of 27/2*r**2 + 3/4*r**4 - 2 + 0*r - 6*r**3. Find g such that b(g) = 0.
0, 3
Let t be 6/10*(-1 - -6). Let k(a) = 4*a**4 + 5*a**3. Let m = 81 + -78. Let i(s) = -s**4 - s**3 + s**2. Let u(p) = m*i(p) + t*k(p). Solve u(g) = 0.
-1, -1/3, 0
Let h(i) be the first derivative of -1/27*i**6 + 0*i**3 + 0*i + 0*i**5 + 1/9*i**4 - 1/9*i**2 - 4. Factor h(n).
-2*n*(n - 1)**2*(n + 1)**2/9
Factor 5/8*r - 3/8*r**2 + 1/8*r**4 - 1/4 - 1/8*r**3.
(r - 1)**3*(r + 2)/8
Find b, given that -8/5*b**4 - 2/5*b**5 - 8/5*b**2 + 0 - 12/5*b**3 - 2/5*b = 0.
-1, 0
Let x(b) = 3*b**2 - b + 1. Let w be x(-2). Suppose h + k = 3, 2*h + 5*k - w = -h. Factor h + 2/11*u - 2/11*u**2.
-2*u*(u - 1)/11
Suppose 2*j + 33 = -27. Let y be 1/(-2) - 21/j. Factor 1/5 - 1/5*a**5 + 1/5*a**4 - 2/5*a**2 + 2/5*a**3 - y*a.
-(a - 1)**3*(a + 1)**2/5
Let j(z) be the first derivative of -z**5/15 + 5*z**4/12 - 2*z**3/3 - 5. Determine c so that j(c) = 0.
0, 2, 3
Factor -4/7*s**2 + 8/7*s + 0.
-4*s*(s - 2)/7
Suppose -5*a = -5, -3*a + a = -2*r + 14. Let u be (2/(-5))/(r/(-10)). Suppose 0 + 1/2*z**2 + 1/2*z**3 - u*z - 1/2*z**4 = 0. What is z?
-1, 0, 1
Factor -10*a**3 + 0*a**2 + 3*a**2 + 7*a**3 - 3*a**4 + 3*a**5.
3*a**2*(a - 1)**2*(a + 1)
Suppose 0 = -0*a + 3*a. Suppose a = 2*n - 3*n + 6. Factor -m**3 + 2*m**3 - n*m**5 + 7*m**5 + 2*m**4.
m**3*(m + 1)**2
Let k(c) be the second derivative of -c**7/1008 - c**6/720 - c**4/2 + 4*c. Let y(i) be the third derivative of k(i). Determine o, given that y(o) = 0.
-2/5, 0
Let j(c) = 18*c + 77. Let i be j(-4). What is m in -2/3*m + 4/3*m**3 + 0 + 0*m**4 - 2/3*m**i + 0*m**2 = 0?
-1, 0, 1
Let i(t) be the second derivative of t**6/2 - 27*t**5/10 + 3*t**4 + 4*t**3 - 3*t. Suppose i(g) = 0. What is g?
-2/5, 0, 2
Let p be 12/(-18)*(18/8)/(-3). Factor -1/4 + 1/4*q**2 + p*q - 1/2*q**3.
-(q - 1)*(q + 1)*(2*q - 1)/4
Solve -2/7*t**3 + 0*t**2 + 0 + 0*t = 0 for t.
0
Factor 0*m - 2*m + 27*m**3 + 14*m - 36*m**2 - 6*m**4.
-3*m*(m - 2)**2*(2*m - 1)
Let v(o) = -2*o**4 + 5*o**3 - 9*o**2 - 8*o + 8. Let z(u) = -4*u**4 + 11*u**3 - 17*u**2 - 16*u + 16. Let r(t) = 5*v(t) - 3*z(t). Suppose r(y) = 0. What is y?
-1, 1, 2
Let s(b) = 2*b**2 - 7*b + 5. Let m(h) be the third derivative of h**5/30 - h**4/3 + h**3 + 4*h**2. Let o(y) = 5*m(y) - 6*s(y). Factor o(l).
-2*l*(l - 1)
Suppose 8 = n + 4*h, 5*n - 6*h = -2*h + 16. Find v, given that -n*v + 0*v + 3*v**2 + v = 0.
0, 1
Determine n so that 0*n**2 + 2/5*n**3 - 8/5*n + 0 = 0.
-2, 0, 2
Let v(o) be the second derivative of o**6/20 - 3*o**5/10 + 5*o**4/8 - o**3/2 - 20*o. Suppose v(r) = 0. Calculate r.
0, 1, 2
Let b = 999/2 + -499. Factor 0 - 1/2*p**3 + 1/2*p**2 + 1/2*p - b*p**4.
-p*(p - 1)*(p + 1)**2/2
Factor -j**2 - 1/2*j**3 + 2*j + 4.
-(j - 2)*(j + 2)**2/2
Let c(j) be the first derivative of -j**3/3 + 3*j + 1. Let p be c(0). Factor -1 + 2*m**2 - 2 + 4*m**p - 10*m + 7.
2*(m - 1)*(m + 2)*(2*m - 1)
Let j(r) be the third derivative of r**5/60 + r**4/24 - r**3/6 + r**2. Let k(p) = -9*p**2 - 21*p + 18. Let i(c) = 12*j(c) + k(c). Suppose i(u) = 0. What is u?
1, 2
Factor -1/3*r + 0 - 1/6*r**2.
-r*(r + 2)/6
Let x(m) = 10*m. Let n be x(1). Find s such that -2*s**2 + 14*s + s**4 - 16*s**2 - 3*s**4 + 6 - 10 + n*s**3 = 0.
1, 2
Let b be (-4)/(-10) + 23/5. Let h be 1/(-5) + 27/60. Factor 1/2*u**2 - h*u**b - 1/4 - 1/4*u**4 + 1/2*u**3 - 1/4*u.
-(u - 1)**2*(u + 1)**3/4
Let w(f) be the second derivative of f**4/24 - 2*f**3/3 + 4*f**2 - 11*f. Factor w(p).
(p - 4)**2/2
Suppose g + 18 = 3*g. Let u be 9*1/g*3. Factor -2/3*y**2 - 2/3*y**4 - 4/3*y**u + 0 + 0*y.
-2*y**2*(y + 1)**2/3
Let k(z) be the first derivative of -3*z - 3/8*z**4 + 7 - 2*z**3 - 15/4*z**2. Factor k(h).
-3*(h + 1)**2*(h + 2)/2
Let r = 9 - 7. Factor s**2 - 3*s**2 + 5*s**r.
3*s**2
Let n(f) = f**3 - 10*f**2 - 16*f + 57. Let q be n(11). Factor 2/3*g**4 - 2/9*g**5 + 0 - 2/3*g**3 + 2/9*g**q + 0*g.
-2*g**2*(g - 1)**3/9
Suppose 3*j + 15 = 4*b, -4*j - 2*b + 8 = 2*b. Let k = j + 3/2. Suppose k*v**2 + 1 + 3/2*v = 0. Calculate v.
-2, -1
Let m(i) = -i**3 + 7*i**2 + 8*i. Let l(q) = q**3 - 15*q**2 - 16*q. Let s = 8 - 15. Let x(y) = s*m(y) - 3*l(y). Determine h so that x(h) = 0.
-1, 0, 2
Let z(a) = -3*a - 1. Let y be z(-1). Let c(s) be the second derivative of -1/42*s**4 + y*s + 0 + 1/21*s**3 + 0*s**2. Factor c(k).
-2*k*(k - 1)/7
Let y = 235/292 - 4/73. Factor -3/4*n**2 + y*n - 1/4 + 1/4*n**3.
(n - 1)**3/4
Let u(d) be the third derivative of 5/72*d**4 + 0*d + 1/630*d**7 + 0 - 1/60*d**5 + 2*d**2 - 1/9*d**3 - 1/360*d**6. Determine f so that u(f) = 0.
-2, 1
Let a(t) be the third derivative of -t**8/672 - t**7/210 + t**5/60 + t**4/48 + 7*t**2. Factor a(b).
-b*(b - 1)*(b + 1)**3/2
Let j = -11 + 19. Suppose -2 = 3*w - j. Determine m, given that 0*m - 2/3 + 2/3*m**w = 0.
-1, 1
Let s be (-67)/(-168) + 2/14. Let l(z) be the third derivative of 2*z**2 + 1/6*z**3 + s*z**4 + 0 + 169/240*z**5 + 0*z. Factor l(q).
(13*q + 2)**2/4
Let v(p) be the second derivative of -p - 1/84*p**7 - 1/30*p**6 + 0*p**2 + 0 + 0*p**4 - 1/40*p**5 + 0*p**3. Factor v(w).
-w**3*(w + 1)**2/2
Let y(b) be the second derivative of -2*b**5/65 - 5*b**4/78 + 4*b**3/39 + 5*b**2/13 + 14*b.