7*j - 22. Let z be m(16). Let k be (10 + z)*(-3)/(-12). Find r such that 1/4*r**2 - r + k = 0.
2
Let a(n) = -n**3 - 6*n**2 + 7*n + 5. Let k be a(-7). Factor f + 3*f**2 + k*f + 0*f.
3*f*(f + 2)
Suppose 1/4*i**2 + 1/2 + 3/4*i = 0. What is i?
-2, -1
Let b be 1/(-1)*(-9)/3. Suppose -3*n + 13 = 2*q, -5*n + 9 = -4*n + b*q. Factor -u**3 + 0*u**3 - n*u + 5*u - u**3.
-2*u*(u - 1)*(u + 1)
Let f(p) be the third derivative of -p**6/720 + p**5/120 - p**3/6 + 3*p**2. Let d(u) be the first derivative of f(u). Factor d(a).
-a*(a - 2)/2
Factor -4/3*y**4 + 4/3*y**2 + 2/3*y**5 + 0 + 0*y**3 - 2/3*y.
2*y*(y - 1)**3*(y + 1)/3
Let b(c) be the second derivative of -c**4/15 - 4*c**3/5 - 2*c**2 + 10*c - 3. Factor b(q).
-4*(q + 1)*(q + 5)/5
Let x(q) be the second derivative of -3/25*q**6 - 1/15*q**7 + 0*q**3 + 5*q + 0*q**4 + 0 + 0*q**2 - 1/25*q**5. Find a, given that x(a) = 0.
-1, -2/7, 0
Find w such that -4*w + 3 - 3*w**2 + 10*w + 6 = 0.
-1, 3
Let d(q) be the first derivative of 1 + 0*q**2 + 1/2*q**6 + 1/5*q**5 + 0*q - 3/4*q**4 - 1/3*q**3. Factor d(n).
n**2*(n - 1)*(n + 1)*(3*n + 1)
Let i(c) be the third derivative of 0*c + 1/60*c**6 + 1/15*c**5 + 0 + 0*c**4 - 4*c**2 + 0*c**3. Factor i(f).
2*f**2*(f + 2)
Let n = 2/139 + 268/695. Suppose 6 = 5*f + 2*a, 5*f + 3*a + 2 = 3*f. Factor -n*g + 3/5*g**f + 0.
g*(3*g - 2)/5
Factor 0*k**2 + 1/3 + 2/3*k - 1/3*k**4 - 2/3*k**3.
-(k - 1)*(k + 1)**3/3
Suppose -19 - 8 = -5*s - 2*z, -3*s = z - 16. Factor s*a - 4*a - 3*a**3 - 2 + 4*a**2 + 0*a.
-(a - 1)**2*(3*a + 2)
Let m = 12 + -5. Suppose 4*l - m = 25. Factor 8 + q - l - q**3.
-q*(q - 1)*(q + 1)
Let s(k) be the second derivative of -8*k**4/3 + 40*k**3/3 - 25*k**2 - 18*k. Factor s(l).
-2*(4*l - 5)**2
Factor -v**2 + 4*v - 4*v.
-v**2
Let w be 4/(-10) + 2/5. Suppose c - 2*n - 9 = -6*n, w = -n + 1. Find y such that -2/5*y**3 + 0 + 0*y**4 + 1/5*y**c + 1/5*y + 0*y**2 = 0.
-1, 0, 1
Let o be 136/(-18) + (-8)/(-36). Let v = -20/3 - o. What is u in -2/3 + 2/3*u**2 + 2/3*u - v*u**3 = 0?
-1, 1
Suppose 12 = 3*g - 9. Let i(v) be the third derivative of -2*v**2 + 1/40*v**6 + 0*v + 0*v**4 - 1/150*v**5 - 1/105*v**8 + 0 + 0*v**3 - 4/175*v**g. Factor i(b).
-b**2*(b + 2)*(4*b - 1)**2/5
Let a(k) = -2*k - 6. Let c be a(-6). Let n(l) be the first derivative of 0*l + 1/24*l**c + 0*l**3 - 1/10*l**5 + 1 + 1/16*l**4 + 0*l**2. Factor n(w).
w**3*(w - 1)**2/4
Let p be (-2)/(-8) - 378/232. Let t = p + 454/203. What is n in -2/7 + 8/7*n**2 - t*n = 0?
-1/4, 1
Factor 1/2*f**3 + 1 - f**2 - 1/2*f.
(f - 2)*(f - 1)*(f + 1)/2
Let a(s) be the second derivative of -s**6/6 + 5*s**4/4 - 5*s**3/3 + 30*s. Factor a(n).
-5*n*(n - 1)**2*(n + 2)
Let t(f) be the third derivative of -1/112*f**8 + 0*f**4 + 1/40*f**6 + 0 - 1/20*f**5 + 0*f**3 + 1/70*f**7 - 4*f**2 + 0*f. Factor t(g).
-3*g**2*(g - 1)**2*(g + 1)
Find j, given that 1/4*j**4 - 1/2*j**2 + 0*j + 1/4 + 0*j**3 = 0.
-1, 1
Let x(b) be the first derivative of b**3/8 - 3*b**2/8 + 11. Determine a so that x(a) = 0.
0, 2
Let s be (6/(-9))/(3/((-108)/8)). Factor 1/5*o - 2/5*o**2 - 1/5*o**s + 2/5*o**4 + 0.
o*(o - 1)*(o + 1)*(2*o - 1)/5
Factor 23*y**3 - 10*y**2 - 16 - 8*y**3 + 16.
5*y**2*(3*y - 2)
Suppose y = 3*y. Let p(b) be the second derivative of 1/60*b**5 + 1/90*b**6 + 0*b**4 + 0 + 0*b**3 - 2*b + y*b**2. Factor p(h).
h**3*(h + 1)/3
Let c(h) = h**2 - 11*h + 2. Let b be c(11). Solve -2*u**3 - b*u**2 - u**3 + 2*u**4 + u**3 + 2*u = 0.
-1, 0, 1
Suppose -14/9*y**5 - 2/3*y**3 + 0*y + 8/3*y**4 + 0 - 4/9*y**2 = 0. Calculate y.
-2/7, 0, 1
Suppose 0*w = 5*w - 20. Let u(q) = q - 4. Let h be u(w). Factor h + 1/2*x**3 - 1/2*x**2 - x.
x*(x - 2)*(x + 1)/2
Let q(z) = -4*z**4 + 4*z**3 - 44*z**2 + 44*z + 24. Let g(y) = y**4 - y**3 + 9*y**2 - 9*y - 5. Let d(b) = -24*g(b) - 5*q(b). Factor d(o).
-4*o*(o - 1)**2*(o + 1)
Let a(z) be the first derivative of -2*z**3/63 + 4*z**2/21 - 8*z/21 - 28. Factor a(q).
-2*(q - 2)**2/21
Let i(l) be the third derivative of -l**5/240 + l**3/24 - 7*l**2. Factor i(d).
-(d - 1)*(d + 1)/4
Factor 0 + 16/15*r**2 - 2/15*r**3 - 32/15*r.
-2*r*(r - 4)**2/15
Let z = 19/1917 + 12839857/21087. Let i = z + -608. Solve -16/11*d + i*d**2 + 8/11 - 2/11*d**3 = 0.
1, 2
Suppose 3*t - 10 - 5 = 0. Let n = t + -3. Factor a**4 + a + n*a**4 + a**5 - 2*a**3 - 3*a**4.
a*(a - 1)**2*(a + 1)**2
Factor 1739*p**3 + 1636*p**3 - 47 - 1350*p**2 + 180*p + 39.
(15*p - 2)**3
Let c be (-5)/(-25) + 38/10. Factor -4*x**2 - c*x + 5*x**4 + 2*x**5 + 2*x - x**4.
2*x*(x - 1)*(x + 1)**3
Let u(x) be the second derivative of -x**8/5040 + x**7/2520 + x**6/2160 - x**4/3 + 2*x. Let c(q) be the third derivative of u(q). Factor c(n).
-n*(n - 1)*(4*n + 1)/3
Factor 11/3*g - 4/3*g**3 - 1 - 8/3*g**2.
-(g + 3)*(2*g - 1)**2/3
Suppose -5*b + 0*b + 10 = 0. Factor 2*h - 2*h**3 - 2*h**b + 2*h**2 + 3 + 2*h**2 - 5.
-2*(h - 1)**2*(h + 1)
Let b = -2/77 + 81/154. Let d be (3/(-1))/((-3)/(-2 + 3)). Let -b*q**2 - 3/2*q - d = 0. What is q?
-2, -1
Let w(o) = o**3 - 14*o**2 + 3*o - 39. Let m be w(14). Let 0*g**2 - 1/3*g - 1/3*g**5 + 0*g**4 + 2/3*g**m + 0 = 0. What is g?
-1, 0, 1
Factor -2 - 1/4*j**3 - 3/2*j**2 - 3*j.
-(j + 2)**3/4
Let j = 39 + -36. Let z(v) be the second derivative of -4*v + 1/20*v**5 + 1/2*v**2 - 1/6*v**j - 1/12*v**4 + 0. Suppose z(k) = 0. What is k?
-1, 1
Factor 1/5*k**2 - 3/5 + 2/5*k.
(k - 1)*(k + 3)/5
Find t, given that -4/7*t**3 + 2/7 + 4/7*t - 2/7*t**2 = 0.
-1, -1/2, 1
Let v(m) = 1. Let d(a) = a - 3. Let o(t) = d(t) + 2*v(t). Let y be o(5). Suppose 3*g**y - g**3 - g**2 + 4*g**4 - 6*g**4 + g = 0. What is g?
-1, 0, 1
Factor 0*r - 4/7*r**4 + 0 + 0*r**3 - 1/7*r**5 + 0*r**2.
-r**4*(r + 4)/7
Let t(l) be the second derivative of -l**4/24 + l**3/6 - l**2/4 + l. Suppose t(m) = 0. What is m?
1
Let f be -1*(3 - 12/3). Let y be (f - 1)*(-6)/12. What is z in y + 0*z - 3*z**3 + 3/4*z**2 = 0?
0, 1/4
Let k(o) = 3*o**3 + 4*o - 1. Let q be k(3). Let p = q + -457/5. Factor -1/5*j**2 + 3/5*j**3 + 1/5 - p*j.
(j - 1)*(j + 1)*(3*j - 1)/5
Let o(s) be the second derivative of -s**5/140 - 5*s**4/84 - 4*s**3/21 - 2*s**2/7 + 6*s. Suppose o(n) = 0. What is n?
-2, -1
Let h(y) be the first derivative of -y**4 - 4*y**3/3 + 29. Let h(v) = 0. Calculate v.
-1, 0
Factor 18/13 + 2/13*l**4 + 8/13*l**3 - 24/13*l - 4/13*l**2.
2*(l - 1)**2*(l + 3)**2/13
Let f = -14 - -18. Let 14/9*y**f + 10/9*y - 2*y**2 - 10/9*y**3 + 4/9 = 0. What is y?
-1, -2/7, 1
Suppose r + r + 6 = 3*j, -4 = r - 2*j. Let b(m) be the second derivative of 0*m**6 + r*m**4 + 1/50*m**5 + m - 1/105*m**7 + 0 + 0*m**2 + 0*m**3. Factor b(u).
-2*u**3*(u - 1)*(u + 1)/5
Suppose -m + 6*m = -5*g + 35, m + 3*g = 13. Suppose -m*s = -5 - 11. Factor 3*y**5 + 8*y**4 - s*y**2 - 4*y**3 + 11*y**3 + 6*y**2.
y**2*(y + 1)**2*(3*y + 2)
Let a(q) be the second derivative of 3*q - 1/33*q**3 - 1/66*q**4 + 0*q**2 + 0. Determine d so that a(d) = 0.
-1, 0
Factor 7*z + 9*z + 33 - 16*z**2 + 2*z**4 - 1 + z**5 - 8*z**3.
(z - 2)**2*(z + 2)**3
Let p(k) = -k**3 + 14*k**2 - 12*k - 8. Let c be p(13). Suppose c*y - 4 = 3*y. Determine u so that -1/2 - 3/2*u**2 - y*u = 0.
-1, -1/3
Suppose -2/7*o**2 - 4/7*o + 0 = 0. What is o?
-2, 0
Let v(y) = -y**5 + 6*y**4 - 12*y**3 - 10*y**2 - 9*y - 9. Let m(l) = l**4 - l**3 - l**2 - l - 1. Let x(h) = -18*m(h) + 2*v(h). Solve x(g) = 0.
-1, 0
Determine z, given that -6*z**4 - 8*z**3 + 9*z**4 - 4*z**5 + 9*z**4 - 8*z**2 - 4 + 12*z = 0.
-1, 1
Let f(a) be the third derivative of 0 + 1/6*a**6 + 0*a + 11/90*a**5 - 2*a**2 - 5/63*a**7 - 1/3*a**4 - 4/9*a**3. Solve f(w) = 0.
-2/5, 1
Let s(g) be the first derivative of g**6/10 - 3*g**5/20 - g**4/4 + g**3/2 - 2*g - 6. Let a(k) be the first derivative of s(k). Factor a(d).
3*d*(d - 1)**2*(d + 1)
Let d be -2 + 2/(-4)*-16. Factor 2 + 5*m**2 - 3*m**2 - d*m + 2 + 0*m.
2*(m - 2)*(m - 1)
Let x(g) be the first derivative of 4*g**3/27 + 4*g**2/3 + 32*g/9 - 12. Factor x(q).
4*(q + 2)*(q + 4)/9
Let q be ((-5)/(-12)*-2)/(15/(-9)). Let g(y) be the second derivative of -1/3*y**4 + 0*y**2 + 0*y**3 - q*y**5 + 2*y + 0. Factor g(w).
-2*w**2*(5*w + 2)
Suppose 3/4*f**3 + 9/2*f**2 - 9/2 - 3/4*f = 0. Calculate f.
-6, -1, 1
Factor 3/2*q**3 + 0*q**2 + 0*q + 0.
3*q**3/2
Let x(c) be the first derivative of c**8/672 - c**7/420 - c**6/240 + c**5/120 - 3*c**2/2 - 1. Let r(d) be the second derivative of x(d). Factor r(u).
u**2*(u - 1)**2*(u + 1)/2
Let m(n) be the third derivative of -n**10/7560