2
Let r(o) be the second derivative of -1/14*o**4 + 1/105*o**6 + 3*o + 0 - 5/21*o**3 + 1/70*o**5 - 2/7*o**2. Solve r(z) = 0.
-1, 2
Suppose c - 8 = -3*c. Factor 2*l - 8*l**c + 17*l**2 - 11*l**2.
-2*l*(l - 1)
Solve -12*p**5 + 4*p**5 - 50*p**2 + 40*p**4 + 7*p**5 + 16*p**5 - 15*p + 10 = 0.
-2, -1, 1/3, 1
Let x(f) be the second derivative of 4*f**7/105 - 2*f**6/15 + 4*f**5/25 - f**4/15 - 11*f. Factor x(c).
4*c**2*(c - 1)**2*(2*c - 1)/5
Factor 1/3*k**3 - 3*k**2 + 8*k - 16/3.
(k - 4)**2*(k - 1)/3
Suppose -3*z + v + 12 = 0, -3*v + 6 = z + 4*z. Determine p, given that 0*p**2 + 1/5*p**4 - 2/5*p - 1/5 + 2/5*p**z = 0.
-1, 1
Let b(x) be the second derivative of x**6/120 - 3*x**5/80 + x**4/48 + x**3/8 - x**2/4 - 23*x. Determine z, given that b(z) = 0.
-1, 1, 2
Let j be (-27)/(-9)*3/9. Let k(q) be the first derivative of j + 1/4*q**4 + 0*q**2 + 1/3*q**3 + 0*q. Factor k(d).
d**2*(d + 1)
Let k(d) be the third derivative of -d**8/2240 + d**7/1680 + d**6/480 - d**5/240 + d**3/3 + d**2. Let u(i) be the first derivative of k(i). Factor u(q).
-q*(q - 1)*(q + 1)*(3*q - 2)/4
Let j(c) be the first derivative of -c**7/840 - c**6/120 - c**5/40 - c**4/24 - 5*c**3/3 + 4. Let i(l) be the third derivative of j(l). Factor i(v).
-(v + 1)**3
Let v = 1 - 1. Suppose 4*d + 6 - 18 = v. Suppose 4*j**2 - 8 - d*j - 6*j**2 - 5*j = 0. Calculate j.
-2
Determine z, given that -3/7*z**2 - 18/7*z - 15/7 = 0.
-5, -1
Let r(s) be the first derivative of s**6/2 + 3*s**5 + 15*s**4/2 + 10*s**3 + 15*s**2/2 + 3*s + 1. Factor r(z).
3*(z + 1)**5
Suppose 4*u - 3 + 7 = 2*o, 0 = 3*o + 3*u - 6. What is d in d**3 - 5*d**2 - d + 8 - 6 + 3*d**o = 0?
-1, 1, 2
Factor -3/5*k**2 + 4/5 - 1/5*k**3 + 0*k.
-(k - 1)*(k + 2)**2/5
Let x(t) be the first derivative of t**6/2 + 24*t**5/5 + 39*t**4/4 + 6*t**3 + 18. Factor x(r).
3*r**2*(r + 1)**2*(r + 6)
Suppose -h = -5*w - 4*h, -3*w = -5*h. Suppose 14 = o - 3*z, -z = 5*o - w - 6. Factor -3*d**3 + 5*d**2 + 7*d**3 + d**4 - 4*d**o - 2*d**3.
d**2*(d + 1)**2
Let b(g) be the first derivative of 4*g**3/15 - 2*g**2/5 - 8*g/5 + 5. Factor b(f).
4*(f - 2)*(f + 1)/5
Let z(d) be the second derivative of -d**4/4 + d**3/6 + 2*d. Factor z(k).
-k*(3*k - 1)
Suppose 4 = 5*m - 8*m + 4*v, 4*v = 2*m + 8. Let k = -5 - -10. Factor 2*n**m + 0 + 2*n**2 + 1/2*n**k + 3*n**3 + 1/2*n.
n*(n + 1)**4/2
Let w(c) be the first derivative of c**5/5 - c**3 - c**2 + 38. Factor w(q).
q*(q - 2)*(q + 1)**2
Determine a, given that 4/5*a**3 + 4/5*a**4 + 0*a**2 + 0 + 0*a = 0.
-1, 0
Let r = 11 - 9. Let g = 4 - r. Factor -18/7*d**g - 32/7*d**4 - 2/7*d - 48/7*d**3 + 0.
-2*d*(d + 1)*(4*d + 1)**2/7
Let z = 1184 + -1181. Find x, given that -4/11*x**z - 6/11*x**2 + 6/11*x + 4/11 = 0.
-2, -1/2, 1
Let g be 28580/18*(-6)/(-15). Let o = g + -634. Determine k, given that 0 + 4/9*k - o*k**2 = 0.
0, 2/5
Let s(v) = -v**2 + 6*v. Let k be s(7). Let b be k/(-21) + 0/1. Factor -b*p + 0 - 1/3*p**2.
-p*(p + 1)/3
Let a(f) = -4*f - 82. Let o be a(-21). Let j = 344 - 3780/11. Factor -8/11*p**3 + 0 - j*p - 10/11*p**o - 2/11*p**4.
-2*p*(p + 1)**2*(p + 2)/11
Let m(p) be the second derivative of -p**4/48 + p**3/12 - p**2/8 + 13*p. Factor m(q).
-(q - 1)**2/4
Let p(k) be the second derivative of k**8/2352 + k**7/490 + k**6/280 + k**5/420 - 7*k**2/2 - 2*k. Let n(b) be the first derivative of p(b). Solve n(c) = 0.
-1, 0
Let o(p) be the second derivative of 1/4*p**3 + 4*p - 1/24*p**4 - 1/2*p**2 + 0. Factor o(b).
-(b - 2)*(b - 1)/2
Suppose 8 = 3*b - b. Factor b*c + 3*c**3 + c**4 + 3*c**2 - 3*c + 0*c.
c*(c + 1)**3
Let k = -286 - -1683/5. Let x = -50 + k. Factor -3/5*s**2 + 0 - x*s.
-3*s*(s + 1)/5
Suppose 4*h - 5*b = -27, -1 = 2*h + b + 2. Let s be h + 75/(-63)*-3. Factor 0*w + 2/7*w**2 + 2/7*w**4 - s*w**3 + 0.
2*w**2*(w - 1)**2/7
Let f(m) = m**3 + 4*m**2 - 5*m + 2. Let s be f(-5). Find b such that 3/4*b**4 - 3/4*b**3 + 0 - 3/4*b**s + 3/4*b = 0.
-1, 0, 1
Let d(p) be the third derivative of -p**9/60480 - p**8/13440 - p**4/24 - 7*p**2. Let q(g) be the second derivative of d(g). Factor q(x).
-x**3*(x + 2)/4
Let g(l) be the first derivative of l**6/3 + 2*l**5/5 - 4*l**4 - 16*l**3/3 + 16*l**2 + 32*l - 9. Find x such that g(x) = 0.
-2, -1, 2
Let s be 0 - 1*6/(-15). Suppose -8*i + 3*i + 4*z + 9 = 0, 0 = i + 5*z - 25. Determine p so that 2/5*p - 4/5*p**2 + s + 2/5*p**i + 2/5*p**4 - 4/5*p**3 = 0.
-1, 1
Suppose -9*r + 20 = -13*r, -5*s + 20 = -r. Factor -2*y**3 + 1/2 - 2*y + s*y**2 + 1/2*y**4.
(y - 1)**4/2
Let a(f) be the first derivative of f**3/7 - 3*f**2 + 21*f - 15. Find n, given that a(n) = 0.
7
Let u be 4 + 1 + -4 + 2. Let p be u - ((-36)/(-14) - 1). Solve -6/7*c**2 - 4/7 - p*c = 0 for c.
-1, -2/3
Suppose 8 + 12 = 5*t. Let x be (-2)/((40/(-2))/t). Factor -s**2 + x*s + 0.
-s*(5*s - 2)/5
Let b(u) be the first derivative of -1/5*u**5 + 0*u - 1/3*u**3 + 0*u**2 - 1 - 1/2*u**4. Let b(v) = 0. Calculate v.
-1, 0
Let f(h) be the second derivative of 0 + 1/60*h**6 + h + 0*h**5 - 1/168*h**7 + 1/24*h**3 + 0*h**2 - 1/24*h**4. Factor f(m).
-m*(m - 1)**3*(m + 1)/4
Let r(u) be the second derivative of u**7/3780 - u**6/270 + u**5/45 + u**4/6 - 7*u. Let c(g) be the third derivative of r(g). Factor c(q).
2*(q - 2)**2/3
Let u be 31/(-8) + (-4)/(-8). Let z = -173/56 - u. Factor -z*q**3 + 0 + 2/7*q + 0*q**2.
-2*q*(q - 1)*(q + 1)/7
Factor 3/4*z**2 - 3/2*z + 0.
3*z*(z - 2)/4
Suppose -3*j = -v - 8, -2*j + 1 = -2*v - 3. Let u be ((-22)/10 - -2)/(-1). Suppose -o**2 - 4/5 + 8/5*o + u*o**j = 0. Calculate o.
1, 2
Suppose 0 = -17*i + 12*i + 30. Let o(n) be the third derivative of 0 + 0*n + 0*n**3 - 1/100*n**5 - 1/1050*n**7 - 1/120*n**4 - 1/200*n**i + n**2. Factor o(r).
-r*(r + 1)**3/5
Suppose 0*b = -b + 4. Factor 0*u**4 + 3*u**4 - u**2 + 3 - u**2 - b*u**2.
3*(u - 1)**2*(u + 1)**2
Let x(f) be the third derivative of 0 + 1/135*f**5 - 1/108*f**4 + 0*f**3 + 3*f**2 + 0*f. Find j such that x(j) = 0.
0, 1/2
Find a, given that 0 + 11/3*a - 1/3*a**2 = 0.
0, 11
Let f = 229 - 227. Factor 0 - 1/3*r**3 + 2/3*r**4 - 2/3*r**f + 1/3*r.
r*(r - 1)*(r + 1)*(2*r - 1)/3
Let q(h) be the second derivative of -h**9/1512 + h**8/840 + h**7/420 - h**6/180 + 2*h**3/3 + 4*h. Let n(v) be the second derivative of q(v). Factor n(j).
-2*j**2*(j - 1)**2*(j + 1)
Factor -3/4*u**2 - 15/2*u - 75/4.
-3*(u + 5)**2/4
Determine x, given that -23*x**2 + 4 - 15*x + 32*x**2 - 1 + 3 = 0.
2/3, 1
Let f(j) be the third derivative of -1/120*j**6 + 1/336*j**8 + 0 - 1/210*j**7 + 0*j**4 + 0*j**3 + 0*j + 2*j**2 + 1/60*j**5. Factor f(l).
l**2*(l - 1)**2*(l + 1)
Let b(c) = -c + 1. Let j be b(1). Factor 3*a**3 + j - 3*a**4 + 0 + 6 - 15*a + 9*a**2.
-3*(a - 1)**3*(a + 2)
Suppose k + 25 = 4*h, 2*k - 3*h = 14 - 89. Let a = 136/3 + k. What is l in 0 + a*l**4 - l**3 - 1/3*l + l**2 = 0?
0, 1
Let z(g) = -3*g + 9. Let a(i) = -10*i + 28. Let f(k) = 2*a(k) - 7*z(k). Let n be f(7). What is o in 3/2*o**3 - o**2 + n - 1/2*o = 0?
-1/3, 0, 1
Factor 0 + 0*q**4 + q**2 - 1 + q**2 - q**4.
-(q - 1)**2*(q + 1)**2
Let n(s) = 4*s**2 - 4*s. Let d(j) = -j**2. Let x(q) = 20*d(q) + 4*n(q). Factor x(h).
-4*h*(h + 4)
Let j be (-147)/(-2)*(-10)/15. Let b = 247/5 + j. Factor -8/5*l - 8/5 - b*l**2.
-2*(l + 2)**2/5
Suppose 0 = -3*n + l, 4*l - 2*l = -2*n. Suppose -2*b + n*b = -4. Suppose 1/2*p + 0 - 1/2*p**b = 0. Calculate p.
0, 1
Let u(g) = 25*g**2 - 38*g + 10. Let k(f) = -49*f**2 + 77*f - 19. Suppose -y - 1 - 4 = 0. Let v(c) = y*u(c) - 2*k(c). What is n in v(n) = 0?
2/3
Let s be (6 + -3)/(3 - 1). Factor 1/2*c**3 + s*c + 1/2 + 3/2*c**2.
(c + 1)**3/2
Let c(f) be the first derivative of 1/20*f**5 + 1/16*f**4 + 0*f - 1/24*f**6 - 1 + 0*f**2 - 1/12*f**3. Find n, given that c(n) = 0.
-1, 0, 1
Let a(v) = v - 3. Let s be a(6). Find y, given that -y**3 + 7*y**2 - 6*y**2 + 2*y**s = 0.
-1, 0
Let 32*q**3 - 12 - 2*q**2 - 32*q + 2*q**5 - 14*q**4 - 15*q**2 + q**2 + 44 = 0. What is q?
-1, 2
Suppose 18 = 3*w + 12. Find s such that s + 1/6*s**w + 3/2 = 0.
-3
Let x be 5*-2*(-1)/(-2). Let d = -5 - x. Solve 0 + d*j**2 + 0*j - 1/3*j**3 = 0 for j.
0
Let w = 2 + -6. Let o be w/10 - 110/(-25). Solve 5*u**5 - u**5 + 2*u**3 + 4*u**o - 2*u**5 = 0 for u.
-1, 0
Let n(w) = w**2 + 14*w + 13. Let p be n(-13). Let h(m) be the second derivative of 1/36*m**4 + 3*m - 1/6*m**2 + 0*m**3 + p. Factor h(d).
(d - 1)*(d + 1)/3
Let a(f) be the second derivative of -f**7/56 + f**6/40 - 10*f. Determine n so that a(n