5
Let r(g) = g**2 + 6. Let c be r(0). Let u(w) = 2*w**2 + 2 + 5*w + 0 + c. Let o(d) = -2*d**2 - 6*d - 8. Let m(k) = 3*o(k) + 2*u(k). Factor m(q).
-2*(q + 2)**2
Suppose -4*u + 4*o = -24, 0 = 3*u + o - 2 - 0. Factor 4*t + 4*t**2 + u - 2.
4*t*(t + 1)
Let a be 5/(-20) - 21/(-12). Suppose 2*t - 4*t - 2*r = 4, -4*r = 5*t + 8. Factor -q + t + 2*q**3 + a*q**4 - 1/2*q**2.
q*(q + 1)**2*(3*q - 2)/2
Let k(v) = -v + 18. Let u be k(8). Factor -u - 2*t**2 + 4 + 38*t - 30*t.
-2*(t - 3)*(t - 1)
Let r(u) be the second derivative of 2*u**6/15 - 4*u**4/3 - 11*u. Factor r(l).
4*l**2*(l - 2)*(l + 2)
Let -11*n + 19*n + 8*n**3 - 6*n**2 + 14*n + 32*n**2 + 4 = 0. What is n?
-2, -1, -1/4
What is a in -1081/2*a**2 + 296*a**4 - 145*a - 25/2 - 32*a**5 - 566*a**3 = 0?
-1/4, 5
Let u(y) = 2*y**2 + 22. Let g(a) = -a**2 - 21. Let k(l) = 6*g(l) + 5*u(l). Factor k(o).
4*(o - 2)*(o + 2)
Let o(b) be the second derivative of 0*b**5 + 0*b**4 - b + 1/420*b**7 + b**2 + 0*b**3 - 1/240*b**6 + 0. Let x(d) be the first derivative of o(d). Factor x(s).
s**3*(s - 1)/2
Suppose 0 = 3*f - 45 - 36. Let c be 18/f + 0/(-1). Suppose c*r**4 + 2/3*r**3 + 0 + 0*r - 2/3*r**2 - 2/3*r**5 = 0. What is r?
-1, 0, 1
Let m be 2 + 2 + 1*-2. Find t, given that -t + 5*t**3 - t**2 - t**3 + 3*t**m - 5*t**3 = 0.
0, 1
Let g(k) be the second derivative of -k**7/294 - k**6/210 + k**5/70 + k**4/42 - k**3/42 - k**2/14 - 5*k. Factor g(a).
-(a - 1)**2*(a + 1)**3/7
Let h(l) be the second derivative of 4/3*l**3 + 0*l**2 - l**4 + 2/15*l**6 + 8*l + 0*l**5 + 0. Solve h(g) = 0.
-2, 0, 1
Let w(a) = -12*a + 146. Let o be w(12). Factor 0 - 6*r**3 - 8/3*r - 7/3*r**4 - 1/3*r**5 - 20/3*r**o.
-r*(r + 1)*(r + 2)**3/3
Let q(u) = 16*u**4 + 72*u**3 + 28*u**2 - 4. Let h(n) = -15*n**4 - 73*n**3 - 29*n**2 + 5. Let b(o) = 4*h(o) + 5*q(o). Factor b(z).
4*z**2*(z + 3)*(5*z + 2)
Let 103*f**2 + 4*f**3 - 109*f**2 + 0*f + 2*f = 0. Calculate f.
0, 1/2, 1
Let x = -19 - -24. Factor -2/5*t**4 + 0 + 0*t**2 + 0*t**3 + 0*t + 2/5*t**x.
2*t**4*(t - 1)/5
Let g be 9/(-117) + (-665)/(-195). Factor 10/3*q**3 + 1/3 + 5/3*q**4 + 1/3*q**5 + 5/3*q + g*q**2.
(q + 1)**5/3
Let v(o) be the third derivative of o**8/1176 + 11*o**7/735 + 43*o**6/420 + 73*o**5/210 + 2*o**4/3 + 16*o**3/21 - 2*o**2 - 6*o. Suppose v(l) = 0. Calculate l.
-4, -1
Let q(v) = -13*v**3 + 48*v**2 - 93*v + 43. Let k(l) = -84*l**3 + 312*l**2 - 604*l + 280. Let f(y) = 5*k(y) - 32*q(y). Find u, given that f(u) = 0.
1, 2, 3
Solve -3/4*z**2 - 21/4 - 6*z = 0.
-7, -1
Factor -12/5*h**3 + 0*h + 3/5*h**4 + 12/5*h**2 + 0.
3*h**2*(h - 2)**2/5
Let u(o) = o**2 + 3*o - 70. Let s be u(-10). Factor 14/3*t**3 + s*t + 2*t**5 - 4/3*t**2 + 0 - 16/3*t**4.
2*t**2*(t - 1)**2*(3*t - 2)/3
Let i(a) be the second derivative of -1/84*a**4 + 0*a**5 + a + 0*a**3 + 0 + 1/420*a**6 - 3/2*a**2. Let r(g) be the first derivative of i(g). Solve r(k) = 0.
-1, 0, 1
Suppose f + f + 2 = -3*h, -18 = -4*f + 5*h. Let g(w) be the first derivative of 1 + w - 3/4*w**f + 1/6*w**3. Find d, given that g(d) = 0.
1, 2
Let q be 12/30 + 18/5. Let v = -91/2 + 47. Factor -2*g + 0*g**2 + 0 + v*g**3 + 1/2*g**q.
g*(g - 1)*(g + 2)**2/2
Let d(j) be the second derivative of 9*j**5/140 - 4*j**4/21 + 5*j**3/42 + j**2/7 - 5*j. Factor d(h).
(h - 1)**2*(9*h + 2)/7
Suppose -32 = 5*h - 3*u, -3*h + u - 12 = -h. Let n(z) = -z**3 - 5*z**2 - 5*z + 3. Let q be n(h). Let 2*y - 3*y - 2*y**4 + q*y**5 + y = 0. What is y?
0, 2/7
Suppose 6*s = 2*s + 8. Let c(w) be the first derivative of 4*w**4 - 2 + 2/3*w**6 - s*w**2 + 4/3*w**3 + 14/5*w**5 - 2*w. Solve c(u) = 0 for u.
-1, 1/2
Let o(l) be the second derivative of -21*l**5/20 + 3*l**4 + 2*l**3 + 45*l. Factor o(n).
-3*n*(n - 2)*(7*n + 2)
Factor -8*d + 4*d + d - 2 - 4 + 3*d**2.
3*(d - 2)*(d + 1)
Let s(u) = u**3 + 3*u**2 - 7*u - 10. Let f(v) = v**2 + 6*v + 5. Let q be f(-3). Let k be s(q). Suppose 7/4*r**2 - 5/4*r**3 - 1 + k*r = 0. Calculate r.
-1, 2/5, 2
Suppose 16*q**3 + 4 + q - q - 58*q**3 + 2*q - 44*q**2 = 0. What is q?
-1, -1/3, 2/7
Let a = 68 + -66. Let j = 3/26 + 7/52. Factor j*r**3 + 1/4*r + 0 - 1/2*r**a.
r*(r - 1)**2/4
Let z(a) be the first derivative of 2 + 0*a**2 + 0*a**3 + 2*a + 1/24*a**4. Let s(k) be the first derivative of z(k). Factor s(w).
w**2/2
Let x be 9/(-4) - -3 - 6/8. Let m(o) be the first derivative of x*o - 1 - o**2 + 0*o**3 + 1/2*o**4. Solve m(w) = 0.
-1, 0, 1
Let q be (-4)/(-6)*((-10)/13 + 1). Determine l, given that 2/13*l - 4/13*l**2 - 4/13*l**3 + 2/13*l**4 + q*l**5 + 2/13 = 0.
-1, 1
Solve 2/11*h**5 - 64/11 + 16/11*h**4 - 52/11*h**2 + 26/11*h**3 - 128/11*h = 0 for h.
-4, -1, 2
Let p(m) = -5*m**3 + 6*m**2 - m. Let i(v) be the first derivative of 1/2*v**2 + 0*v**3 - 1/4*v**4 - 1 + 0*v. Let w(o) = 2*i(o) - p(o). Factor w(h).
3*h*(h - 1)**2
Let h = 1827/20 - 453/5. Factor -3/2*r**3 + 9/4*r**2 + 0*r - h.
-3*(r - 1)**2*(2*r + 1)/4
Let p = 7 + -5. Factor -c**p + 7*c - 4*c**4 - 4*c**3 + 5*c**2 - 3*c.
-4*c*(c - 1)*(c + 1)**2
Let f(k) be the third derivative of -2*k**7/35 - k**6/40 + 3*k**5/5 - 5*k**4/8 - k**3 + 10*k**2. Let f(c) = 0. What is c?
-2, -1/4, 1
Suppose 0*f + 3 = f. Let t be (-28)/(-6) + -1 - f. Factor 0 + 4/3*g**2 + 2/3*g + t*g**3.
2*g*(g + 1)**2/3
Let r(b) be the third derivative of 6*b**2 + 1/60*b**5 + 0*b - 1/120*b**6 - 1/210*b**7 + 0 + 0*b**3 + 1/24*b**4. Factor r(p).
-p*(p - 1)*(p + 1)**2
Let p = 1 + -3. Let c = p - -1. Let x(j) = j**3 + j**2 + j + 1. Let v(w) = 5*w**3 + 7*w**2 + 7*w + 5. Let q(n) = c*v(n) + 4*x(n). Find r such that q(r) = 0.
-1
Let 23*j - 12 - 57*j - 8*j**2 - 6*j**2 + 4*j**2 = 0. Calculate j.
-3, -2/5
Suppose -4*c = 5*j - 23, -5*c + 0*c = j - 13. Suppose 3*r + 0*r = 5*z + c, -r + 4*z = 4. Factor 0*t**2 + t**r + 1 + 0 - 2*t**2.
(t - 1)**2*(t + 1)**2
Let m(u) = -u**2 - 3*u + 2. Let k be m(0). Suppose -f + 2/3 + 1/3*f**k = 0. Calculate f.
1, 2
Suppose 2*w = 4*x + 20, -w + 1 = x + 3. Suppose -1/2*p - 1/4*p**w + 0 = 0. Calculate p.
-2, 0
Suppose -6/7*j - 3/7*j**2 + 0 = 0. Calculate j.
-2, 0
Let c(f) be the first derivative of f**3/6 + 3*f**2/4 + f - 10. Factor c(b).
(b + 1)*(b + 2)/2
Let y be 3 + -2 - 1 - 0. Suppose l - 4 + 2 = 0. Factor y*h + 0 - 1/4*h**l.
-h**2/4
Factor 3*u - 8 + 8 - 2*u**3 + 5*u**2.
-u*(u - 3)*(2*u + 1)
Let b(i) = i + 12. Let w be b(-10). Factor -3*c**3 - 3*c**2 - 4*c**4 + 2*c**w - 2*c**3.
-c**2*(c + 1)*(4*c + 1)
Let a(b) be the second derivative of b**5/40 + 11*b**4/96 - b**3/12 + b**2 - 5*b. Let n(m) be the first derivative of a(m). Solve n(v) = 0.
-2, 1/6
Let u be 28/(-6) - (10 + 195/(-13)). Factor b**2 - 2/3*b - u.
(b - 1)*(3*b + 1)/3
Suppose 4*r = -4*w + 66 + 46, 0 = 3*w - 4*r - 70. Let x = w + -70/3. What is s in -2/3*s**2 + 0 + 10/3*s**3 + 0*s - x*s**4 = 0?
0, 1/4, 1
Suppose 2*c = -5*z + 2, -2*c = -4*z + c - 3. Let m(f) be the second derivative of 2*f - 1/3*f**3 - 1/30*f**6 + z + 0*f**4 + 1/10*f**5 + 1/2*f**2. Factor m(y).
-(y - 1)**3*(y + 1)
Let c(n) be the first derivative of -2*n**6/15 - 6*n**5/25 + n**4/10 + 2*n**3/5 + n**2/5 + 14. Suppose c(x) = 0. What is x?
-1, -1/2, 0, 1
Let i(s) = -5*s**3 + 18*s**2 - 72*s - 3. Let x(p) = 14*p**3 - 56*p**2 + 216*p + 8. Let q(h) = -8*i(h) - 3*x(h). Factor q(n).
-2*n*(n - 6)**2
Let p be (-1 + 0)*(6 + -1). Let n(c) = c + 5. Let j be n(p). Determine v, given that -1 + 0*v + v**2 + j*v = 0.
-1, 1
Let c(o) be the first derivative of -4 + 0*o + 1/12*o**3 - 1/20*o**5 + 3/8*o**2 - 3/16*o**4. Suppose c(n) = 0. What is n?
-3, -1, 0, 1
Let s = 5111/10 + -510. Let j = 18/5 - s. Factor 3/2*y**2 + y - j*y**3 + 0.
-y*(y - 1)*(5*y + 2)/2
Let d(j) = 13*j**4 + j**3 - 5*j**2 - 9*j - 9. Let n(h) = -3*h**4 + h**2 + 2*h + 2. Suppose 0 = -4*k + 7 - 79. Let t(b) = k*n(b) - 4*d(b). Factor t(l).
2*l**2*(l - 1)**2
Let q = -1 - -1. Factor 6*h + 6*h**2 - h**3 + 3*h**3 + q + 2.
2*(h + 1)**3
Let k be (-3)/18*15/(-10). Let x(s) be the third derivative of -2*s**2 + k*s**4 + 0 + 0*s**5 - 1/60*s**6 + 0*s - 2/3*s**3. Factor x(a).
-2*(a - 1)**2*(a + 2)
Let i(t) be the third derivative of -1/28*t**4 + 0 - 1/420*t**6 + 1/70*t**5 + 1/21*t**3 + 0*t + 2*t**2. Factor i(r).
-2*(r - 1)**3/7
Suppose 4*j - 24 = -4*y, -3*y - y + 15 = -5*j. Determine m so that -m**2 - 3 + y + 2 + 0 = 0.
-2, 2
Let d(u) be the second derivative of u**5/15 + 2*u**4/3 + 8*u**3/3 + 16*u**2/3 + 7*u. Solve d(s) = 0 for s.
-2
Factor 6/5*w + 1/5*w**2 + 8/5.
(w + 2)*(w + 4)/5
Let c be (-3