
Let k(n) = -n + 5. Let y be k(2). Suppose 2/9*g**2 + 2/9*g - 2/9*g**y - 2/9 = 0. What is g?
-1, 1
Let l(o) = o**4 + o**3 + o**2 + o. Let i(p) = p**4 + 4*p**3 + p**2 - 2*p. Let g(d) = i(d) + 2*l(d). Factor g(m).
3*m**2*(m + 1)**2
Let f(q) be the first derivative of -2*q**5/25 + q**4/2 - 16*q**3/15 + 4*q**2/5 + 3. Factor f(t).
-2*t*(t - 2)**2*(t - 1)/5
Factor -3*q - 3 + 6*q**2 - 6 + 3 - q**3 + 4*q**3.
3*(q - 1)*(q + 1)*(q + 2)
Let r = 10 + 4. Suppose 4*m + 6 = r. Factor -2/7*b + 2/7*b**m + 2/7*b**3 - 2/7.
2*(b - 1)*(b + 1)**2/7
Let 43*f - 28*f - 3*f**2 - 6*f**3 - 1 - 5 = 0. What is f?
-2, 1/2, 1
Let j(k) be the third derivative of k**6/200 + k**5/20 - k**4/40 - k**3/2 + 14*k**2. Suppose j(g) = 0. Calculate g.
-5, -1, 1
Let b = 8/15 - -4/5. Determine g, given that 14/3*g**3 + 0 + 10/3*g**2 - b*g = 0.
-1, 0, 2/7
Let v = 510 + -508. Factor 4/3*o**v + 4/3 + 8/3*o.
4*(o + 1)**2/3
Let k = 0 + 2. Solve -z - z + 6*z**2 + z**k - 9*z**3 + 2*z**3 + 2*z**4 = 0.
0, 1/2, 1, 2
Let x(l) = l**5 - l**4 - l**3 + l**2 - l + 1. Let w(d) = -4*d**5 + 5*d**4 + d**3 - 7*d**2 + 8*d - 3. Let r(v) = 2*w(v) + 10*x(v). Find s, given that r(s) = 0.
-1, 1, 2
Let a(o) be the third derivative of o**7/70 - o**6/10 + 3*o**5/10 - o**4/2 + o**3/2 - 5*o**2. Find f such that a(f) = 0.
1
Let x be ((-32)/(-9) - 2) + 0. Find c, given that -x*c + 8/9*c**2 - 4/9 = 0.
-1/4, 2
Factor 25*q**2 - 50*q**2 + 21*q**2.
-4*q**2
Let h(k) = k**2 - 5*k + 3. Let w be h(3). Let a = -3 - w. Determine y so that -1/2*y + a + 5/4*y**2 = 0.
0, 2/5
Determine x so that 8/5*x**3 + 0*x + 8/5*x**2 + 2/5*x**4 + 0 = 0.
-2, 0
Let z(a) be the first derivative of 0*a + a**3 + 3 - 3*a**2 - 3/2*a**6 - 3/5*a**5 + 15/4*a**4. Solve z(s) = 0 for s.
-1, 0, 2/3, 1
Let h(j) be the third derivative of 0 + 1/45*j**5 + 0*j**4 + 0*j**3 - 4*j**2 + 0*j + 1/36*j**6. Factor h(r).
2*r**2*(5*r + 2)/3
Let p = -5 + 5. Let o be p/(-2 + 6 + -2). Find d, given that -2 + 3*d**5 + o + 20*d**3 - 20*d**2 - d**5 + 10*d - 10*d**4 = 0.
1
Let a = -7513271/161 + 46666. Let o = 1/161 - a. Find g, given that 0*g + 0 - o*g**2 = 0.
0
Let m(x) be the second derivative of 1/18*x**4 + 1/135*x**6 + 1/18*x**5 + 0 + 0*x**2 - 1/3*x**3 + 5*x. Factor m(t).
2*t*(t - 1)*(t + 3)**2/9
Let h = 128 + -126. Let q(l) be the first derivative of -1/2*l**4 + 0*l - 4/5*l**5 + 1 - 2*l**h + 10/3*l**3. Factor q(d).
-2*d*(d - 1)*(d + 2)*(2*d - 1)
Let s = -68 + 173. Let o be -1 + (s/(-25))/(-3). Factor -1/5*h**5 + 0*h**2 + 0*h**4 - 1/5*h + o*h**3 + 0.
-h*(h - 1)**2*(h + 1)**2/5
Let g(d) be the third derivative of -1/600*d**6 + 0*d**3 + 1/1680*d**8 + 0*d**4 + 0*d + 0*d**5 + 0*d**7 + 0 + 4*d**2. Factor g(b).
b**3*(b - 1)*(b + 1)/5
Let f(a) be the third derivative of -1/12*a**4 + 0*a + 0*a**3 + 0 + 1/20*a**5 + 1/24*a**6 + 2*a**2. Determine r so that f(r) = 0.
-1, 0, 2/5
Let q(l) be the third derivative of -5*l**8/336 + l**7/12 - 3*l**6/16 + 5*l**5/24 - 5*l**4/48 + 13*l**2. Solve q(c) = 0 for c.
0, 1/2, 1
Solve -r**2 + 1/4 + 3/4*r = 0.
-1/4, 1
Suppose 0 = 5*x - 3*x + 4. Let a(m) = m**5 - m**4 + m. Let r(q) = 3*q**5 + 3*q**4 + 9*q**3 + 7*q**2 + 4*q. Let t(s) = x*a(s) + r(s). Factor t(k).
k*(k + 1)**3*(k + 2)
Let a be 4*((-117)/(-63))/13. Factor a*p + 0 - 4/7*p**2.
-4*p*(p - 1)/7
Suppose 3 = -0*q - 2*q - 3*h, h - 13 = -3*q. Solve 0*f**5 + q*f**5 + 22*f**4 + 18*f**3 + 6*f**3 + 8*f**2 = 0 for f.
-2, -1, -2/3, 0
Let q = -566/33 - -52/3. Determine w, given that 0 - 4/11*w + q*w**2 = 0.
0, 2
Let o(f) be the second derivative of 2*f**6/15 - 13*f**5/20 + f**4/4 + 8*f**3/3 - 2*f**2 - 26*f. Factor o(h).
(h - 2)**2*(h + 1)*(4*h - 1)
Let u(h) be the second derivative of -h**5/30 - 13*h**4/54 - 16*h**3/27 - 4*h**2/9 - 16*h. Determine d so that u(d) = 0.
-2, -1/3
Let b = -33 - -35. Let 6/7*m - 2/7*m**3 + 0*m**b - 4/7 = 0. Calculate m.
-2, 1
Suppose 8*j = 3*j + 15. Let a be (j - 29/10)*4. Factor -a - 6/5*o**2 - 2/5*o**3 - 6/5*o.
-2*(o + 1)**3/5
Let f(v) be the first derivative of 1/5*v**2 - 2 - 1/10*v**4 + 2/15*v**3 - 2/5*v. Factor f(r).
-2*(r - 1)**2*(r + 1)/5
Let u = -52 + 52. Factor -3/2*g**2 + 0 + u*g.
-3*g**2/2
Let z(f) be the third derivative of f**5/100 + f**4/40 + 13*f**2. Factor z(j).
3*j*(j + 1)/5
Determine k so that -50*k**2 - 60*k - 28*k**2 - 5*k**4 - 30*k**3 + 13*k**2 + 0*k**4 - 20 = 0.
-2, -1
Suppose 10 = 5*g - 0. Solve -d + g + d**3 + 5*d - d - 4*d + d**4 - 3*d**2 = 0 for d.
-2, -1, 1
Let s be (-6)/42*2 + 48/21. Factor -4/7*j - 2*j**s + 0.
-2*j*(7*j + 2)/7
Let h(f) be the third derivative of 0*f**5 + 0*f**3 - 7*f**2 + 0*f**4 + 0*f + 0 + 0*f**6 - 1/70*f**7. Factor h(i).
-3*i**4
Factor -3*v**4 + 12 + 9*v**2 + 0*v**4 + 0*v**4 - 6*v**3 + 24*v.
-3*(v - 2)*(v + 1)**2*(v + 2)
Let x = 91 - 91. Let u(r) be the third derivative of x*r**3 + 0*r + 3/80*r**5 + 2*r**2 + 1/16*r**4 + 0. Factor u(y).
3*y*(3*y + 2)/4
Let d(r) be the third derivative of -1/1008*r**8 + 6*r**2 + 1/180*r**5 + 0*r**4 + 0*r**3 - 1/630*r**7 + 0 + 1/360*r**6 + 0*r. Factor d(f).
-f**2*(f - 1)*(f + 1)**2/3
Let o(q) = 10*q**2 + 10*q - 2. Let l(t) = -3*t**2 + t + 5. Let s(p) = -2*p**2 + p + 4. Let m(b) = -3*l(b) + 4*s(b). Let d(j) = 6*m(j) - o(j). Factor d(r).
-4*(r - 1)*(r + 2)
Let o(v) = 4*v**3 - 14*v**2 - 14*v + 6. Let u(i) = i**3 - i**2 - i + 1. Let d(k) = -o(k) + 6*u(k). Solve d(x) = 0.
-2, 0
Factor -2*q**2 + 0 + 2/3*q**3 + 4/3*q.
2*q*(q - 2)*(q - 1)/3
Let g(o) be the third derivative of -o**6/2160 + o**5/360 + o**3/2 + o**2. Let b(c) be the first derivative of g(c). Let b(y) = 0. Calculate y.
0, 2
Suppose -5*v - 3*c - 2*c = 0, 4*c + 18 = 5*v. Suppose 0 = -s + 3*s - 6. Find g, given that 2*g**2 - s*g**2 + v - 2 = 0.
0
Let j(x) be the first derivative of -9/7*x**2 - 2/3*x**3 + 2 - 4/7*x. Find r, given that j(r) = 0.
-1, -2/7
Let l(b) be the third derivative of -b**7/945 + b**6/180 - b**5/90 + b**4/108 - 3*b**2. Factor l(s).
-2*s*(s - 1)**3/9
Suppose -3*s = -12*s. Factor -2/9*f**3 + 2/9*f + s*f**2 + 0.
-2*f*(f - 1)*(f + 1)/9
Factor 27*m - 7*m + 4*m**2 + 20 - 2*m**2 + 3*m**2.
5*(m + 2)**2
Let n(l) be the third derivative of -l**9/272160 - l**8/90720 - l**5/60 + l**2. Let r(d) be the third derivative of n(d). Solve r(i) = 0.
-1, 0
Let p be 4/(-1) - (-248)/32. Let 0 + 3/2*g + 21/4*g**4 - 21/4*g**2 + 9/4*g**3 - p*g**5 = 0. What is g?
-1, 0, 2/5, 1
Let u(m) be the first derivative of -m**5/25 - m**4/10 - m**3/15 + 6. Let u(h) = 0. What is h?
-1, 0
Find k such that 6*k**4 - 5*k - 20*k**2 - 5*k**5 + 24*k**3 - 44*k**3 - 10*k**3 - 26*k**4 = 0.
-1, 0
Suppose f - 4*g = 28, 3*f + g = 3*g + 44. Suppose -3*c + 2*c = -f. Factor -4*m - m**4 + 3*m + 9*m**2 - m**3 - 2*m**3 - c*m**2.
-m*(m + 1)**3
Let g = 3286/615 - 2/205. Solve g*k - 3*k**5 - 7/3*k**3 + 4/3 - 7*k**4 + 17/3*k**2 = 0 for k.
-1, -2/3, 1
Let f(y) = y**3 + 9*y**2 + 8. Let z be f(-9). Suppose -2*w + x + z = 0, -2*w + x = 3*w - 17. Factor -4*h**2 + 4*h**2 + 6*h**w - 6*h**2 + 4*h**3 - 4*h.
2*h*(h - 1)*(5*h + 2)
Factor 8/7*p**3 + 0 + 0*p - 2/7*p**2.
2*p**2*(4*p - 1)/7
Let y = 67/14 + -30/7. Let u(h) be the first derivative of 2 + 0*h**3 + 0*h**2 - 4/5*h**5 + y*h**4 + 1/3*h**6 + 0*h. Factor u(k).
2*k**3*(k - 1)**2
Let t(u) be the second derivative of -1/2*u**3 + 3*u**2 + 5*u + 0 - 1/14*u**7 - u**4 + 1/5*u**6 + 3/10*u**5. Let t(s) = 0. Calculate s.
-1, 1, 2
Let p(c) = -2*c**2 - 4*c. Let r(n) = -4*n**2 - 9*n. Suppose 9 = i + 3. Let w(a) = i*r(a) - 13*p(a). Factor w(t).
2*t*(t - 1)
Let s(h) be the third derivative of h**8/840 + h**7/525 - h**6/150 - 9*h**2. Suppose s(w) = 0. What is w?
-2, 0, 1
Let a(f) be the second derivative of -1/4*f**4 - 2/3*f**3 + 0 - 1/30*f**6 + 2*f**2 + 1/5*f**5 + f. Let a(v) = 0. What is v?
-1, 1, 2
Solve 14*c + 10*c**3 - 10*c + 2*c - 15*c**4 + 35*c**2 + 4*c = 0.
-1, -1/3, 0, 2
Factor -6/5 + 4/5*z + 2/5*z**2.
2*(z - 1)*(z + 3)/5
Suppose 2*q - 11 + 7 = 0. Factor 0 + 4*k**q + 12*k + 5*k**2 - 12.
3*(k + 2)*(3*k - 2)
Let b(u) be the second derivative of -u**5/10 - 2*u**4/3 - 5*u**3/3 - 2*u**2 - 7*u. Factor b(o).
-2*(o + 1)**2*(o + 2)
Let l(f) = -f**3 + 4*f**2 - f - 4. Let j be l(3). Factor -1/2*o**2 - j - 2*o.
-(o + 2)**2/2
Let l = 8 + -2. Let n(o) = 2*o + 27. Let t be n(-12). Let 8*j**2 - t*j + l - 6*j - 5*j**2 = 0. What is j?
1, 2
Let x(a) = a**2 - 4. Let h be x(-3). Suppose -3*d**3 + 0*d**4 + 4*d**3 + d**h + d**5 + 3*d**4 = 0. What is d?
-1, -1/2, 0
Solve 7*s - 