- 57 + 6*j.
-2*(j + 1)*(4*j + 1)*(5*j - 2)
Suppose -k + 16 = 2*x, -5*k = -x - 4*x - 80. Let l = k - 16. Determine m so that l - 3/2*m**3 + 0*m**2 + 3/4*m + 0*m**4 + 3/4*m**5 = 0.
-1, 0, 1
Let x = -386/3 + 277/2. Let g = x + -19/2. Factor 5/3*t - 10/3*t**2 + 1/3*t**5 + 10/3*t**3 - g - 5/3*t**4.
(t - 1)**5/3
Let t(z) be the first derivative of 1/4*z**4 + 6*z**2 - 2 - 2*z**3 - 8*z. Factor t(n).
(n - 2)**3
Let s(w) be the first derivative of w**5/210 - w**3/21 + 3*w**2/2 + 3. Let g(i) be the second derivative of s(i). Suppose g(x) = 0. What is x?
-1, 1
Let j(w) = 7*w - 31. Let m be j(5). Let t(f) be the second derivative of 0*f**3 - 1/50*f**5 + m*f - 4/5*f**2 + 0 + 1/10*f**4. What is v in t(v) = 0?
-1, 2
Let w(f) be the second derivative of -f**6/75 - f**5/50 + 7*f**4/30 + f**3/15 - 6*f**2/5 - 33*f. Solve w(j) = 0 for j.
-3, -1, 1, 2
Let s be (-5)/2*(-36)/15. Let g(b) be the second derivative of 1/90*b**s + 0*b**3 + 0 + 0*b**5 - 1/18*b**4 + 2*b + 1/6*b**2. Factor g(v).
(v - 1)**2*(v + 1)**2/3
Suppose -2*r - 14 = -4*r. Suppose 3*x**3 - 2*x**5 - r*x**4 + x**4 + 6*x**2 - x**5 = 0. What is x?
-2, -1, 0, 1
Suppose -34 - 11 = -5*k. Suppose -m = 5, -t + 3*m + k = -4*t. What is o in 2*o - 7*o**2 - 2*o**3 + t*o**4 + 6*o**2 - o**2 = 0?
-1, 0, 1
Let t = -946 - -948. Factor 2*o + 2 + 1/2*o**t.
(o + 2)**2/2
Let b(l) be the first derivative of 2*l**3/39 - 40. Determine c, given that b(c) = 0.
0
Let a(v) = v - 6. Let w be a(4). Let t(r) = 1. Let n(p) = 1 - 16 + 7*p**2 - 12*p + 0. Let c(j) = w*n(j) - 22*t(j). Solve c(s) = 0 for s.
-2/7, 2
Let l(m) be the first derivative of 117*m**4/10 - 86*m**3/5 + 16*m**2/5 + 24*m/5 - 18. Factor l(h).
2*(3*h - 2)**2*(13*h + 3)/5
Let v(d) be the second derivative of -2/3*d**3 + 0*d**2 - 5*d - 1/6*d**4 + 0. Let v(c) = 0. What is c?
-2, 0
Suppose -4*d + 16 + 4 = 0. Solve -4*m**3 - d*m**2 - 4 - 8*m + 3*m**3 + 0 = 0 for m.
-2, -1
Determine f, given that 0*f + 0 + 1/6*f**4 + 1/3*f**2 - 1/2*f**3 = 0.
0, 1, 2
Let v(f) = -f - 5. Let h be v(-6). Let r(d) = 4*d**2 + 3*d + 3. Let c be r(-1). Factor 6*u**2 + 1 - h - c*u.
2*u*(3*u - 2)
Let z = -17 + 17. Let f be -4*((-3)/20 - z). Solve 0*h**2 + 0 + f*h**3 + 0*h = 0 for h.
0
Let n be 1/7*(-22917)/3. Let r = n - -1093. Solve 0*j + 6/7*j**4 - 2/7 + 16/7*j**3 + r*j**2 = 0 for j.
-1, 1/3
Let q(o) be the second derivative of -o**5/40 + o**3/3 + 7*o. What is g in q(g) = 0?
-2, 0, 2
Solve -3*l**5 + 5*l - 16*l**2 + 4*l**5 + 26*l**2 - 6*l**5 - 10*l**4 = 0.
-1, 0, 1
Suppose -4*i + 4*v + 4 = 0, -6*v - 4 = 4*i - 2*v. Solve 0 + 2/5*k**4 - 2/5*k**2 + i*k + 0*k**3 = 0 for k.
-1, 0, 1
Let g(c) = -c**3 - 3*c**2 - 2*c - 3. Let q be g(-3). Suppose -f**2 + f**q + f**2 - 5*f + 4*f = 0. What is f?
-1, 0, 1
Let r(c) be the first derivative of -c**6/3 + 4*c**5/5 - 9. Find q such that r(q) = 0.
0, 2
Let w(x) be the second derivative of -x**4/30 + 2*x**3/5 - 9*x**2/5 - 11*x. Find r such that w(r) = 0.
3
Let w(x) = 11*x**2 - 38*x - 32. Let y(a) = 4*a**2 - 13*a - 11. Let k(b) = 3*w(b) - 8*y(b). Let n be k(11). Factor 0 + 0*p**2 - 1/4*p**n + 1/4*p.
-p*(p - 1)*(p + 1)/4
Let r(t) be the first derivative of -t**4/18 - t**3/9 + 3*t - 1. Let m(a) be the first derivative of r(a). Suppose m(p) = 0. What is p?
-1, 0
Let k(l) be the second derivative of 0*l**2 + 0 - 1/40*l**5 + 3*l - 1/12*l**4 + 1/4*l**3. Factor k(h).
-h*(h - 1)*(h + 3)/2
Let d(h) be the first derivative of 0*h + 4 + 1/10*h**4 + 0*h**2 + 0*h**3 - 2/25*h**5. Factor d(y).
-2*y**3*(y - 1)/5
Let g(a) be the third derivative of -a**6/24 + a**5/6 + 5*a**4/24 - 5*a**3/3 - 34*a**2. Factor g(c).
-5*(c - 2)*(c - 1)*(c + 1)
Suppose f + 2 + 5 = 3*u, 3*u - 17 = -f. Suppose q + u*q - 15 = 0. Determine p so that -45*p**2 + 38*p**3 - q + 21*p + 2*p**2 - 2*p**2 - 11*p**3 = 0.
1/3, 1
Let h = -21 + 23. Let l(w) be the second derivative of 0*w**4 + 0*w**3 - 1/60*w**6 + 0 + w - 1/84*w**7 + 0*w**5 + 0*w**h. Factor l(t).
-t**4*(t + 1)/2
Let k(f) be the third derivative of 0*f + 1/100*f**6 + 4/525*f**7 + 1/840*f**8 + f**2 - 2/75*f**5 + 0 - 1/15*f**4 + 0*f**3. Suppose k(d) = 0. What is d?
-2, -1, 0, 1
Let y(t) be the first derivative of 17*t**4 + 10/3*t**6 + 0*t**3 - 8*t**2 + 0*t - 72/5*t**5 + 4. Determine f so that y(f) = 0.
-2/5, 0, 1, 2
Let m = -26/5 + 88/15. Determine w so that m*w - 2/3*w**3 - 2/3*w**2 + 2/3 = 0.
-1, 1
Let f(i) = -677*i**3 + 403*i**2 - 72*i + 2. Let d(l) = -678*l**3 + 402*l**2 - 72*l + 1. Let r(j) = 2*d(j) - 3*f(j). Find v, given that r(v) = 0.
2/15, 1/3
Let k be (3 - (1 + 1))/105. Let b(l) be the second derivative of 0 - k*l**6 + 2*l - 1/21*l**3 - 3/70*l**5 - 1/14*l**4 + 0*l**2. Suppose b(g) = 0. Calculate g.
-1, 0
Let q(h) = -h**3 + 5*h**2 + 6*h + 2. Let t be q(6). Find y, given that -t*y**2 + 2*y + 8*y**3 - 2*y - 9*y**3 - y = 0.
-1, 0
Let g = 1511/5 - 301. Let d(o) be the first derivative of -7/15*o**6 + 2/5*o**2 + 0*o - g*o**3 + 1/2*o**4 + 18/25*o**5 + 3. Find x, given that d(x) = 0.
-1, 0, 2/7, 1
Suppose 4*m - 3/4*m**2 + 7/4*m**4 - 4*m**3 - 1 = 0. What is m?
-1, 2/7, 1, 2
Let p(v) be the third derivative of 0*v**5 + 1/30*v**6 + 3*v**2 + 0*v**3 + 0*v**4 - 1/105*v**7 + 0 + 0*v. Factor p(k).
-2*k**3*(k - 2)
Let u be -3 - (0/2)/4. Let d = u + 3. Determine k, given that -1/4 - 1/4*k**4 + d*k + 1/2*k**2 + 0*k**3 = 0.
-1, 1
Let i(m) be the third derivative of 0*m + 1/20*m**4 + 1/150*m**5 - 4*m**2 + 0*m**3 + 0. Factor i(y).
2*y*(y + 3)/5
Let w(c) be the third derivative of -c**8/1344 - c**7/840 + c**6/480 + c**5/240 - 17*c**2. Factor w(u).
-u**2*(u - 1)*(u + 1)**2/4
Suppose -5*v - 8 = 2. Let a be (4 - 6)*v/2. Factor s + 1/2*s**3 + 0 + 3/2*s**a.
s*(s + 1)*(s + 2)/2
Let j(h) be the first derivative of -1/10*h**2 - 1/60*h**4 + 1/15*h**3 + h + 2. Let b(n) be the first derivative of j(n). Factor b(w).
-(w - 1)**2/5
Let t(u) be the third derivative of -5*u**2 + 0*u + 0*u**3 - 1/15*u**4 - 1/300*u**6 + 2/75*u**5 + 0. Find f, given that t(f) = 0.
0, 2
Let a(o) = 14*o**2 + 11*o + 4. Let i = 2 + 5. Let t(x) be the first derivative of -7*x**3/3 - 5*x**2/2 - 2*x - 1. Let v(k) = i*t(k) + 4*a(k). Factor v(m).
(m + 1)*(7*m + 2)
Let u(b) = -b**3 + 5*b**2 + 6*b + 5. Let z be u(6). Find c, given that -2*c**4 + 2*c**z - 21*c**2 - 16*c**4 - 6*c - 27*c**3 - 5*c**5 + 3*c**4 = 0.
-2, -1, 0
Let h be (-22)/77 - 38/(-168)*2. Let n(s) be the second derivative of -1/12*s**4 + 0 + 0*s**2 + s + h*s**3. Suppose n(d) = 0. What is d?
0, 1
Let u(t) be the first derivative of -1/9*t**3 - 2 + 2/3*t + 1/6*t**2. Find s, given that u(s) = 0.
-1, 2
Suppose 3*z = 4*z + 24. Let x be 28/3*z/(-42). Solve 0 + 14/3*q**3 - 98/9*q**4 + x*q**2 + 8/9*q = 0.
-2/7, 0, 1
Determine m so that -4*m + 2*m**2 + 24*m - 15 - 7*m**2 = 0.
1, 3
Let i be (-53)/(-17) + (-2 - 1). Let q = 28/51 + i. Let q*w**5 + w**4 + 1/3*w**3 + 0*w + 0 + 0*w**2 = 0. Calculate w.
-1, -1/2, 0
Factor 15*f**2 + 33 - 3*f**3 - 40*f + 47 - 2*f**3 - 50*f**2.
-5*(f - 1)*(f + 4)**2
Let z(s) be the third derivative of s**6/15 + s**5/10 - s**4/12 - 8*s**2. Factor z(k).
2*k*(k + 1)*(4*k - 1)
Let p(q) be the second derivative of q**6/60 + q**5/30 - q**4/12 - q**3/3 - 3*q**2/2 + q. Let d(n) be the first derivative of p(n). Factor d(c).
2*(c - 1)*(c + 1)**2
Let y(p) = 6*p**3 + 12*p**2 - 21*p - 21. Let g(z) = 11*z**3 + 23*z**2 - 41*z - 43. Let r(v) = -3*g(v) + 5*y(v). Find c, given that r(c) = 0.
-4, -1, 2
Let c(f) = f**3 - 1. Let d(u) be the first derivative of u**4/2 + 2*u**2 - 6*u + 6. Let i(p) = 6*c(p) - d(p). Factor i(l).
4*l*(l - 1)*(l + 1)
Let u(k) be the second derivative of 7*k**4/12 + k**3/6 + 7*k**2/2 - 2*k. Let a(s) = 8*s**2 + 2*s + 8. Let r(d) = 5*a(d) - 6*u(d). Factor r(x).
-2*(x - 1)**2
Let x be (-8 - (-234)/30)*-5. Factor -9/4*a**2 - x + 1/2*a**3 + 3*a.
(a - 2)**2*(2*a - 1)/4
Let w be 610/210 + (-16)/(-168). What is y in -1/5*y + 1/5*y**w + 2/5*y**2 - 2/5 = 0?
-2, -1, 1
Let r(o) = 8*o**4 + 12*o**3 + 12*o**2 + 4*o - 12. Let g(k) = k + 1 + 34*k**4 - 35*k**4 - 2*k - k**3. Let w(z) = 12*g(z) + r(z). Factor w(l).
-4*l*(l - 1)**2*(l + 2)
Find x such that -9*x - 4*x**2 + 0*x**2 - 4*x**3 + 17*x = 0.
-2, 0, 1
Let t(d) be the second derivative of 0 - 3*d - 1/12*d**4 - 1/168*d**7 - 1/30*d**6 - 1/24*d**3 - 3/40*d**5 + 0*d**2. Find l such that t(l) = 0.
-1, 0
Let g be (-18)/(-5) + 3/(-5). Suppose 3*r**2 - 7*r**g - 6*r**3 + 9*r**4 - 2*r**3 + 3*r = 0. Calculate