 = -p + 7, -3*a + 5 = -p + 5*p. Let z be p + 2*(-18)/21. Suppose -2/7*s**2 + 0*s + z = 0. What is s?
-1, 1
Let s = 625 + -6880/11. Let n = -9/44 - s. Solve -1/2*x**3 + n*x**4 + 1/4*x**2 + 0*x + 0 = 0 for x.
0, 1
Let t = -328/11 - -30. Suppose 0 + 0*c + 0*c**2 - 2/11*c**4 + 0*c**3 - t*c**5 = 0. What is c?
-1, 0
Let o be (-1 - 3/2)*-6. Let w be (-3)/o + (-3)/(-15). Determine x, given that w*x - 1/4*x**2 + 0 = 0.
0
Suppose 5*w + 11 = -9, -5*w - 4 = 4*c. Let j(o) be the third derivative of 0 + 0*o - 2/525*o**7 + 0*o**3 + 0*o**c + 0*o**5 + 1/300*o**6 - 2*o**2. Factor j(u).
-2*u**3*(2*u - 1)/5
What is f in 42*f**2 - 15*f**2 - 22*f**2 - 20*f + 15 = 0?
1, 3
Let z be (-1 + 1 - (-18)/10) + -1. Factor -z*h**3 - 2/5 + 6/5*h**2 + 0*h.
-2*(h - 1)**2*(2*h + 1)/5
Let f(h) = 16*h**3 - 20*h**2 + 52*h - 28. Let t(b) = 5*b**3 - 7*b**2 + 17*b - 9. Let m(s) = -6*f(s) + 20*t(s). Determine a, given that m(a) = 0.
1, 3
Let w(v) = v**2 + 8*v + 14. Let y be w(-6). Let o(n) be the first derivative of 0*n**y + 0*n**4 + 2/5*n**5 + 3 + 0*n - 1/3*n**6 + 0*n**3. Factor o(d).
-2*d**4*(d - 1)
Find l such that 8/15*l + 2/15*l**2 + 8/15 = 0.
-2
Let z(u) = -3*u**3 + 10*u**2 - 8*u. Let b(q) = q**3. Let v(l) = -b(l) - z(l). Factor v(p).
2*p*(p - 4)*(p - 1)
Let z be 4/(-8)*(4/2 + -2). Let q(x) be the third derivative of -x**2 - 1/3*x**3 + 1/60*x**6 + z*x + 0 - 1/10*x**5 + 1/4*x**4. Determine t, given that q(t) = 0.
1
Let c(x) be the third derivative of 2/9*x**3 - 2*x**2 + 0*x - 1/36*x**4 - 1/90*x**5 + 0. Let c(q) = 0. What is q?
-2, 1
Let k = 18 - 18. Let y(h) be the second derivative of 0*h**3 + k - 3/20*h**5 - 1/2*h**4 + 3*h + 1/10*h**6 + 0*h**2. Factor y(g).
3*g**2*(g - 2)*(g + 1)
Let j(s) = s**2 - 10*s + 13. Let c be j(9). Factor -4*n**4 + 2*n**3 - 2*n**5 - 4*n**4 + 4*n**5 + c*n**4.
2*n**3*(n - 1)**2
Let f(u) = -20*u - 58. Let g be f(-3). Factor 0 - 1/2*y**g + 1/2*y**4 + 1/2*y**3 - 1/2*y**5 + 0*y.
-y**2*(y - 1)**2*(y + 1)/2
Suppose -14 = -0*q - 4*q + y, -2*y = -q. Find i such that 0*i + 2/9*i**2 + 2/9*i**q + 0 - 4/9*i**3 = 0.
0, 1
Let -2/3*s**4 - 2/3*s**2 + 0 + 0*s + 4/3*s**3 = 0. Calculate s.
0, 1
Let p(g) be the third derivative of 1/30*g**5 - 1/336*g**8 - 1/24*g**4 + 0*g + g**2 + 0 - 1/6*g**3 - 1/210*g**7 + 1/60*g**6. Solve p(d) = 0 for d.
-1, 1
Let z(r) = -23*r**4 - 4*r**3 + 21*r**2 + 4*r - 2. Let a(f) = 70*f**4 + 11*f**3 - 63*f**2 - 11*f + 7. Let o(t) = -2*a(t) - 7*z(t). Suppose o(p) = 0. Calculate p.
-1, -2/7, 0, 1
Let n = 205 - 1843/9. Factor 0 - 16/9*f**2 - 8/9*f - n*f**4 - 10/9*f**3.
-2*f*(f + 1)*(f + 2)**2/9
Let u(c) = -4*c + 26. Let f(q) = q**2 - 7*q - 2. Let z be f(8). Let p be u(z). Find s, given that 0 - 1/2*s**p - 1/4*s - 1/4*s**3 = 0.
-1, 0
Solve 7*x - 7*x - 3*x - 36 - 9*x - x**2 = 0 for x.
-6
Suppose 2*h + i = -0*h, 4*i + 8 = -4*h. Factor -2*c**3 + 2*c + 2*c**2 - 3 + h - 1 + 0*c**3.
-2*(c - 1)**2*(c + 1)
Let v(t) = -t - 1. Let o(w) = -w**3 - 4*w**2 + 5*w - 4. Let b be o(-5). Let m(a) = -18*a**2 - 8*a - 4. Let l(j) = b*v(j) + m(j). Find z, given that l(z) = 0.
-2/9, 0
Determine l so that -93*l**3 + 138 + 3*l**2 + 30*l**4 - 138 + 18*l = 0.
-2/5, 0, 1/2, 3
Let w(f) = f**4 - 5*f**3 + 2*f**2 + 2*f - 3. Let k(n) = 6*n**4 - 26*n**3 + 10*n**2 + 10*n - 16. Let j(d) = -3*k(d) + 16*w(d). Solve j(p) = 0 for p.
-1, 0, 1
Let t(p) be the third derivative of -p**6/160 + p**5/120 + 7*p**4/96 + p**3/12 + 3*p**2. Factor t(i).
-(i - 2)*(i + 1)*(3*i + 1)/4
Let j(q) be the third derivative of 1/40*q**5 - 2*q**2 - 1/16*q**4 - 1/240*q**6 + 0 + 1/12*q**3 + 0*q. Let j(s) = 0. Calculate s.
1
Let p be 27/5 + (-21)/(-35). Let t(d) be the second derivative of d - 1/45*d**5 + 1/189*d**7 + 1/27*d**3 - 1/27*d**4 + 0 + 1/9*d**2 + 1/135*d**p. Factor t(j).
2*(j - 1)**2*(j + 1)**3/9
Suppose 2*v - 2*n = 3*n + 20, -3*v - 5*n = -5. Let h = -5 + v. Factor 3*m + 2*m**2 + 2*m**2 - m**2 + h*m.
3*m*(m + 1)
Let c(m) = -m**3 - 3*m**2 - 2*m + 2. Let t be c(-2). Suppose -5*n = 0, 20 = 4*v + n - 4*n. Factor 2*b**2 - v*b + 0*b + b - 2 - 4*b**t.
-2*(b + 1)**2
Let z = 11 + -7. Let q(c) = -3*c**2 + 2*c - 4. Let y(p) = 4*p**2 - 2*p + 5. Let j(w) = z*y(w) + 5*q(w). Find a, given that j(a) = 0.
-2, 0
Suppose 14/5*i**4 - 4/5*i + 0 + 12/5*i**3 - 14/5*i**2 - 8/5*i**5 = 0. What is i?
-1, -1/4, 0, 1, 2
Let m(v) be the first derivative of v**4/4 - v**3/2 + 3*v + 4. Let s(z) be the first derivative of m(z). Find r such that s(r) = 0.
0, 1
Solve -3*r**3 + 2*r**3 - 109*r**2 - 4*r**3 + 89*r**2 = 0.
-4, 0
Let v = 1/703 - -1395/7733. What is q in 0 + 2/11*q**2 + v*q = 0?
-1, 0
Let y(k) be the first derivative of -3/4*k**2 - 1 - 1/12*k**3 - 9/4*k. Factor y(r).
-(r + 3)**2/4
Let p = -5 + 8. Factor -v**p - v**4 + 4*v + v**5 - 7*v + 3*v + v**2.
v**2*(v - 1)**2*(v + 1)
Let m(f) be the second derivative of f**4/12 - f**3/3 - 15*f. Factor m(y).
y*(y - 2)
Let n be 2478/13720*4/1. Let b = n + -6/49. Factor 0 + 3/5*z**2 + b*z.
3*z*(z + 1)/5
Factor -s - s**5 - 7*s**5 + 26*s**4 - s + 14*s**2 - 30*s**3.
-2*s*(s - 1)**3*(4*s - 1)
Let j(k) be the first derivative of -k**8/1176 - 2*k**7/735 - k**6/420 + 3*k**2/2 - 2. Let w(o) be the second derivative of j(o). Determine d so that w(d) = 0.
-1, 0
Solve 1 + 0*r**2 - 5 - 2*r**2 - 6*r = 0.
-2, -1
Let d(y) be the second derivative of -1/3*y**3 + 0 + y**2 + 5*y + 1/10*y**5 - 1/6*y**4. Factor d(f).
2*(f - 1)**2*(f + 1)
Let p be (0/2)/(-1) + 200/50. Factor -1/3 + 5/6*r + 2/3*r**p - 1/3*r**2 - 1/6*r**5 - 2/3*r**3.
-(r - 2)*(r - 1)**3*(r + 1)/6
Let h(l) = -38*l**2 - 63*l + 43. Let t(s) = -13*s**2 - 21*s + 14. Let w(z) = 3*z - 11. Let d be w(5). Let x(a) = d*h(a) - 11*t(a). Suppose x(m) = 0. What is m?
-3, 2/3
Let l(y) be the first derivative of y**4/4 + 2*y**3/3 - 28. Factor l(r).
r**2*(r + 2)
Let n(x) be the first derivative of x**6/6 - 11*x**5/5 + 23*x**4/4 + 47*x**3/3 - 12*x**2 - 36*x + 11. Factor n(a).
(a - 6)**2*(a - 1)*(a + 1)**2
Let v = 1 - -1. Let j(m) be the third derivative of 0 + 1/840*m**7 - v*m**2 - 1/480*m**6 + 0*m**4 + 0*m**5 + 0*m + 0*m**3. Determine y so that j(y) = 0.
0, 1
Let l(v) be the first derivative of 3*v**4/8 + 7*v**3/2 + 12*v**2 + 18*v - 2. Factor l(r).
3*(r + 2)**2*(r + 3)/2
Factor 2*n**3 - 2*n**5 - n**2 - 8*n**4 - n**2 + 10*n**4.
-2*n**2*(n - 1)**2*(n + 1)
Let h be (-38)/(-12) - (-14)/(-21). Factor 7/2*w - 9/2*w**2 - 1 - 1/2*w**4 + h*w**3.
-(w - 2)*(w - 1)**3/2
Let t = 37 + -143/4. Suppose -t*l**2 - 1/4*l**4 + l**3 + 0 + 1/2*l = 0. Calculate l.
0, 1, 2
Suppose -2*s**4 - 2*s**5 + 15*s**4 - 14*s**2 + s**4 + 37*s**3 - 35*s**3 = 0. What is s?
-1, 0, 1, 7
Let g(x) be the first derivative of 21*x**4/4 - 2*x**3 - 21*x**2/2 + 6*x - 20. Factor g(y).
3*(y - 1)*(y + 1)*(7*y - 2)
Let h(j) be the third derivative of j**7/840 + j**6/96 - j**5/240 - 5*j**4/96 + 24*j**2. Factor h(t).
t*(t - 1)*(t + 1)*(t + 5)/4
Suppose 4*g - 6*g + 5*n = -14, -3*g = 5*n + 4. Suppose i - 1/2*i**g - 1/2 = 0. Calculate i.
1
Let y be (6 - 4)/((-2)/(-2)). Let v(u) be the second derivative of 1/12*u**4 + 0*u**2 - y*u + 0 - 1/6*u**3. Factor v(h).
h*(h - 1)
Let u be (2/(-3))/(4/(-12)). Factor -1 - 1 - 2*l**2 + 4*l**2 + u*l**3 - 2*l.
2*(l - 1)*(l + 1)**2
Let o(x) be the third derivative of x**5/180 - x**4/24 + x**3/9 - 27*x**2. Determine d so that o(d) = 0.
1, 2
Suppose -t + 2*w = -6, 0*t - 5*w - 21 = -4*t. Factor v**4 - 4*v + 4 + 12*v**2 - 12*v**3 + 3*v**4 - t.
4*v*(v - 1)**3
Let v(c) be the second derivative of -1/70*c**5 - 3*c + 0 - 5/21*c**3 - 2/7*c**2 - 2/21*c**4. Suppose v(k) = 0. What is k?
-2, -1
Let -2/7*f**3 - 6/7*f**2 + 4/7 + 2/7*f + 2/7*f**4 = 0. What is f?
-1, 1, 2
Let p(c) be the second derivative of c**5/140 - c**4/28 + c**3/21 + 3*c - 4. Find k, given that p(k) = 0.
0, 1, 2
Suppose -w + 10 = -12. Let s be w/(-8) - 0 - -3. Let 0 - s*g**2 + 0*g = 0. Calculate g.
0
Suppose 0*c + 1/4*c**4 + 0 + 0*c**2 - 1/4*c**3 = 0. Calculate c.
0, 1
Let f(y) = -2*y**3 + y**2 + 1. Suppose 0 = -2*d + 6*d - 8. Let p(i) = i**3 - i**d - 1 + 3*i**3 - 2. Let k(c) = 5*f(c) + 2*p(c). Factor k(n).
-(n - 1)**2*(2*n + 1)
Let v(t) = 4*t**3 + 10*t**2 - 8*t - 38. Let f(u) = 5*u**3 + 11*u**2 - 9*u - 39. Let s(j) = -2*f(j) + 3*v(j). Suppose s(x) = 0. Calculate x.
-3, 2
Let i(s) be the first derivative of -s**4/12 - s**3/3 - s**2/2 + 10*s + 2. Let o(r) be the first derivative of i(r). Find y such that o(y) = 0.
-1
Let q be (2 - (-18)/(-