 Let v = -2 - z. Find p, given that -v*p**2 + 0*p - 3*p + 0 + 0 = 0.
-1, 0
Let a(t) be the third derivative of t**7/735 + t**6/210 - t**4/42 - 3*t**3/2 - 9*t**2. Let d(f) be the first derivative of a(f). Let d(r) = 0. What is r?
-1, 1/2
Suppose 3*l + 25 = 5*w, -5*w + 5*l + 5 = 6*l. Factor 1/2*k**5 + 3*k**3 + w*k**4 + 2*k**2 + 0 + 1/2*k.
k*(k + 1)**4/2
Suppose -3*s - 26 + 11 = -2*q, 4*q + 10 = -2*s. Factor -1/2*i**4 - 5/6*i**3 + q + 0*i - 1/3*i**2.
-i**2*(i + 1)*(3*i + 2)/6
Let y(u) be the second derivative of 49*u**5/30 - 119*u**4/18 - 80*u**3/9 - 4*u**2 + 5*u. Factor y(s).
2*(s - 3)*(7*s + 2)**2/3
Let r(u) = -u**2 - 7*u - 4. Let q be r(-5). Factor -1 - q*v**3 - 3*v**4 + 4 + v + 0*v**4 + 5*v.
-3*(v - 1)*(v + 1)**3
Let v(o) be the second derivative of o**8/840 + o**7/350 - o**6/300 - o**5/75 + o**3/30 - o**2/2 + 3*o. Let t(h) be the first derivative of v(h). Factor t(y).
(y - 1)*(y + 1)**3*(2*y - 1)/5
Let s(y) be the second derivative of -y**4/4 - y**3 - 3*y**2/2 + 5*y. Factor s(x).
-3*(x + 1)**2
Let w(h) = 2*h - 8. Let z be w(6). Factor -2*o + 3*o + z*o - o**3 - 4*o.
-o*(o - 1)*(o + 1)
Suppose 11*n**3 - 4*n**4 + 12*n**2 - 7*n**3 - 24 + 28*n - 16*n**3 = 0. Calculate n.
-3, -2, 1
Let p(z) be the third derivative of -z**5/240 - z**4/48 - z**3/24 - 40*z**2. Factor p(c).
-(c + 1)**2/4
Let c = 3 + -11. Let o(p) = -11*p**4 + 8*p**3 + 6*p**2 - 3. Let q(t) = 7*t**4 - 5*t**3 - 4*t**2 + 2. Let f(g) = c*q(g) - 5*o(g). Find j such that f(j) = 0.
-1, 1
Let c(j) = 6*j**4 + 63*j**3 + 180*j**2 + 162*j. Let t(i) = 3*i**4 + 31*i**3 + 89*i**2 + 81*i. Let g(a) = -4*c(a) + 9*t(a). Determine d, given that g(d) = 0.
-3, 0
Let i(s) be the second derivative of s**8/1680 - s**6/180 + s**4/24 + s**3/6 - 2*s. Let u(v) be the second derivative of i(v). Factor u(z).
(z - 1)**2*(z + 1)**2
Let z be (-2)/(-3) + 1/3. Let f be (-2 + 2)*z/(-2). Factor 1/3*m**4 + 1/3*m**3 + 0 + f*m + 0*m**2.
m**3*(m + 1)/3
Suppose -2*g + 3 + 1 = 0. Suppose q**3 + 0*q + q - q**2 + 1 + 0*q**2 - g*q = 0. What is q?
-1, 1
Suppose 54/7*g**5 - 72/7*g + 8/7 + 214/7*g**2 - 54/7*g**4 - 198/7*g**3 = 0. Calculate g.
-2, 1/3, 2
Let z be 13/26*1*(-2 - -3). Find m, given that z*m**3 - 1/4*m + 1/4*m**4 + 1/4 - 1/4*m**5 - 1/2*m**2 = 0.
-1, 1
Let a(u) = 2*u - 6. Let m be a(5). Suppose 0 = -2*x + 5*r - 4 - 12, 5*x - 26 = -m*r. Let -3*f**3 - 2*f**5 - 2*f**4 + f**3 - x*f**4 = 0. What is f?
-1, 0
Let x = 1517 - 1514. Solve 0 + 4/7*h**x + 5/7*h**2 + 1/7*h**4 + 2/7*h = 0 for h.
-2, -1, 0
Let u be 155/150 - (-3 - -4). Let d(r) be the third derivative of -1/3*r**3 + 0*r - u*r**5 - r**2 + 1/6*r**4 + 0. Factor d(h).
-2*(h - 1)**2
Let r(f) = -f + 10. Let y be r(-7). Suppose -h + y = -5*q, 11 = 2*h - 2*q + 1. Solve -4*p**3 + 5*p**3 + h*p**5 - 3*p**3 = 0 for p.
-1, 0, 1
Let f(l) = l**3 + l**2 + l - 1. Let x be f(1). Solve 2*i**3 + x*i**3 + 2*i**3 + 3*i**5 + 3*i**4 - 12*i**4 = 0 for i.
0, 1, 2
Suppose -1/6*p**4 - 2/3*p**3 + 0 - 1/3*p - 5/6*p**2 = 0. Calculate p.
-2, -1, 0
Let f(s) = 2*s**5 - 7*s**4 + s**2 + s. Let w(k) = 2*k**2 + 6*k**5 - 16 + 4*k - 22*k**4 + 16. Let l(g) = -10*f(g) + 3*w(g). Factor l(i).
-2*i*(i - 1)**3*(i + 1)
Let g be 10/150*(-2)/(-22). Let w(f) be the second derivative of 0 - 3*f - 1/55*f**5 + 0*f**2 - g*f**6 + 0*f**3 - 1/66*f**4. What is y in w(y) = 0?
-1, 0
Determine l so that -18/5*l**2 - 6/5*l**3 + 2/5*l**4 + 0 + 54/5*l = 0.
-3, 0, 3
Let m = 161 - 158. Let 1/4*l**2 + l - l**m - 1/4 = 0. What is l?
-1, 1/4, 1
Let d(p) = -p**2 - 10*p - 22. Let o be d(-6). Find q, given that -4/7*q**o + 0 + 0*q**3 - 2/7*q**5 + 4/7*q**4 + 2/7*q = 0.
-1, 0, 1
Factor 1/5*p**2 - 1/5 + 0*p.
(p - 1)*(p + 1)/5
Let d(g) = -6*g**2 + 16 + g - 13 - 4 + 25*g. Let x(n) = n**2 - 5*n. Let z(j) = 6*d(j) + 33*x(j). Solve z(a) = 0 for a.
-2, -1
Suppose -6*n = -18 + 6. Factor -32*y**3 - 1/2 - 6*y - 24*y**n.
-(4*y + 1)**3/2
Factor 1/6*p**2 + 0 + 1/3*p.
p*(p + 2)/6
Let d(q) = -2*q**2 + 22*q - 12. Let p(r) = -r**2. Let m(t) = -d(t) - 6*p(t). Factor m(f).
2*(f - 2)*(4*f - 3)
Factor 8*h + 4*h**4 + 38*h**2 - 12*h**3 - 5 + 4*h - 34*h**2 - 3.
4*(h - 2)*(h - 1)**2*(h + 1)
Let r(p) be the second derivative of 9*p**8/140 - 3*p**6/25 - 8*p**5/75 - p**4/30 - 5*p**2/2 - 7*p. Let b(c) be the first derivative of r(c). Factor b(o).
4*o*(o - 1)*(3*o + 1)**3/5
Suppose -4*h + 3*g + 4 = 0, -2*g + g = -h. Let c be (-9)/(-4) + (-1)/h. Suppose -8/7 - 8/7*j - 2/7*j**c = 0. What is j?
-2
Let n = -23/9 - -29/9. Solve -a**4 + a**2 + n*a + 0 - 7/3*a**3 + 5/3*a**5 = 0.
-1, -2/5, 0, 1
Let s(i) = i**2 - 8*i + 7. Let x be s(7). Let t be ((-4)/(-4) - 1) + x. Factor 2/5*j**3 - 2/5*j**5 + 0*j**4 + t*j + 0*j**2 + 0.
-2*j**3*(j - 1)*(j + 1)/5
Let v(p) = -p**4 - p**3 - p + 1. Let b(y) = -2*y**3 + 2*y**2 + 6*y - 2. Let d(g) = b(g) + 2*v(g). Factor d(a).
-2*a*(a - 1)*(a + 1)*(a + 2)
Let q(g) = -g + 6. Let v be q(6). Let a(l) be the first derivative of v*l + 0*l**3 - 1/2*l**4 + 1 + 0*l**2 - 2/5*l**5. Suppose a(j) = 0. What is j?
-1, 0
Let j(w) = -w**3 - 4*w**2 + 2*w + 14. Let n be j(-2). Factor 3/2*x**n + 6 - 6*x.
3*(x - 2)**2/2
Let x be (15/(-6) - -3)*4. Let d = -2 + x. Solve d*g - 1/2*g**3 + 1/4*g**2 + 0 + 1/4*g**4 = 0.
0, 1
What is j in -40*j**2 + 8*j - 2/5 = 0?
1/10
Let k = 51 + -48. Factor 12/5*t**k + 6/5*t + 0 - 27/5*t**2.
3*t*(t - 2)*(4*t - 1)/5
Let d(j) be the third derivative of 2*j**2 - 1/40*j**7 + 0 + 0*j**4 + 0*j + 0*j**3 - 1/60*j**6 + 1/60*j**5. Factor d(w).
-w**2*(3*w + 2)*(7*w - 2)/4
Let w(k) be the second derivative of -k + 0 - 6*k**2 - 2*k**3 - 1/4*k**4. Find g, given that w(g) = 0.
-2
Let k(t) = -4*t - 3. Let x be (-14)/8 + 2/(-8). Let o be k(x). Factor -2*s**3 - 4*s**5 + 2*s**o + 3*s**4 - 7*s**4.
-2*s**3*(s + 1)**2
Let j be (-1)/(-5)*-9 - -2. Let d(a) be the second derivative of -25/168*a**7 - 1/24*a**6 + j*a**5 + 0 + 0*a**3 - 1/12*a**4 + 2*a + 0*a**2. Factor d(r).
-r**2*(r + 1)*(5*r - 2)**2/4
Let r(x) be the second derivative of -x**7/14 + x**6/5 - 3*x**5/20 + 2*x. Let r(y) = 0. What is y?
0, 1
Let v(g) be the first derivative of -g**6/18 - g**5/3 - 7*g**4/12 + g**3/9 + 4*g**2/3 + 4*g/3 - 7. Suppose v(j) = 0. Calculate j.
-2, -1, 1
Let r(p) = p**2 - 34*p + 240. Let n be r(24). Factor n + 2/9*f - 2/9*f**2.
-2*f*(f - 1)/9
Suppose j - 31 = -3*u, -3*j + j + u = -55. Suppose 5*l = -o + 20, -6*o + o = l - j. Factor 0*t**4 - 3*t**4 + 2*t**5 - t**5 - t**2 + l*t**3.
t**2*(t - 1)**3
Let m(n) be the first derivative of 2*n**3/15 + 3*n**2/5 + 4*n/5 - 1. Determine l, given that m(l) = 0.
-2, -1
Let g(n) be the first derivative of 5*n**4/4 + 10*n**3 + 45*n**2/2 + 8. Factor g(j).
5*j*(j + 3)**2
Let b(t) be the first derivative of t**3/3 - 3*t**2/2 + 2*t - 3. Let h be b(3). Suppose 0*j**3 - 1/2*j**4 + 0*j + 0 + 1/2*j**h = 0. Calculate j.
-1, 0, 1
Let z = 7/4 + -17/12. Factor 2/3 + z*q**3 - 2/3*q**2 - 1/3*q.
(q - 2)*(q - 1)*(q + 1)/3
Let z(b) = 2*b**2 + 3*b. Let y be z(-2). Find j such that -6*j + j + y*j + 6*j**2 - 3*j**2 = 0.
0, 1
Let u(h) = 56*h**3 + 52*h**2 + 4*h + 8. Let c(g) = -19*g**3 - 17*g**2 - g - 3. Let x(t) = -8*c(t) - 3*u(t). Solve x(v) = 0.
-1, -1/4, 0
Let h = -153 - -273. Let y be 6/10 + 8/h. Solve 1/3*q - 2/3*q**2 + y - 1/3*q**3 = 0 for q.
-2, -1, 1
Let x(j) be the second derivative of -3*j**5/20 + j**3/2 - 2*j. Suppose x(o) = 0. Calculate o.
-1, 0, 1
Let u(t) be the first derivative of t**3/4 - 3*t**2/8 - 4. Factor u(w).
3*w*(w - 1)/4
Let x(g) be the first derivative of -g**5 + 45*g**4/4 - 25*g**3 - 125*g**2/2 + 27. Find i, given that x(i) = 0.
-1, 0, 5
Suppose 0 - 1/2*c**5 - 1/4*c**2 + 1/4*c**4 + 1/2*c**3 + 0*c = 0. Calculate c.
-1, 0, 1/2, 1
Let o be (-1 - -5) + -4 + 1/2. Factor 0 - k**4 + o*k + 0*k**3 - 1/2*k**5 + k**2.
-k*(k - 1)*(k + 1)**3/2
Suppose -5*b = -3*p + 10, 21 = b + 3*p + p. Suppose 7 + b = 4*l. Find q such that 2/5 - 4/5*q + 2/5*q**l = 0.
1
Solve 0 - 11/6*u**4 - 5/6*u**5 - 1/6*u**2 + 0*u - 7/6*u**3 = 0.
-1, -1/5, 0
Let r(b) be the second derivative of b**8/5040 - b**7/840 + 5*b**3/6 + 7*b. Let p(w) be the second derivative of r(w). Factor p(v).
v**3*(v - 3)/3
Let m(k) = -36*k**5 - 8*k**4 + 4*k**3 - 6*k**2 - 6. Let z(f) = 35*f**5 + 7*f**4 - 4*f**3 + 5*f**2 + 5. Let g(a) = -5*m(a) - 6*z(a). Factor g(t).
-2*t**3*(3*t - 1)*(5*t + 2)
Let y(x) be the second derivative of 0*x**2 - 3/10*x**5 + 1/21*x**7 - 1/6*x**4 + 7*x + 2/3*x**3 + 0 + 1/15*x**6. Fa