9 + 1). Let i = g - 4. Suppose 0 + 2/5*q - 2/5*q**i = 0. What is q?
0, 1
Let v(q) = -q**3 - 2*q**2 + q + 1. Let g(k) = -2*k**3 - k**2 + 17*k + 21. Let o(m) = -2*g(m) + 2*v(m). Let o(p) = 0. Calculate p.
-2, 5
Factor 6/7*t**4 + 0*t + 0 - 10/7*t**3 + 4/7*t**2.
2*t**2*(t - 1)*(3*t - 2)/7
Let z(p) be the third derivative of 0*p + 2/105*p**5 + 2/21*p**3 - 5*p**2 + 0 - 1/420*p**6 - 5/84*p**4. Suppose z(x) = 0. Calculate x.
1, 2
Let h = 10 - 2. Find f, given that 4 + 4 + f**2 - h*f + 2*f**2 - f**2 = 0.
2
Suppose -1/4*d**4 + 0*d**2 - 3/4*d**3 + d + 0 = 0. Calculate d.
-2, 0, 1
Let n be -3*((-40)/12 - -2). Suppose -7*q = -n*q. Factor -1/3*c**3 + 0*c + 0 + q*c**2.
-c**3/3
Let r be (-7)/(-35) + (-18)/(-10). Factor 18 - 12 - 9*y - 21*y**3 - 59*y**2 + 23*y**r.
-3*(y + 1)**2*(7*y - 2)
Let q(t) be the second derivative of t**6/30 - t**5/10 - t**4/12 + t**3/3 + 10*t. Factor q(o).
o*(o - 2)*(o - 1)*(o + 1)
Suppose 13 - 45*h**5 + 20*h**3 + 131*h - 106*h - 3 - 9*h**4 - 90*h**2 + 89*h**4 = 0. What is h?
-1, -2/9, 1
Let i(t) = -3*t + 7. Let h be i(-3). Let f be (-1)/(1 + (-36)/h). Suppose -2/5*k**2 - f - 6/5*k = 0. Calculate k.
-2, -1
Let h = -1 + -3. Let k(j) = 5*j**4 - 8*j**3 + 10*j**2 + 1. Let r(l) = l**4 - l**3 + l**2 + l. Let z = 17 + -16. Let y(t) = h*r(t) + z*k(t). Factor y(o).
(o - 1)**4
Let i = 358 + -354. Suppose -4 = r, 4*r + 16 = l - 3. Determine q so that 4/7*q**2 - 8/7*q**l + 4/7*q**5 - 2/7*q**i - 2/7 + 4/7*q = 0.
-1, 1/2, 1
Let s(i) = 6*i**2 - 4*i. Let r(a) = -a**2 + a. Let d(q) = 15*r(q) + 3*s(q). Factor d(o).
3*o*(o + 1)
Let n be 6 - 4/(-8)*-12. Factor 1/2*l**2 + n*l - 1/2.
(l - 1)*(l + 1)/2
Let j(f) be the third derivative of -5*f**2 + 0*f**4 - 1/60*f**5 + 0 - 1/120*f**6 + 0*f + 0*f**3. Factor j(l).
-l**2*(l + 1)
Let c be (-8)/(-10)*(9/6 + 1). Let p(u) be the first derivative of 0*u - 1/7*u**4 + 3 + 0*u**c + 2/21*u**3 + 2/35*u**5. Factor p(v).
2*v**2*(v - 1)**2/7
Suppose -3*z + 78 = -5*z - 2*q, z - 2*q = -42. Let j be z/12*(-3)/2. Factor 4*g**5 + g**j - 4*g**5.
g**5
Let v(n) be the first derivative of n**2 + 0*n + 3 + 0*n**4 - 1/30*n**5 + 1/60*n**6 + 0*n**3. Let j(p) be the second derivative of v(p). Factor j(y).
2*y**2*(y - 1)
Factor 27/7*n**2 + 3/7 + 18/7*n.
3*(3*n + 1)**2/7
Suppose -3 + 273*x**2 + 17 - 83*x**2 - 45*x**3 + 16 - 175*x = 0. Calculate x.
2/9, 1, 3
Let t(g) = 7*g**2 + 5*g + 1. Let w(b) = 13*b**2 + 9*b + 2. Let q(f) = -5*t(f) + 3*w(f). Let o be q(-1). What is j in j**o + 2 - 2 + 4 - 3*j**2 + 0 = 0?
-1, 2
Factor -g**4 + 0*g**4 + 11 - 12 + 2*g**2.
-(g - 1)**2*(g + 1)**2
Let h(d) = 3*d + 6. Let f(m) = m**3 + 17*m**2 + 16*m - 2. Let k be f(-16). Let s be h(k). Factor -2/9*b**2 + s + 2/9*b.
-2*b*(b - 1)/9
Determine m, given that 4*m**2 - 18*m**5 - 5*m**3 - 67*m**4 + 31*m**4 - 11*m**3 + 2*m = 0.
-1, -1/3, 0, 1/3
Let p(s) be the first derivative of -s**6/30 + 6*s**5/25 - s**4/4 + 57. Factor p(j).
-j**3*(j - 5)*(j - 1)/5
Let f(v) be the first derivative of v**8/336 - v**7/70 + v**6/60 - v**2/2 - 2. Let w(p) be the second derivative of f(p). Factor w(i).
i**3*(i - 2)*(i - 1)
Suppose -4*s + 2*a + 2*a + 8 = 0, 5*s = -3*a + 18. Let u(y) be the first derivative of 2 + 1/6*y**s + 1/8*y**4 + 0*y**2 + 0*y. Factor u(r).
r**2*(r + 1)/2
Let b be (-6)/10 - (-1)/((-105)/(-93)). Solve -6/7*q**3 - b*q + 0 + 6/7*q**2 + 2/7*q**4 = 0 for q.
0, 1
Let t(w) be the first derivative of w**3 + 9*w**2/2 + 6*w + 4. Factor t(i).
3*(i + 1)*(i + 2)
Let f = 1 - -5. Suppose -f - 14 = -5*p. Let -1 - 16*q + 18*q - p*q**2 + 3*q**2 = 0. What is q?
1
Suppose h + 9 - 21 = 4*l, -2*l - 6 = h. Solve h + 0*j + 2/9*j**2 - 2/9*j**3 = 0.
0, 1
Let p be (-2)/27*(-60)/40. Suppose p*j + 1/9*j**2 + 0 = 0. Calculate j.
-1, 0
Suppose 5*r = -3*y + 32, y - 6 = -r + 2. Factor -2/7*w**3 + 2/7*w**r + 2/7*w**5 - 2/7*w**2 + 0 + 0*w.
2*w**2*(w - 1)*(w + 1)**2/7
Let v(z) = z**3 - 18*z**2 + 17*z + 3. Let q be v(17). Let s be 42/9 - 2/(-6). Solve m**s - 2*m**5 - m + 0*m + 2*m**q = 0 for m.
-1, 0, 1
Let n(l) = -4*l**3 - 55*l**2 - 98*l - 44. Let z(v) = -28*v**3 - 384*v**2 - 684*v - 308. Let j(w) = 20*n(w) - 3*z(w). Factor j(d).
4*(d + 1)**2*(d + 11)
Let f(x) be the second derivative of x**4/12 - 2*x**3/3 + 3*x**2/2 + 2*x. Let s be f(3). Factor 2*o + 6*o**3 - 6*o**2 + s*o**2 + 2*o**2 - 4*o**3.
2*o*(o - 1)**2
Let o(l) = l**2 - 9*l. Let w be o(8). Let n = -3 - w. Factor 1/2*m**3 + 1/4*m**n + 1/4 - 3/4*m**4 - 3/4*m + 1/2*m**2.
(m - 1)**4*(m + 1)/4
Let t = 4 - 4. Suppose 5*n = 4*a - 2 + 4, 3*a - 6 = t. Let 5*g**4 + 0*g**2 - 4*g**4 - n*g**2 + 1 = 0. Calculate g.
-1, 1
Let r(a) be the third derivative of a**6/210 - 2*a**5/105 + 2*a**2. Solve r(d) = 0.
0, 2
Factor -6*c**4 - 24*c**2 + 13*c**2 + 16*c**2 + c**4.
-5*c**2*(c - 1)*(c + 1)
Factor 1/2*b**4 + 1/2*b**3 + 0 + 0*b - b**2.
b**2*(b - 1)*(b + 2)/2
Suppose 2*c + 2*w - 40 = 0, -4*c + 3*w + 70 = 5*w. Factor c*s**5 + 12*s - 4*s**2 - 2*s**2 - 12*s + 24*s**4 + 3*s**3.
3*s**2*(s + 1)**2*(5*s - 2)
Let h(o) be the second derivative of o**4/24 + o**3/3 - 7*o. Suppose h(v) = 0. What is v?
-4, 0
Factor 196 + 60*z**2 - 47*z**3 + 43*z**3 + 22*z - 274*z.
-4*(z - 7)**2*(z - 1)
Suppose 4*r - 2*r - 1 = -a, -5*r + 4*a = -22. Find n such that -r*n**3 + 9*n - 7 - 45*n + 31 - n**3 + 18*n**2 = 0.
2
Let s(f) be the second derivative of -1/35*f**5 - 1/105*f**6 + 0*f**3 - 1/42*f**4 + f + 0*f**2 + 0. Factor s(o).
-2*o**2*(o + 1)**2/7
Let a(l) = l**3 + l**2 + 1. Let t(w) = -4*w**3 + 2*w**2 + 2*w - 6. Let p(o) = 2*a(o) + t(o). Find c, given that p(c) = 0.
-1, 1, 2
Let m(v) be the third derivative of v**7/1785 - v**6/170 + 2*v**5/85 - 2*v**4/51 + 36*v**2. Determine a so that m(a) = 0.
0, 2
Let s(v) be the second derivative of v**6/150 - v**5/100 - v**4/20 + v**3/30 + v**2/5 + 5*v. Suppose s(h) = 0. Calculate h.
-1, 1, 2
Let v(k) be the first derivative of 10*k**3/9 + 7*k**2/3 + 4*k/3 - 8. Find p such that v(p) = 0.
-1, -2/5
Let h(o) be the first derivative of o**7/840 + o**6/180 + o**5/120 - 2*o**3/3 - 2. Let k(f) be the third derivative of h(f). Factor k(g).
g*(g + 1)**2
Let u(z) be the third derivative of -z**6/420 + 3*z**5/70 - 9*z**4/28 + 9*z**3/7 - 2*z**2. Factor u(i).
-2*(i - 3)**3/7
Let r(a) be the first derivative of -2*a**5/5 - 5*a**4/2 + 26*a**3/3 - 7*a**2 - 48. Determine u, given that r(u) = 0.
-7, 0, 1
Suppose 0 = 4*m - 0*m. Factor -1/6*u**5 + 0*u**3 - 1/3*u**2 + m + 1/6*u + 1/3*u**4.
-u*(u - 1)**3*(u + 1)/6
Let p = -41 + 13. Let g = 30 + p. Suppose 1/2*t + 2*t**4 + 3*t**3 + 0 + 1/2*t**5 + 2*t**g = 0. Calculate t.
-1, 0
Suppose -18 = -2*m + 2. Find x, given that m*x**3 - 48*x**3 - 6*x**4 - 3 - 72*x + 7*x**2 - 13 - 91*x**2 = 0.
-2, -1/3
Suppose -6*c + 58 = -4*c. Factor 14*w**2 - 34*w - c*w**2 + 12 + 10*w.
-3*(w + 2)*(5*w - 2)
Let u(p) = 2*p**2. Let z(y) be the first derivative of 8*y**3/3 - y**2/2 - 3. Let v(n) = -9*u(n) + 2*z(n). Factor v(l).
-2*l*(l + 1)
Let k = 31 - 29. Let u(s) be the first derivative of -3 + 2/5*s**5 + 0*s**k + 0*s + 2/3*s**3 + s**4. Solve u(v) = 0.
-1, 0
Let y(l) be the second derivative of l**6/180 + l**5/30 + l**4/12 - l**3/2 + 3*l. Let s(n) be the second derivative of y(n). Factor s(f).
2*(f + 1)**2
Suppose w - 3*w + 12 = 2*s, -s + 22 = 5*w. Factor 1/4*b**3 + 1/2 - 1/2*b**s - 1/4*b.
(b - 2)*(b - 1)*(b + 1)/4
Solve 4/5*i - 2/5*i**4 + 0*i**2 - 4/5*i**3 + 2/5 = 0.
-1, 1
Let u(k) be the second derivative of 0 + k**2 - 1/6*k**4 + 0*k**3 + 3*k. Solve u(j) = 0 for j.
-1, 1
Let o(z) be the first derivative of z**5/10 - 3*z**4/8 + z**3/3 + 12. Let o(f) = 0. What is f?
0, 1, 2
Suppose 0 = -7*c + 2*c + 7*c. Determine o so that 4/7*o**4 + 0*o**3 + 2/7*o**5 + c - 2/7*o - 4/7*o**2 = 0.
-1, 0, 1
Let l(v) be the third derivative of -v**5/5 - 2*v**4/3 - 2*v**3/3 + 4*v**2. Suppose l(r) = 0. What is r?
-1, -1/3
Let v(z) be the first derivative of -z**6/135 - 4*z**5/45 - 4*z**4/9 - 32*z**3/27 - 16*z**2/9 + 2*z + 1. Let l(q) be the first derivative of v(q). Factor l(g).
-2*(g + 2)**4/9
Let h(q) = 11*q**4 + 5*q**3 - 6*q**2 - 5*q + 9. Let b(j) = 5*j**4 + 2*j**3 - 3*j**2 - 2*j + 4. Let v(g) = -7*b(g) + 3*h(g). Factor v(u).
-(u - 1)**2*(u + 1)*(2*u + 1)
Factor 3*i**2 + 41*i - 28 - 2 - 28*i - 22*i.
3*(i - 5)*(i + 2)
Find b such that -2*b**3 + 2*b - 2*b**4 + 2*b**2 + 62 - 62 = 0.
-1, 0, 1
Let g(t) be the second derivative of 0 + 12/13*t**2 + 9/130*t**5 + 1/2*t**4 + 6*t + 40