se 5*v + v = 18. Let q(y) be the first derivative of -2/5*y**4 - 2/5*y - 2/25*y**5 - 4/5*y**3 - v - 4/5*y**2. Determine g so that q(g) = 0.
-1
Determine w, given that 4/5*w - 2/5*w**3 + 1/5*w**4 + 4/5 - 3/5*w**2 = 0.
-1, 2
Let n(b) = -b**3 + 11*b**2 - 11*b + 13. Let s be n(10). Factor s*y + 103 - 3*y**3 - 103.
-3*y*(y - 1)*(y + 1)
Let z(c) = -c**2 + 2*c + 2. Let r(o) = 4*o**2 - 6*o - 7. Let y(s) = -2*r(s) - 7*z(s). Factor y(x).
-x*(x + 2)
Let g = -24 + 28. Suppose h - 5 = -0*d + 3*d, 4*d = g*h - 20. Factor 0*y - 2/7*y**3 + d*y**2 + 0.
-2*y**3/7
Let i = -13852/7 + 1988. Factor i*x**2 + 0 + 16/7*x + 4*x**3.
4*x*(x + 2)*(7*x + 2)/7
Let t(u) be the first derivative of 0*u - 6 + 3*u**2 - 3/2*u**4 - 3/5*u**5 + u**3. Determine h, given that t(h) = 0.
-2, -1, 0, 1
Solve -4*z**5 - 5*z**2 - 4*z - 4*z**4 + 8*z**2 + 5*z**2 + 8*z**3 - 4 = 0 for z.
-1, 1
Let z(d) be the third derivative of -3*d**8/112 - 2*d**7/35 + d**6/20 + d**5/5 + d**4/8 + 27*d**2. What is r in z(r) = 0?
-1, -1/3, 0, 1
Let c = -18 - -31. Let p = c + -10. Determine v so that 3/2*v**p + 1/2*v - 3/2*v**2 - 1/2*v**4 + 0 = 0.
0, 1
Factor -b**5 + 5*b + 3*b - b**4 - 8*b.
-b**4*(b + 1)
Let y(r) = -r**2 + r. Let f = 2 - 5. Let b(i) = -2*i**2 + 2*i. Let o(a) = f*b(a) + 5*y(a). What is g in o(g) = 0?
0, 1
Let l = 3 - 2. Let y = 2 + -1. Find x such that -x**5 + l - x**4 - y = 0.
-1, 0
Solve 1/2*h - 1/6*h**2 - 1/3 = 0.
1, 2
Let v(m) = -m**4 + 1 - m**2 + m**2 - 2. Let f(s) = -s**5 + 5*s**4 + s**3 + s**2 + 6. Let x(c) = f(c) + 6*v(c). Factor x(y).
-y**2*(y - 1)*(y + 1)**2
Let s(r) be the third derivative of -r**6/90 - r**5/5 - 3*r**4/2 + r**3/6 + 5*r**2. Let c(x) be the first derivative of s(x). Factor c(n).
-4*(n + 3)**2
Let l(h) be the second derivative of -h**6/10 + 3*h**5/10 + h**4/4 - h**3 + 2*h. Factor l(f).
-3*f*(f - 2)*(f - 1)*(f + 1)
Let x be ((-1)/(-15))/(-12 - -13). Let i(g) be the first derivative of x*g**3 + 1/10*g**4 - 1 - 1/10*g**2 + 0*g. Factor i(s).
s*(s + 1)*(2*s - 1)/5
Let m = -27/2 + 14. Suppose -m*n**4 + 0*n**2 + 0*n**3 + 0*n + 0 = 0. What is n?
0
Let m(z) be the second derivative of z**7/12 - 4*z**6/15 + z**5/10 + 7*z**4/12 - 11*z**3/12 + z**2/2 + 11*z. Factor m(w).
(w - 1)**3*(w + 1)*(7*w - 2)/2
Let b(s) = s**3 - 6*s**2 - 8*s + 10. Let c be b(7). Factor -21*q + 6*q**2 + 10*q + 14*q + 3*q**c.
3*q*(q + 1)**2
Let a(s) = 20*s**3 + 5*s**2 - 5*s. Let l(g) = g**4 + g**3 + g**2 - g. Let d(x) = -a(x) + 5*l(x). Factor d(c).
5*c**3*(c - 3)
Let f(b) be the first derivative of b**3/15 - b**2/5 + b/5 - 22. Determine z so that f(z) = 0.
1
Solve -2/9*m**3 + 2/9*m - 2/9*m**2 + 2/9*m**4 + 0 = 0.
-1, 0, 1
Let v(n) = n + 9 + 10 - 5. Let h be v(-12). Determine q so that -2/7*q**3 + 8/7*q**h + 4/7 - 10/7*q = 0.
1, 2
Let w(y) be the second derivative of y**7/70 + y**6/10 + 9*y**5/50 - y**4/5 - 4*y**3/5 + 18*y. Factor w(t).
3*t*(t - 1)*(t + 2)**3/5
Suppose 0*p = 4*p - 4*a - 8, 0 = -5*p + 3*a + 12. Suppose -3*o**4 + 10*o**2 + 6 - 3*o**p - 6*o - o**2 + 21*o = 0. What is o?
-1, 2
Let p be 196/42 + (-2)/3. Factor -18/7*b**5 - 8/7*b**2 + 0*b - 6*b**p + 0 - 32/7*b**3.
-2*b**2*(b + 1)*(3*b + 2)**2/7
Let m = -6 - -6. Let j(o) be the first derivative of m*o + 0*o**3 - 1/5*o**2 + 0*o**5 + 1/5*o**4 - 1/15*o**6 + 1. Let j(p) = 0. What is p?
-1, 0, 1
Let o(x) = x**2 - 11*x + 10. Let y be o(10). Suppose 0 = 4*u - y - 8. Let 1/4*p**u + 1/4 + 1/2*p = 0. What is p?
-1
Factor -6*o**2 + 14*o + 9*o**3 - 2*o**4 + 16 - 40 + 5*o**4 - 50*o.
3*(o - 2)*(o + 1)*(o + 2)**2
Let c(l) be the third derivative of l**5/100 - 3*l**4/20 + l**3/2 + 9*l**2. Factor c(g).
3*(g - 5)*(g - 1)/5
Let a(l) = -7*l**4 - 8*l**3 + 13*l**2 - 7*l + 3. Let g(v) = -v**3 - v**2 - v + 1. Let f(z) = -5*a(z) + 15*g(z). Find w, given that f(w) = 0.
-2, 0, 2/7, 1
Let g(l) be the first derivative of l**6/4 - 3*l**4 - 3*l**3 + 21*l**2/4 + 9*l + 4. Determine r so that g(r) = 0.
-2, -1, 1, 3
Let y(s) be the first derivative of -s**7/1050 + s**6/200 - s**5/100 + s**4/120 - s**2 - 2. Let v(j) be the second derivative of y(j). Let v(u) = 0. What is u?
0, 1
Let p = -2 - -7. Let f = p - 1. Determine c, given that -c**f - 2*c + c**2 + c**2 + c**2 = 0.
-2, 0, 1
Let a(u) be the first derivative of 3 - 2/15*u**3 + 0*u + 1/10*u**4 + 0*u**2. Suppose a(w) = 0. Calculate w.
0, 1
Let u(x) be the first derivative of -x**4/18 - 2*x**3/9 - x**2/3 - 2*x/9 + 27. Factor u(c).
-2*(c + 1)**3/9
Factor 4*u**3 - 4*u - u**2 + 4*u - 7*u**2.
4*u**2*(u - 2)
Let n = 11 + -11. Let z(v) be the third derivative of 0 + 0*v**3 + 3*v**2 + 0*v - 1/120*v**6 - 1/60*v**5 + n*v**4. Suppose z(h) = 0. Calculate h.
-1, 0
Solve 36/5*z**3 + 2/5*z**5 + 0 + 14/5*z**4 + 16/5*z + 8*z**2 = 0.
-2, -1, 0
Let b(c) be the first derivative of -c**3/3 + 6*c**2 - 36*c - 4. Suppose b(o) = 0. What is o?
6
Let k be 0 - ((-5)/2 + (-8)/(-16)). Factor -1/2*q**k + 0 + q**3 + 0*q.
q**2*(2*q - 1)/2
Suppose -33/2*v + 5 + 9*v**2 + 5/2*v**3 = 0. What is v?
-5, 2/5, 1
Let m(t) be the first derivative of 0*t + 1/2*t**4 + t**2 - 5 - 4/3*t**3. Determine f, given that m(f) = 0.
0, 1
Let t(k) be the second derivative of 3*k + 1/12*k**4 + 0*k**2 - 1/60*k**5 + 0 - 1/30*k**6 + 1/9*k**3 - 1/126*k**7. Determine c, given that t(c) = 0.
-2, -1, 0, 1
Let m(f) = -f**2 + 2*f + 1. Let a be m(2). Let n = 5 - a. Factor -2*i**n + 3 + 6*i**3 - 3 - 2*i**3.
-2*i**3*(i - 2)
Solve -2/13*y**4 + 0 + 0*y - 2/13*y**5 + 0*y**2 + 0*y**3 = 0.
-1, 0
Let m = 1465 + -1463. Factor -1/5*q + 0 + 1/5*q**m + 1/5*q**3 - 1/5*q**4.
-q*(q - 1)**2*(q + 1)/5
Let l(y) be the second derivative of 3*y + 0*y**4 + 0*y**2 + 1/50*y**5 + 0 - 1/15*y**3. Factor l(f).
2*f*(f - 1)*(f + 1)/5
Let p(h) be the third derivative of 27*h**6/5 + 129*h**5/10 + 31*h**4/3 + 4*h**3 + 2*h**2 - 30. Find a such that p(a) = 0.
-3/4, -2/9
Suppose 14*a = 9*a. Let n(j) be the first derivative of 0*j + 2 + a*j**3 - j**2 + 1/2*j**4. Factor n(x).
2*x*(x - 1)*(x + 1)
Let z be ((-27)/(-12))/(6/4). Let f = -5 + 7. Factor 2 + k**3 - z*k**2 + 1/2*k**4 - f*k.
(k - 1)**2*(k + 2)**2/2
Suppose 2*u + 26 = 4*u - 4*c, -2*u - 5*c = 19. Factor 33*z**3 - 34*z**3 - u*z**2 - 2*z + 0*z.
-z*(z + 1)*(z + 2)
Let n(f) = f**2 + 5*f - 6. Let y be n(-6). Suppose 2*i + 2*i = y. Factor i + 1/3*j + 0*j**2 - 1/3*j**3.
-j*(j - 1)*(j + 1)/3
Let k(z) be the second derivative of z**7/105 - z**6/60 - z**5/30 + z**4/12 + z**2 + 3*z. Let s(g) be the first derivative of k(g). Factor s(y).
2*y*(y - 1)**2*(y + 1)
Let w(i) be the first derivative of 2/35*i**5 + 2/7*i - 4/21*i**3 + 1/7*i**4 - 1/21*i**6 - 1/7*i**2 + 5. What is t in w(t) = 0?
-1, 1
Let n(j) = -39 + 18 + 10 - j**2 + 9. Let d = 32 + -18. Let z(t) = 3*t**2 + 7. Let o(c) = d*n(c) + 4*z(c). Factor o(p).
-2*p**2
Suppose 3 = -u + 6. Let a = u + 2. Factor a*r - 5*r + 2*r**4 + 2 - 4*r**2.
2*(r - 1)**2*(r + 1)**2
Let b(k) = 13*k**3 - 12*k**2 + 9*k + 8. Let t(g) = 27*g**3 + 11 + 5*g + 14*g - 24*g**2 + 6. Let x(s) = -13*b(s) + 6*t(s). Let x(c) = 0. Calculate c.
-2/7, 1
Determine l so that -2/3*l - 1/3 - 1/3*l**2 = 0.
-1
Determine z so that 4/3*z + 1/6*z**2 + 8/3 = 0.
-4
Let i(o) be the second derivative of -o**6/540 + o**5/60 - o**4/18 + o**3/6 + o. Let g(p) be the second derivative of i(p). Factor g(s).
-2*(s - 2)*(s - 1)/3
Let s(o) be the second derivative of o**8/30240 - o**6/1080 + o**5/270 + o**4/4 - o. Let k(r) be the third derivative of s(r). Factor k(f).
2*(f - 1)**2*(f + 2)/9
Let d be (-80)/12 + 4/6. Let n(t) = t**2 + 7*t + 8. Let g be n(d). Find o, given that o**3 - 2*o**4 + g*o**3 + 0*o**3 - 3*o**5 + 2*o**2 = 0.
-1, -2/3, 0, 1
Let w = 10 - 24. Let a(u) = 3*u**3 + 9*u**2 - 3*u - 4. Let n(p) = -8*p**3 - 26*p**2 + 8*p + 12. Let c(i) = w*a(i) - 5*n(i). Factor c(o).
-2*(o - 2)*(o - 1)*(o + 1)
Let v(r) = -2*r**5 - 2*r**4 + 12*r**3 + 8*r**2 - 10*r + 6. Let u(y) = -9*y + y**2 + 1 + y**3 + y + 7*y. Let q(l) = 6*u(l) - v(l). Factor q(o).
2*o*(o - 1)**2*(o + 1)*(o + 2)
Let d be (-125)/45 - (5 + -10 + 2). Factor -2/9*r + d*r**3 + 0 - 2/9*r**4 + 2/9*r**2.
-2*r*(r - 1)**2*(r + 1)/9
Let b = 129 - 126. Let -b + 3/2*a**2 + 3/2*a = 0. What is a?
-2, 1
Suppose 3*a = -2*h - 2, -26 = -6*a + 3*a + 5*h. Factor 18/13*g**a + 4/13 + 2/13*g**4 + 10/13*g**3 + 14/13*g.
2*(g + 1)**3*(g + 2)/13
Let k(t) be the third derivative of t**8/112 - t**7/70 - t**6/40 + t**5/20 - 9*t**2. Factor k(q).
3*q**2*(q - 1)**2*(q + 1