Let i = -10 + 16. Let m(r) = i*q(r) + 3*x(r). Suppose m(w) = 0. Calculate w.
-1, 1
Let l(n) be the third derivative of n**5/45 - 2*n**4/9 + 8*n**3/9 - 9*n**2. Let l(j) = 0. Calculate j.
2
Let j(u) = u**2 + 4*u - 12. Let v be j(-6). What is y in -4*y**2 - y**2 - 2*y + 7*y**2 + v*y = 0?
0, 1
Suppose -4*t - 4*z = t - 30, 3*z - 30 = -5*t. Factor -4*h**3 - t*h**2 - 5 - 3*h**3 - 6*h + 5*h**3 + 3.
-2*(h + 1)**3
Let n(t) be the second derivative of -t**7/189 - t**6/45 + t**5/90 + t**4/18 - 18*t. Determine z so that n(z) = 0.
-3, -1, 0, 1
Let b(x) = x**3. Suppose -3*i + 3*d + 6 = -6*i, 5*d = 0. Let q(z) = -15*z**3 - 5*z**2 - z. Let g = 18 - 40. Let n(f) = g*b(f) + i*q(f). Factor n(a).
2*a*(a + 1)*(4*a + 1)
Suppose -2*v - 20 + 6 = 0. Let s be 10/35 - 33/v. Solve 2/9*a + 4/9*a**4 - 4/9*a**2 - 2/9*a**s + 0 + 0*a**3 = 0 for a.
-1, 0, 1
Let m(v) = v**3 + v**2 + v - 1. Let h(y) = 4*y**4 + 12*y**3 - 12*y**2 - 4*y + 8. Let f(t) = h(t) - 4*m(t). Determine l so that f(l) = 0.
-3, -1, 1
Determine p, given that 27/5*p**4 + 0*p + 0 + 3/5*p**5 + 12*p**2 + 72/5*p**3 = 0.
-5, -2, 0
Find r, given that -10*r**3 + 11*r**3 + 3*r**4 - 6*r**2 + 3 - r**3 = 0.
-1, 1
Let d(a) be the first derivative of 2*a**3/33 + 3*a**2/11 - 8*a/11 + 29. Factor d(s).
2*(s - 1)*(s + 4)/11
Let i(z) be the second derivative of 1/66*z**4 + 0 + 1/165*z**6 + 0*z**2 + 0*z**3 + 3*z - 1/55*z**5. Suppose i(w) = 0. Calculate w.
0, 1
Let t be (-8)/9*(-42)/56. Let o be (2/(-36))/(2/(-16)). Let 2*s**2 - t*s - o = 0. What is s?
-1/3, 2/3
Let g(r) = r. Let z be g(3). Let w = 1 + z. Factor -w*y + 2*y**2 + y + 2*y + 2 + 5*y.
2*(y + 1)**2
Let n(p) = -p**3 + 6*p**2 + 6*p + 10. Let y be n(7). Factor 24*i**4 - 9*i**5 - 19*i**3 + i**y + 2*i + i.
-3*i*(i - 1)**3*(3*i + 1)
Let a(o) = -4*o + 16. Let l be a(3). Let v(y) be the third derivative of -1/108*y**l + 0*y - 1/135*y**6 + 2*y**2 + 0*y**3 + 0 + 1/54*y**5. Factor v(t).
-2*t*(t - 1)*(4*t - 1)/9
Let r be 3 + 4/(-3 - -5). Suppose -i - 18 = -4*p, -3*p + 10 = -r*i + p. Factor 2 + 0*s**i + s**3 + 2*s**2 + 7*s - 4*s**3.
-(s - 2)*(s + 1)*(3*s + 1)
Suppose -2*t = -6*t + 84. Let o be (-7)/6*(-12)/t. Suppose 0*p + 0 - o*p**3 - 2/3*p**5 + 0*p**2 + 4/3*p**4 = 0. What is p?
0, 1
Let x(q) be the third derivative of q**7/1050 + q**6/1200 - q**5/600 - 8*q**2. What is f in x(f) = 0?
-1, 0, 1/2
Let n(b) = -b**2 + 6*b + 7. Let p be n(6). Let u be p/4*(-4)/(-14). What is i in 3/4*i**2 - u*i - 1/4 = 0?
-1/3, 1
Let x(l) = 2*l**3 - 13*l**2 + 6*l. Let r be x(6). Find s, given that 2/3*s + 2/3*s**2 + r - 13/6*s**3 + 5/6*s**4 = 0.
-2/5, 0, 1, 2
Suppose 2*a - 4 = 6. Solve x**4 - 3*x**4 - x**3 + 2*x**2 - x**5 + 2*x**a = 0 for x.
-1, 0, 1, 2
Let q(p) be the third derivative of -p**7/70 + p**6/8 - 3*p**5/10 - p**4/2 + 4*p**3 - 2*p**2. Factor q(k).
-3*(k - 2)**3*(k + 1)
Let x = -362/1354605 - -3/1843. Let c(a) be the third derivative of -x*a**7 + 0 + 0*a**3 + 1/84*a**4 - 1/420*a**6 + 2*a**2 + 0*a + 1/210*a**5. Factor c(r).
-2*r*(r - 1)*(r + 1)**2/7
Suppose -3*k - 1 = g - 2*g, -2*g + 4*k = 2. Let n(p) = -3*p - 13. Let d be n(g). Factor 0 + 0*z + 2/5*z**d.
2*z**2/5
Let s(x) = -57*x**5 - 54*x**4 - 18*x**3 - 2*x**2 - 3. Let f(y) = y**5 + 1. Let g(z) = 6*f(z) + 2*s(z). Factor g(o).
-4*o**2*(3*o + 1)**3
Let 82/13*k - 32/13*k**4 - 82/13*k**2 - 12/13 - 16*k**3 = 0. Calculate k.
-6, -1, 1/4
Factor 0*s**3 + 0*s + 2/5 - 4/5*s**2 + 2/5*s**4.
2*(s - 1)**2*(s + 1)**2/5
Factor 0*w**3 + 0*w + 0 + 0*w**2 - 1/4*w**5 - 1/2*w**4.
-w**4*(w + 2)/4
Let s(k) be the first derivative of -4*k**5 + 0*k**2 + 0*k + 1 - 16/3*k**3 - 8*k**4 - 2/3*k**6. Factor s(m).
-4*m**2*(m + 1)*(m + 2)**2
Let r be (0 - 1)/((-2)/12). Let v be (-9)/(-6)*8/r. Solve 5*u**2 + 0*u**2 - 4*u**v = 0 for u.
0
Let p(d) = 4*d - 20. Let h be p(5). Factor -1/4*s + 0*s**2 + h + 1/4*s**3.
s*(s - 1)*(s + 1)/4
Let -6 - 19*r**2 - 19*r**2 + 40*r**2 - 4*r = 0. What is r?
-1, 3
Let x be 225/63 + 3/7. Factor -5/3*h**3 + 7/6*h**2 + 2/3*h + 1/2*h**x - 2/3.
(h - 2)*(h - 1)**2*(3*h + 2)/6
Suppose -x + c - 2*c = -33, 2*c = 5*x - 130. Let o = x - 55/2. Factor 1/2*n + 0 + o*n**2.
n*(n + 1)/2
Suppose g - 2*g = -l - 1, -29 = -l - 5*g. Determine f so that 0*f**3 - f**2 + f**l + 2*f**3 + 0*f**3 - 3*f**3 + f = 0.
-1, 0, 1
Let u(j) = -j**3 + 9*j**2 + 9*j + 13. Let r be u(10). Solve -3*i**2 - 3*i**4 - 3*i + 3*i - 4*i**3 - 2*i**r = 0 for i.
-1, 0
Let c(a) be the second derivative of -3*a - a**3 - 3/2*a**2 + 0 - 1/4*a**4. Let c(r) = 0. Calculate r.
-1
Let v(g) be the third derivative of 0 + 0*g + 0*g**6 + 1/150*g**5 - 1/525*g**7 + 0*g**3 - 3*g**2 + 1/120*g**4 - 1/1680*g**8. Suppose v(f) = 0. What is f?
-1, 0, 1
Suppose -4/5*p + 28/5*p**4 + 49/5*p**5 - 9*p**3 + 0 - 28/5*p**2 = 0. What is p?
-1, -2/7, 0, 1
Let n(x) be the second derivative of -2*x**4/3 - x**3/3 + 3*x**2 - 3*x. Let i(l) = -l**2 + 1. Let r(f) = -6*i(f) + n(f). Suppose r(t) = 0. Calculate t.
-1, 0
Let g(y) be the second derivative of -y**7/14 + 3*y**5/10 - y**3/2 - 10*y. Factor g(x).
-3*x*(x - 1)**2*(x + 1)**2
Suppose 5*r + 0*f - 7 = -3*f, 2*r - f - 5 = 0. Suppose -r*g = -o + 13, -5*o - 13 = -o + 5*g. Factor -1/4*w**2 + 1/4*w**4 - 1/4*w**5 + 1/4*w**o + 0 + 0*w.
-w**2*(w - 1)**2*(w + 1)/4
Let v(m) be the second derivative of -1/30*m**6 + 0 + 1/12*m**4 + 0*m**2 - 1/20*m**5 + 1/6*m**3 - 3*m. Factor v(n).
-n*(n - 1)*(n + 1)**2
Let x be ((-84)/232)/((-1)/(-4)). Let m = 3/58 - x. Factor -m*k + 1/2*k**2 + 1.
(k - 2)*(k - 1)/2
Let y = -3 + 5. Factor -d + d - 2*d**2 - d + 3*d**y.
d*(d - 1)
Let k(p) be the first derivative of -5*p**3 - 6*p**2 + 6*p**3 + 3 + p**3 - p**3 + 12*p. Determine m, given that k(m) = 0.
2
Let o(w) = -w**2 + 5*w - 4. Let l = -6 + 10. Let i be o(l). Suppose i - 2/7*a**3 + 0*a + 0*a**2 = 0. Calculate a.
0
Let p(g) be the third derivative of -g**5/120 + g**4/16 - g**3/6 + 5*g**2 - 2. Factor p(m).
-(m - 2)*(m - 1)/2
Let o(m) be the first derivative of 6*m**6 - 84*m**5/5 - 2*m**4 + 80*m**3/3 - 16*m**2 + 5. Solve o(b) = 0 for b.
-1, 0, 2/3, 2
Let o(t) be the first derivative of 0*t - 2/3*t**3 + 3 + t**2. Factor o(m).
-2*m*(m - 1)
Let s(u) = -u**4 + 3*u**3 - 3*u**2 + 7*u - 6. Let o(n) = n - 1. Suppose 0*r + r + 1 = 0. Let h(m) = r*s(m) + 6*o(m). Factor h(l).
l*(l - 1)**3
Let z(s) = -3*s**5 - s**4 + 7*s**3 + 6*s**2 + s. Let k(v) = 4*v**5 - 8*v**3 - 6*v**2 - 2*v. Let t(o) = 5*k(o) + 6*z(o). Solve t(p) = 0.
-1, 0, 1, 2
Suppose 7*b = 3*b - 4*n + 12, -5*b + 3*n + 31 = 0. Factor 7*p**4 - 4*p + 5*p**b - 4*p**2 + 17*p**3 - 25*p**4 + 4*p**2.
p*(p - 2)*(p - 1)**2*(5*p + 2)
Let 81*j**4 - 81*j**4 + j**3 - j**5 = 0. What is j?
-1, 0, 1
Let t(g) = 4*g**4 - 8*g**3 - 4*g + 4. Let a(b) = 4*b**4 - 8*b**3 - b**2 - 5*b + 5. Let m(z) = -4*a(z) + 5*t(z). Suppose m(p) = 0. Calculate p.
0, 1
Factor 12 - 10*q**3 - 3*q**4 + 12*q - 18*q**3 + 3*q**2 - 12*q**2 + 16*q**3.
-3*(q - 1)*(q + 1)*(q + 2)**2
Let 4/5*g - 3/5*g**2 + 0 - 1/5*g**3 = 0. What is g?
-4, 0, 1
Let q be (1 + (-10)/8)/(-1). Solve -1/4*b**2 - q + 1/2*b = 0.
1
Suppose m = 4*h - 8*h + 2, -4*h + 4*m - 8 = 0. Suppose 2*b - 4*b = h. Solve -1/4*c - 1/2*c**4 + b*c**3 + 1/4*c**5 + 0 + 1/2*c**2 = 0.
-1, 0, 1
Let y = -127/3 + 383/9. Suppose -2/9*q**4 + 8/9*q - 4/3*q**2 - y + 8/9*q**3 = 0. What is q?
1
Let w(a) be the second derivative of 0*a**2 + 2*a + 0 + 3/4*a**4 - 1/3*a**3 - 7/20*a**5. Determine v, given that w(v) = 0.
0, 2/7, 1
Let l(z) be the second derivative of 3*z**5/4 + 2*z**4 - 2*z**3 + 3*z. Factor l(r).
3*r*(r + 2)*(5*r - 2)
Let o = 7 + -4. Factor -2*j**o + j - 4*j + 4*j**2 + j.
-2*j*(j - 1)**2
Let t(b) = -9*b**3 + 33*b**2 - 44*b + 20. Let w(y) = -4*y**3 + 16*y**2 - 22*y + 10. Let l(p) = 2*t(p) - 5*w(p). Factor l(d).
2*(d - 5)*(d - 1)**2
Let d(k) = -k**2. Let q(j) = -j**3 + 9*j**2 - j. Let v(w) = -35*d(w) - 5*q(w). Let v(i) = 0. What is i?
0, 1
Let r(y) = -5*y**2 - 13*y + 20. Let w(o) = -15*o**2 - 38*o + 60. Let j(m) = -7*r(m) + 2*w(m). Find z such that j(z) = 0.
-4, 1
Let s(n) be the second derivative of -n**4/18 + 2*n**3/3 + 7*n**2/3 - 16*n. Factor s(g).
-2*(g - 7)*(g + 1)/3
Suppose -2*v = -4*g - 14, 3*g = -3*v - 0*g + 12. What is d in -2*d**2 - d + d**4 - 14*d**5 + 3*d**3 + 13*d**v - d**3 + 1 = 0?
-1, 1
Let h(i) be the second derivative of -2*i + 1/50*i**5 + 0*i**3 - 2/75*i**6 + 0*i**4 + 0*i**2 + 0. Solve h(r) = 0.
0, 1/2
Let j(g) be the first derivative of 1/36*g**4 