Let f(r) = -r - 1. Let p(m) = 5*m + 5. Let t(w) = 9*f(w) + 2*p(w). Let a be t(-1). Find x such that -3/2*x - 3/2*x**4 + a + 3/2*x**3 + 3/2*x**2 = 0.
-1, 0, 1
Let n(s) be the third derivative of s**5/15 + s**4/6 - 4*s**3/3 + 19*s**2. Suppose n(a) = 0. Calculate a.
-2, 1
Let h be -1*((-2)/(-7) - 52/84). Determine w, given that -1/3*w**3 + 1/3*w + h - 1/3*w**2 = 0.
-1, 1
Let l(h) be the second derivative of -h**7/21 + 2*h**6/15 - h**5/8 + h**4/24 - 11*h. Let l(z) = 0. Calculate z.
0, 1/2, 1
Let c be 0 - (2 - 7) - 1. Determine z, given that 0*z + 8/3*z**c + 0 - 12*z**5 - 8/3*z**2 + 12*z**3 = 0.
-1, 0, 2/9, 1
Let b be (-13)/(-5) - 9/15. Factor -3*v**b + 2*v**2 + 2*v**2 + v.
v*(v + 1)
Let l(w) be the second derivative of -w**6/120 - 2*w**5/75 - w**4/120 + w**3/15 + w**2/2 + 3*w. Let y(j) be the first derivative of l(j). Factor y(k).
-(k + 1)**2*(5*k - 2)/5
Let r(z) be the second derivative of -z**6/40 + 3*z**5/4 - 75*z**4/8 + 125*z**3/2 - 1875*z**2/8 - 4*z. Factor r(p).
-3*(p - 5)**4/4
Suppose 4 + 2 = 3*a. Factor -6/7*p - 2/7*p**3 + 2/7 + 6/7*p**a.
-2*(p - 1)**3/7
Let u(w) be the second derivative of w**4/18 + 4*w**3/9 + 4*w**2/3 - 7*w. Factor u(j).
2*(j + 2)**2/3
Let u(j) be the first derivative of 2*j**3/9 + 5*j**2/3 - 7. Factor u(w).
2*w*(w + 5)/3
Let m(f) be the third derivative of -1/42*f**4 + 0*f - 2*f**2 + 0 + 1/210*f**5 + 1/21*f**3. Find s such that m(s) = 0.
1
Suppose -u = -7*u + u. Factor 3*a + u + 42*a**4 + 12*a**5 + 99/4*a**3 - 21*a**2.
3*a*(a + 2)**2*(4*a - 1)**2/4
Factor -4*o - o**5 - 2*o**3 + 5*o + 2*o**5.
o*(o - 1)**2*(o + 1)**2
Let v(i) = 2*i - 6. Let r be v(4). Solve 5*h**2 - h + r*h**2 - 6*h**2 = 0 for h.
0, 1
Let y(n) = -n**3 + 9*n - 4. Let g(d) = -d + 1. Let w(s) = 6*g(s) + y(s). Suppose w(a) = 0. Calculate a.
-1, 2
Let d be 18/40 - (-1)/(-4). Let u be (-4)/(-14) + 21/(-245). Factor -d*r**2 + 2/5*r - u.
-(r - 1)**2/5
Let l(n) = 35*n**2 + 13*n + 2. Let m(j) = 174*j**2 + 66*j + 10. Let k(v) = 14*l(v) - 3*m(v). Find s such that k(s) = 0.
-1/4
Let k be 10 + -11 + (-7)/(-1). Solve -k*c**3 - c**4 - 3*c**4 + c**4 + 3*c**5 = 0.
-1, 0, 2
Let u(k) = k**3 + 3*k**2 - 4*k - 8. Let g be u(-3). Let j(w) be the first derivative of 1/4*w**g - 2/5*w**5 + 0*w**3 - 3 + 1/6*w**6 + 0*w**2 + 0*w. Factor j(n).
n**3*(n - 1)**2
Factor 2*w**2 + 0 - 3/2*w - 2*w**4 + w**3 + 1/2*w**5.
w*(w - 3)*(w - 1)**2*(w + 1)/2
Suppose -2*n = -4*n. Determine b, given that -1/3*b**5 + 1/3*b**2 + 0 + 1/3*b**3 - 1/3*b**4 + n*b = 0.
-1, 0, 1
Let z(o) be the second derivative of o**5/80 - 3*o. Find t, given that z(t) = 0.
0
Factor 1/4*z**2 - 5/2*z + 25/4.
(z - 5)**2/4
Let b(p) be the second derivative of 0 + 1/2*p**2 + 0*p**3 - 1/12*p**4 + p. Let b(t) = 0. What is t?
-1, 1
Let j = 18 + -14. Factor d**j + 4 - 2*d**2 - 2*d**3 + d - d**2 + 3*d.
(d - 2)**2*(d + 1)**2
Let q(a) be the third derivative of a**6/480 - a**5/80 + a**3/6 - 10*a**2. Suppose q(y) = 0. What is y?
-1, 2
Let q(f) be the first derivative of -1/42*f**6 + 1/14*f**4 + 0*f**5 + 0*f**3 - 1/14*f**2 - 5 + 0*f. Factor q(x).
-x*(x - 1)**2*(x + 1)**2/7
Factor -1/2*x**2 - 1/4*x**3 + 0 + 0*x.
-x**2*(x + 2)/4
Let q = 54/175 - 4/175. Let l = -1/274 + 555/1918. Factor -l*k**3 - 2/7 + 2/7*k**2 + q*k.
-2*(k - 1)**2*(k + 1)/7
Factor -4/3 + 1/3*v**4 - v**2 + 2/3*v**3 - 8/3*v.
(v - 2)*(v + 1)**2*(v + 2)/3
Let z(b) be the second derivative of -15*b**7/14 - 13*b**6/5 - 9*b**5/20 + 3*b**4 + 2*b**3 + b. Let z(o) = 0. What is o?
-1, -2/5, 0, 2/3
Let h be (-122)/(-140) + (-32)/56. Let f(q) be the second derivative of q + h*q**2 + 1/20*q**4 + 1/5*q**3 + 0. Factor f(u).
3*(u + 1)**2/5
Let b be -1 + 3 + 384/(-216). Determine t so that -b*t**2 - 4/9 + 2/3*t = 0.
1, 2
Let a(q) be the first derivative of -q**5/25 + q**3/15 + 6. Let a(l) = 0. Calculate l.
-1, 0, 1
Determine n, given that -4/5*n + 4/5*n**3 - 2/5*n**4 + 2/5 + 0*n**2 = 0.
-1, 1
Let n(m) = m**4 + m + 1. Let q(k) = k**4 + 16*k**3 + 16*k**2 - 3*k - 3. Let j(a) = 3*n(a) + q(a). Determine d, given that j(d) = 0.
-2, 0
Factor 1/4*i**3 + 1/4 + 3/4*i + 3/4*i**2.
(i + 1)**3/4
Let i(d) be the second derivative of -d**8/672 + d**7/840 - d**2/2 + 2*d. Let b(y) be the first derivative of i(y). Factor b(g).
-g**4*(2*g - 1)/4
Suppose 2 = 2*a + 5*y - 6, -a = y - 4. Let d(k) = -5*k**3 - k**2 + 5*k + 5. Let l(i) = -i**3 + i + 1. Let f(u) = a*l(u) - d(u). Factor f(c).
(c - 1)*(c + 1)**2
Suppose 2*i = i. Solve i*b - 1/4*b**2 + 3/4*b**3 + 1/4*b**5 + 0 - 3/4*b**4 = 0.
0, 1
Let i(o) be the third derivative of -5*o**8/1008 + 4*o**7/315 - o**6/360 - o**5/90 - 4*o**2. Suppose i(p) = 0. Calculate p.
-2/5, 0, 1
Let h(b) be the third derivative of -b**7/560 + 3*b**6/160 - 13*b**5/160 + 3*b**4/16 - b**3/4 - b**2. Let h(g) = 0. What is g?
1, 2
Let q(i) be the second derivative of 16*i**5/25 + 8*i**4/3 + 34*i**3/15 + 4*i**2/5 - 5*i. Factor q(v).
4*(v + 2)*(4*v + 1)**2/5
Let x(u) be the third derivative of -1/1050*u**7 + 0 + 1/150*u**5 + 0*u - 1/30*u**3 + 0*u**6 - 4*u**2 + 0*u**4. Factor x(l).
-(l - 1)**2*(l + 1)**2/5
Let h(y) be the first derivative of -14*y**5/15 - 3*y**4/2 - 4*y**3/9 + 2. Let h(n) = 0. What is n?
-1, -2/7, 0
Let q(u) = 12*u**3 + 46*u**2 + 24*u + 6. Let x(o) = -4*o**3 - 15*o**2 - 8*o - 2. Let b(n) = 5*q(n) + 16*x(n). Factor b(c).
-2*(c + 1)**2*(2*c + 1)
Let h = 20 + -20. Factor 3*q + 3/2*q**2 + h - 3/2*q**3.
-3*q*(q - 2)*(q + 1)/2
Let z(a) be the third derivative of -5*a**8/84 - 2*a**7/105 + 4*a**6/3 + 8*a**5/15 - 40*a**4/3 - 32*a**3/3 - 43*a**2. Solve z(j) = 0 for j.
-2, -1/5, 2
Factor -2*g**4 + 4*g**2 - 4*g**3 - 2*g**4 + 120*g - 116*g.
-4*g*(g - 1)*(g + 1)**2
Let v(f) be the second derivative of -f**6/10 - 9*f**5/10 - 3*f**4 - 5*f**3 - 9*f**2/2 + 4*f. Suppose v(x) = 0. Calculate x.
-3, -1
Let w(l) = -l**3 - l**2 - l + 3. Let q be w(0). Factor b**5 + q*b**4 + 0*b**5 - 3*b**4 - b**3.
b**3*(b - 1)*(b + 1)
Let u(r) be the first derivative of 9*r**4/8 - 7*r**3/2 + 4*r**2 - 2*r - 14. Factor u(t).
(t - 1)*(3*t - 2)**2/2
Let m(l) = -2*l**3 + 24*l**2 + 2*l. Let u(t) = -t**3 - t**2 - t. Let o(z) = m(z) + 6*u(z). Factor o(x).
-2*x*(x - 2)*(4*x - 1)
Let g(l) be the third derivative of 36*l**8/7 - 48*l**6/5 - 124*l**5/15 - 19*l**4/6 - 2*l**3/3 - 4*l**2. Suppose g(k) = 0. Calculate k.
-1/2, -1/6, 1
Let d(h) = -16*h**3 + 4*h**2 + 6*h + 6. Let t(q) = 5*q**3 - q**2 - 2*q - 2. Let o(u) = 3*d(u) + 10*t(u). Factor o(j).
2*(j - 1)*(j + 1)**2
Let f(a) be the second derivative of -a**4/6 - a**3 - 2*a**2 + 11*a. Determine m so that f(m) = 0.
-2, -1
Let s(h) = 54*h**4 + 104*h**3 + 14*h**2 - 36*h. Let w(c) = -11*c**4 - 21*c**3 - 3*c**2 + 7*c. Let l(m) = 3*s(m) + 16*w(m). Factor l(b).
-2*b*(b + 1)**2*(7*b - 2)
Let d be (1/(-4))/(29/8 - 4). Factor 1/3 - d*b + 1/3*b**2.
(b - 1)**2/3
Let t be -3 - 2/(2/2). Let y = t + 8. Factor 0*d + 2/11*d**y + 0 + 0*d**2.
2*d**3/11
Let f(k) be the first derivative of -k**7/420 + k**5/20 + k**4/6 - 4*k**3/3 - 4. Let b(z) be the third derivative of f(z). Suppose b(o) = 0. What is o?
-1, 2
Let g(b) = -3. Suppose y + 0*y + 1 = 0. Suppose -3*s = -4*s + 1. Let l(h) = -h**2 - h - 1. Let k(c) = s*g(c) + y*l(c). Solve k(i) = 0.
-2, 1
Let u(v) = v**2 - 6*v + 3. Let w(f) = f - 2. Let p be w(8). Let n be u(p). Factor 4*y**3 + y**n - 3*y**3 - 2*y**5.
-2*y**3*(y - 1)*(y + 1)
Let c(z) be the third derivative of -z**11/1829520 + z**9/166320 - z**7/27720 + z**5/20 - 5*z**2. Let i(o) be the third derivative of c(o). Factor i(t).
-2*t*(t - 1)**2*(t + 1)**2/11
Let p(q) be the first derivative of -9/2*q**6 - 3*q**3 + 0*q + 3*q**2 - 63/4*q**4 - 15*q**5 - 4. Factor p(k).
-3*k*(k + 1)**3*(9*k - 2)
Let k(i) = i**3 - 6*i**2 + 4*i + 1. Let b be k(5). Let s = 8 + b. Factor -2*a**s + 0*a**5 + 2*a**5 - 4*a**5.
-2*a**4*(a + 1)
Let u(s) = s**3. Let v(q) = 1336*q**3 - 726*q**2 + 132*q - 8. Let c(x) = 15*u(x) - 3*v(x). Determine i so that c(i) = 0.
2/11
Let x(j) be the third derivative of -1/70*j**7 - 1/8*j**4 + 0*j**3 + 0 + 0*j + j**2 - 3/20*j**5 - 3/40*j**6. Find i, given that x(i) = 0.
-1, 0
Let j = 278 - 275. What is m in 0 + 2/7*m**5 + 12/7*m**j + 8/7*m**2 - 10/7*m**4 - 16/7*m = 0?
-1, 0, 2
Let h(l) be the first derivative of -2*l - 2/3*l**3 - 2*l**2 + 2. Let h(b) = 0. What is b?
-1
Let h(r) be the first derivative of 4 + 3*r**2 - 10/3*r**3 + 4*r. Factor h(i).
-2*(i - 1)*(5*i + 2)
Let f(z) = 6*z**3 - z**2 + 