f be p(-6). Let w be -2 + -2 + 5 - f. Solve 1/2*r**w + 0 + 0*r - 1/2*r**4 + 0*r**2 = 0.
0, 1
Let g(h) be the first derivative of -h**5/20 - h**4/2 - 2*h**3 - 4*h**2 - 4*h + 9. Factor g(c).
-(c + 2)**4/4
Solve 24/5 + 237/5*r - 15*r**3 + 114*r**2 = 0 for r.
-1/5, 8
Let z = -7 - -17. Let g be 3/5 - (-14)/z. Solve 2*w - 4*w**g - 2*w**2 + 4*w**2 = 0 for w.
0, 1
Let f(m) be the first derivative of -m**8/9240 - m**7/1540 - m**6/990 - m**3 - 3. Let h(y) be the third derivative of f(y). Factor h(l).
-2*l**2*(l + 1)*(l + 2)/11
Let s(a) be the first derivative of -a**2 - 1 + 7/4*a**5 + 37/8*a**4 + 0*a + 1/3*a**3. Solve s(g) = 0.
-2, -2/5, 0, 2/7
Factor 0*t + 32/5*t**3 - 16/5*t**2 - 12/5*t**4 + 0.
-4*t**2*(t - 2)*(3*t - 2)/5
Let g = 14 + -14. Find a, given that -2*a**3 + 8*a**3 + g*a**4 + a**4 - 5*a**3 = 0.
-1, 0
Let f(j) be the first derivative of j**7/105 + j**6/60 - j**5/15 + 9*j**2/2 - 4. Let c(n) be the second derivative of f(n). Factor c(k).
2*k**2*(k - 1)*(k + 2)
Let a(y) = 4*y**2 - y - 1. Let k be a(-1). Suppose k*m - 60 = -20. Determine c so that -m*c - 9*c**3 + 21*c**2 - 7*c + 3*c - 2*c + 4 = 0.
2/3, 1
Let b = -2 + 3. Let n(i) = -i**4 - i + 1. Let p(f) = 2*f**4 - 2*f**3 - f**2 + 3*f - 3. Let t(k) = b*p(k) + 3*n(k). Solve t(z) = 0.
-1, 0
Let f(x) be the third derivative of -x**6/360 - x**5/180 - 10*x**2. Let f(n) = 0. What is n?
-1, 0
Let c(i) = i + 10. Let y be c(-6). Let m(q) be the second derivative of 0 + 7/48*q**4 + 1/2*q**2 + y*q - 2/3*q**3. Factor m(x).
(x - 2)*(7*x - 2)/4
Let i(b) be the second derivative of b**6/120 + b**5/60 + b**2/2 - b. Let z(a) be the first derivative of i(a). Factor z(m).
m**2*(m + 1)
Let p(g) = -2*g**2 - g - 4. Suppose 0 = -0*v + 3*v - 36. Let a(w) = -v + 12 + w. Let s(z) = -5*a(z) + p(z). Factor s(j).
-2*(j + 1)*(j + 2)
Let x(y) be the second derivative of 4/75*y**6 + 0*y**2 - 2/105*y**7 - 1/25*y**5 + 0 + 2*y + 0*y**3 + 0*y**4. Factor x(s).
-4*s**3*(s - 1)**2/5
Let w(r) = -r. Let d(q) = -7*q + 3. Let y(p) = d(p) - 6*w(p). Let o be y(0). What is j in 2/5*j - 4/5 + 4/5*j**2 - 2/5*j**o = 0?
-1, 1, 2
Let n(u) = 38*u**2 + 20*u - 29. Let o(d) = 10 + 2 - 4 - 13*d**2 - 7*d + 2. Let b(k) = 4*n(k) + 11*o(k). Suppose b(h) = 0. What is h?
-1, 2/3
Let u = -68 + 68. Let t(k) be the third derivative of u + 1/9*k**3 - 3*k**2 - 1/630*k**7 + 0*k + 1/24*k**4 - 1/180*k**5 - 1/120*k**6. Solve t(w) = 0 for w.
-2, -1, 1
Let h be (-81)/(-18)*((-16)/6)/(-4). Suppose 0 + 2/7*l - 8/7*l**h + 6/7*l**2 = 0. What is l?
-1/4, 0, 1
What is j in 0*j - 4/3*j**2 + 0 - 2/3*j**3 + 2/3*j**4 = 0?
-1, 0, 2
Let v = 383433/1900 + -27/475. Let p = 203 - v. Determine a, given that p*a**2 - a**3 + 1/4*a**4 + 0 - 1/2*a = 0.
0, 1, 2
Let b = -2 - -4. Solve 2*h**4 - h**2 + 0*h**3 - 6*h**3 + b*h**3 + 3*h**2 = 0 for h.
0, 1
Let c(j) be the first derivative of j**6/18 - j**4/6 + j**2/6 + 3. Factor c(i).
i*(i - 1)**2*(i + 1)**2/3
Suppose -2*m - 3 = -11. Factor -1/2*w + 1/2*w**2 + 0 + 1/2*w**3 - 1/2*w**m.
-w*(w - 1)**2*(w + 1)/2
Let m(k) be the first derivative of -3 - 1/16*k**4 - 1/20*k**5 + 1/8*k**2 + 1/12*k**3 + 0*k. Factor m(c).
-c*(c - 1)*(c + 1)**2/4
Let c = -19 - -23. Suppose c*a = 3*a. Let a + l**2 + 7/5*l**3 - 2/5*l = 0. Calculate l.
-1, 0, 2/7
Let v be (-8)/3*(-15)/10. Let s(h) be the third derivative of 0*h**3 + 2*h**2 + 0*h + 0 + 0*h**v - 1/270*h**5. Find x such that s(x) = 0.
0
Suppose 3*a + 11 = -4. Let l be ((-24)/(-30))/((-2)/a). Let -2*o**l + 18/7*o - 4/7 = 0. What is o?
2/7, 1
Let m(z) be the first derivative of 3/2*z**2 + 3 + 6*z - 2*z**3 - 3/4*z**4. Find d, given that m(d) = 0.
-2, -1, 1
Suppose 2*j - 4*j - 12 = 0. Let g(l) = l**2 + l. Let y(v) = 3*v**2 + 3*v - 1. Let u(f) = j*y(f) + 15*g(f). Factor u(k).
-3*(k - 1)*(k + 2)
Suppose -2*v + 6 = -2. Let b be 1*v*(-20)/(-25). Factor 12/5*f**2 + b - 24/5*f - 2/5*f**3.
-2*(f - 2)**3/5
Let x(y) be the second derivative of -y**7/630 - y**6/180 - y**5/180 - y**2/2 - 4*y. Let j(d) be the first derivative of x(d). Factor j(o).
-o**2*(o + 1)**2/3
Let v(f) be the first derivative of -f**5/15 + 5*f**4/12 - 4*f**3/9 - 30. Factor v(p).
-p**2*(p - 4)*(p - 1)/3
Suppose 3*r - 2*x - 12 = 0, 4*x + 9 = x. Let -2*q - 2*q**2 - 1 - q**2 + r*q**3 + 3 + q**2 = 0. What is q?
-1, 1
Find g, given that 0 - 2/5*g**2 + 0*g = 0.
0
Let z be (-2)/(2/(-12)*-4). Let b = z - -7. Factor -2/5*w**b - 4/5*w**3 + 0*w - 2/5*w**2 + 0.
-2*w**2*(w + 1)**2/5
Let n(o) = -11*o + 23. Let w be n(2). Factor 1/2*m**3 - w + 5/2*m - 2*m**2.
(m - 2)*(m - 1)**2/2
Let y(k) be the second derivative of -k**5/70 - k**4/84 + k**3/21 + k**2/14 - 4*k + 2. What is v in y(v) = 0?
-1, -1/2, 1
Let k be (0 + 4)*(0 - -1). Determine n, given that 27 + 2*n**4 + n**k - 17*n - 55*n - 24*n**3 + 66*n**2 = 0.
1, 3
Suppose -4*x = -15*x + x. Let k(q) be the first derivative of 1/14*q**4 - 4/21*q**3 + x*q + 0*q**2 + 3. Factor k(t).
2*t**2*(t - 2)/7
Factor -1/3*m**4 + 1/3*m**2 + 1/3*m - 1/3*m**3 + 0.
-m*(m - 1)*(m + 1)**2/3
Let c = -3 + 8. Let y be (-2)/c + (-22)/(-55). Find t, given that 0*t - 2/3*t**4 + 7/3*t**5 - 7/3*t**3 + 2/3*t**2 + y = 0.
-1, 0, 2/7, 1
Let k(m) = -m**3 - 8*m**2 + 8*m - 7. Let s be k(-9). What is c in 3*c - s*c + 2 + c**2 - 2 = 0?
-1, 0
Let x(u) = u**2 + 7*u + 8. Let g be x(-6). Let s**3 + s**2 - 2*s**3 + s**g + 2*s**3 = 0. What is s?
-2, 0
Let d = -99 - -397/4. Let y(i) be the second derivative of d*i**2 + 0 + 1/8*i**3 + 1/48*i**4 + 4*i. Factor y(m).
(m + 1)*(m + 2)/4
Let a(h) be the second derivative of h**4/8 + h**3/2 - 2*h - 11. Factor a(m).
3*m*(m + 2)/2
Let d(k) = 7*k**3 - k + 6. Let j(i) = -6*i**3 + i - 5. Let t(c) = -5*d(c) - 6*j(c). Find w, given that t(w) = 0.
-1, 0, 1
Let v be 5 + 6/(-2) + 0. Let p(o) = -o**3 + 5*o**2 - 3*o + 3. Let g be p(4). Factor 4*k**2 - 6*k**2 - g*k**5 - 2*k**v + 16*k**4 - 3*k**5 - 2*k**3.
-2*k**2*(k - 1)**2*(5*k + 2)
Let a(c) = -5*c**4 - 61*c**3 + 5*c**2 + 85*c - 11. Let t(r) = r**4 + 10*r**3 - r**2 - 14*r + 2. Let j(g) = -6*a(g) - 39*t(g). Let j(k) = 0. Calculate k.
-2, 1/3, 1
Let k(r) be the third derivative of -r**10/151200 + r**9/60480 + r**5/15 - 2*r**2. Let j(m) be the third derivative of k(m). What is u in j(u) = 0?
0, 1
Let h(m) be the second derivative of -1/42*m**7 + 1/15*m**6 + 0*m**4 + 0*m**3 - 5*m + 0 + 0*m**2 - 1/20*m**5. Factor h(t).
-t**3*(t - 1)**2
Let t(m) be the second derivative of 9*m**5/130 - m**4/39 - 12*m**3/13 + 8*m**2/13 - 43*m. Factor t(g).
2*(g - 2)*(g + 2)*(9*g - 2)/13
Let z(k) be the second derivative of -k**7/168 - k**6/30 - k**5/20 + 2*k. Factor z(p).
-p**3*(p + 2)**2/4
Factor -14/3*t**3 + 2/3*t**4 - 34/3*t + 34/3*t**2 + 4.
2*(t - 3)*(t - 2)*(t - 1)**2/3
Suppose 11*o - 7*o = -60. Let i = -12 - o. Find w such that 0*w**2 + 1/2*w**4 - 1/2 + w**i - w = 0.
-1, 1
Let a(l) be the third derivative of l**7/1260 - l**5/60 - l**4/24 - 4*l**2. Let u(h) be the second derivative of a(h). Suppose u(q) = 0. Calculate q.
-1, 1
Let w = -786 + 789. Factor -1/3*h**2 - w - 2*h.
-(h + 3)**2/3
Let m(b) be the third derivative of 5*b**8/63 + 4*b**7/9 - 23*b**6/8 + 47*b**5/9 - 295*b**4/72 + 5*b**3/3 + 32*b**2. Solve m(z) = 0.
-6, 1/4, 1
Let h(t) = t**2 - 2*t - 12. Let w be h(5). Find l, given that 54/7*l**w + 0*l - 8/7 + 54/7*l**2 = 0.
-2/3, 1/3
Let n = 2/25 + -12/25. Let m = n - -9/10. Let -3/2*q**4 + m*q**5 + q**3 + 1/2 - 3/2*q + q**2 = 0. What is q?
-1, 1
Let y = 903 + -901. Determine l, given that -4/5*l**2 - 2/5*l**5 - 8/5*l**4 - y*l**3 + 0*l + 0 = 0.
-2, -1, 0
Determine m so that -32*m**2 + 15*m**2 + 3*m + 20*m**2 - 6 = 0.
-2, 1
Factor -j**3 - 2*j - 2 + 7*j - 4*j + 2*j**2.
-(j - 2)*(j - 1)*(j + 1)
Let p(u) = u**3 - 2*u - 1. Suppose -4*x - 2 - 2 = 0. Let t be p(x). Factor t + 2/5*i**4 - 2/5*i**2 + 0*i - 2/5*i**5 + 2/5*i**3.
-2*i**2*(i - 1)**2*(i + 1)/5
Let u = 15 + -13. Let f be (u - 52/(-12)) + -3. Factor 0*c**2 + 0 + f*c**4 + 0*c + 8/3*c**5 + 2/3*c**3.
2*c**3*(c + 1)*(4*c + 1)/3
Let l(g) be the third derivative of -g**7/105 + g**5/15 - g**3/3 + 7*g**2. Factor l(r).
-2*(r - 1)**2*(r + 1)**2
Suppose -5*f + 0*u + 2*u + 19 = 0, -4*f - 5*u = -35. Let -f*k**3 + 2*k**4 + 3*k**2 + 0*k**4 - k**4 + 9*k = 0. Calculate k.
-1, 0, 3
Let o(b) be the first derivative of 2 + 0*b**2 + 1/30*b**4 + 1/15*b**3 + 3*b. Let f(i) be the first derivative of o(i). Factor f(s).
2*s*(s + 1)/5
Let p be ((-1)/3)/(2/(-12)). Determine k 