/8*c = 0. Calculate c.
-5
Let y(n) be the second derivative of -2*n**7/147 + n**6/21 - 5*n**4/42 + 2*n**3/21 + 6*n. Determine r so that y(r) = 0.
-1, 0, 1/2, 1, 2
Let k be 2/(-3) + (-52)/(-6). Find c such that -k*c - 4*c**4 + 4 - 5*c**2 - c**4 + 6*c**2 + c**5 + 7*c**3 = 0.
-1, 1, 2
Let u(m) = -5*m**2 - 8*m - 1. Let k(w) = 81*w**2 + 129*w + 15. Let v(c) = 2*k(c) + 33*u(c). Suppose v(f) = 0. What is f?
-1
Let u = 32/59 - -1536/649. Let c = u + -52/33. Let 0*m**3 - c*m**2 + 2/3*m + 0 + 4/3*m**4 - 2/3*m**5 = 0. What is m?
-1, 0, 1
Let g(s) be the second derivative of s**4/3 - 4*s**3/3 + 40*s. Factor g(l).
4*l*(l - 2)
Let j(f) be the second derivative of 0*f**2 + 1/2*f**3 - 1/10*f**6 + 0 + 9/20*f**5 - 4*f - 3/4*f**4. Find i, given that j(i) = 0.
0, 1
Let b(q) be the third derivative of -49*q**5/270 - 28*q**4/27 - 64*q**3/27 + 40*q**2. Factor b(w).
-2*(7*w + 8)**2/9
Let g = 48 + -30. Let l be (g/189)/((-1)/(-3)). Solve -2/7*h**2 + l + 0*h = 0.
-1, 1
Let s be (3/21)/(48/28). Let w(g) be the second derivative of -1/30*g**6 + 0*g**2 + 2*g + 0*g**3 + s*g**4 + 1/20*g**5 - 1/42*g**7 + 0. Factor w(c).
-c**2*(c - 1)*(c + 1)**2
Let p(h) = h**2 + 6*h + 2. Let u(b) = 15*b**2 + 96*b + 33. Suppose -3 = -4*m + 5. Let a(r) = m*u(r) - 33*p(r). Factor a(d).
-3*d*(d + 2)
Factor 8*a**4 + 4*a**4 - 9*a**4 + 6*a**3 - 3*a**5.
-3*a**3*(a - 2)*(a + 1)
Let i = -70/9 - 8/9. Let d = 28/3 + i. Factor 1/3*p + d - 1/3*p**2.
-(p - 2)*(p + 1)/3
Let h(f) be the third derivative of -f**8/672 - f**7/420 + f**6/240 + f**5/120 - 7*f**2. Factor h(q).
-q**2*(q - 1)*(q + 1)**2/2
Let n(v) be the second derivative of -v**6/20 + 13*v**5/40 - 19*v**4/24 + 11*v**3/12 - v**2/2 - 27*v. Suppose n(y) = 0. Calculate y.
1/3, 1, 2
Factor -1/2*m**3 - 2 - 4*m - 5/2*m**2.
-(m + 1)*(m + 2)**2/2
Let q(u) be the first derivative of u**4/6 - 4*u**3/27 - u**2/3 + 4*u/9 + 9. Factor q(f).
2*(f - 1)*(f + 1)*(3*f - 2)/9
Let t = 63/1100 - -1/44. Let b(h) be the first derivative of 0*h**2 + 1 + 0*h + t*h**5 + 1/10*h**4 + 0*h**3. Determine c, given that b(c) = 0.
-1, 0
Let o(h) = -2*h**3 + h**2 + 2*h + 2. Let k be o(-1). Factor 2*j**k + 16/7 + 72/7*j + 60/7*j**2.
2*(j + 2)**2*(7*j + 2)/7
Let o = -4 - -6. Suppose o*t + t = 0. Suppose 6/5*s**2 - 3/5*s**4 + 0*s + t*s**3 - 3/5 = 0. Calculate s.
-1, 1
Let s be (-18)/(-6) - (0 + -4). Let m = s - 11. Let l(p) = -6*p**2 + 6*p. Let n(g) = -13*g**2 + 13*g - 1. Let z(a) = m*n(a) + 9*l(a). Let z(r) = 0. Calculate r.
-1, 2
Let 8/15*c + 2/15*c**2 + 8/15 = 0. Calculate c.
-2
Let q(o) = -4*o**2 + 4. Let d(c) = 19 + 0 - 4 - 15*c**2. Let u be -3 - 0 - -5 - -4. Let a(i) = u*d(i) - 22*q(i). Factor a(s).
-2*(s - 1)*(s + 1)
Let v(n) = -n**2 + n + 1. Let m(t) = -20*t**3 - 24*t**2 + 36*t + 24. Let o(i) = m(i) - 16*v(i). What is c in o(c) = 0?
-1, -2/5, 1
Factor 4 - 3*l + 60*l**2 - 62*l**2 - 4 + l**3.
l*(l - 3)*(l + 1)
Let b(m) be the first derivative of m**9/3024 + m**8/560 + m**7/280 + m**6/360 - m**3/3 + 5. Let r(k) be the third derivative of b(k). Solve r(y) = 0.
-1, 0
What is a in -9*a**4 - 28*a**2 - 8*a - 4*a**5 - 52*a**3 - 11*a**4 + 16*a**3 = 0?
-2, -1, 0
Let n(c) be the third derivative of -2*c**2 + 1/1176*c**8 + 0*c + 4/735*c**7 + 0*c**3 + 2/105*c**5 + 1/84*c**4 + 0 + 1/70*c**6. Factor n(k).
2*k*(k + 1)**4/7
Let i(p) = -3*p**2 - 5*p. Let u(v) = -v**2 - 2*v. Let g(f) = 4*i(f) - 11*u(f). Find c such that g(c) = 0.
0, 2
Suppose 5*h - 28 = -t, 3*h - 31 = -4*t - 4. Suppose 0*q + 10 = h*q. Find l, given that 4*l**q - l + 3*l**2 - 6*l**2 = 0.
0, 1
Let r(f) be the first derivative of -f**6/540 + f**5/90 - f**4/54 - 5*f**2/2 + 4. Let y(i) be the second derivative of r(i). Factor y(d).
-2*d*(d - 2)*(d - 1)/9
Let p(v) be the second derivative of v**5/4 - 5*v**4/6 - 20*v**3/3 + 3*v + 1. Factor p(s).
5*s*(s - 4)*(s + 2)
Let b(g) = -g**2 + 5*g + 5. Let s be b(5). Suppose -7 - s = -4*l. Factor 1/2*t**l + 1/2 - 1/2*t**2 - 1/2*t.
(t - 1)**2*(t + 1)/2
Suppose -3*g**3 - 3/7*g**4 - 51/7*g - 18/7 - 51/7*g**2 = 0. What is g?
-3, -2, -1
Let q(j) be the first derivative of -1/3*j**2 - 1/3*j**3 + 5/12*j**4 + 0*j - 4. Let q(d) = 0. Calculate d.
-2/5, 0, 1
Let m(s) be the second derivative of -s - 1/50*s**5 - 1/15*s**4 + 0*s**3 - 1/21*s**7 + 0 + 8/75*s**6 + 0*s**2. Determine a, given that m(a) = 0.
-2/5, 0, 1
Factor 3/2 + 1/2*f**4 - 2*f**2 + f - f**3.
(f - 3)*(f - 1)*(f + 1)**2/2
Factor 6*p**2 - 93/2*p - 12.
3*(p - 8)*(4*p + 1)/2
Let g(v) be the first derivative of -v**4/8 + v**3/2 - 6. Factor g(i).
-i**2*(i - 3)/2
Let r(t) = 18*t**3 + 102*t**2 + 49*t + 8. Let x(h) = -19*h**3 - 101*h**2 - 49*h - 9. Let s(i) = -3*r(i) - 2*x(i). Factor s(n).
-(n + 6)*(4*n + 1)**2
Let a(m) = 7*m**4 + m**3 + 9*m**2. Let b(g) = 10*g**4 + 2*g**3 + 13*g**2. Let i(y) = -7*a(y) + 5*b(y). Factor i(d).
d**2*(d + 1)*(d + 2)
Let i be (9/(-4))/((-15)/40). Let y(f) be the second derivative of 0*f**3 - 1/10*f**5 - 1/15*f**i + 0*f**4 + 0 + 0*f**2 - f. Factor y(l).
-2*l**3*(l + 1)
Let v = 27811/54 - 515. Let j(u) be the second derivative of 1/27*u**3 - 2/9*u**2 - 2*u + 0 + v*u**4. Factor j(t).
2*(t - 1)*(t + 2)/9
Suppose -8 = -5*s + 2. Factor -2*c + 0*c**3 + 1 - c**3 - 2*c + 3*c**s + c.
-(c - 1)**3
Factor -2/5*o**2 + 2/5*o**3 - 6/5 - 2*o.
2*(o - 3)*(o + 1)**2/5
Let b(y) be the first derivative of -5*y**4/4 + 5*y**3/3 + 5*y**2/2 - 5*y - 7. Suppose b(p) = 0. Calculate p.
-1, 1
Factor 30/7*g**4 + 0 + 26/7*g**3 + 0*g + 4/7*g**2.
2*g**2*(3*g + 2)*(5*g + 1)/7
Let t(h) = -6*h**4 - 6*h**3 - 5*h**2 - 5*h + 5. Let l(s) = s**4 + s**3 + s**2 + s - 1. Let d(b) = -5*l(b) - t(b). Determine x so that d(x) = 0.
-1, 0
Let y(r) be the third derivative of r**9/2016 + r**8/672 + r**7/720 + r**6/2160 + r**3/2 - 2*r**2. Let t(d) be the first derivative of y(d). Factor t(z).
z**2*(z + 1)*(3*z + 1)**2/6
What is u in -8/7*u + 0 - 4/7*u**2 + 4/7*u**3 = 0?
-1, 0, 2
Suppose 5 + 1 = 2*z. Let o(u) = -2*u - 4. Let n be o(-3). Solve 0*l**4 - 3*l**3 - 4*l**2 - z*l**5 + 4*l**n - 6*l**4 = 0 for l.
-1, 0
Let v be (-96)/(-56) + 4/14. Factor w**2 + 4*w**4 - w**5 - 3*w**3 - v*w**3 + w**2.
-w**2*(w - 2)*(w - 1)**2
Let d(q) = q**2 + 4*q - 4. Let v be d(-6). Suppose 2*t - v = -0*t. Let -y + y + y + y**2 - y**3 - y**t = 0. What is y?
-1, 0, 1
Let w(m) = -9*m**4 + 2*m**3 + 9*m**2 - 13*m + 11. Let c(n) = -5*n**4 + n**3 + 5*n**2 - 7*n + 6. Let f = 15 + -9. Let h(b) = f*w(b) - 11*c(b). Solve h(q) = 0.
-1, 0, 1
Let n(m) = -m**3 - 6*m**2 + 6*m - 5. Let p be n(-7). Factor -3 + 7*o**2 + p*o**2 + 4*o - 10*o**2.
-(o - 3)*(o - 1)
Let k = 20 - 11. Factor 6*h**2 + 14*h**3 + 7*h**3 + 9*h**4 + 15*h**4 + k*h**5.
3*h**2*(h + 1)**2*(3*h + 2)
Suppose 0 = 4*z + z - 4*o + 10, 3*o - 7 = 4*z. Solve 2*r**z - 6*r**2 + r**3 + r**3 + 2*r**2 = 0.
0, 1
Let j(g) be the first derivative of -3 - 15/2*g**4 + 3/2*g**2 - 33/10*g**5 - 7/2*g**3 + 0*g. Factor j(i).
-3*i*(i + 1)**2*(11*i - 2)/2
Let r(u) be the first derivative of u**5/30 - u**3/6 - u**2/6 + 4. Determine s, given that r(s) = 0.
-1, 0, 2
Let l(n) = 7*n**2 - n + 1. Let s be l(1). Let t(b) = b**3 - 8*b**2 + 8*b - 5. Let w be t(s). Factor -3*d**3 + 4*d**3 + 0*d**2 + d**w.
d**2*(d + 1)
Let p be -1*(-2)/2 - (-65)/(-91). Factor -4/7*c + 4/7*c**3 + p*c**2 + 0 - 2/7*c**4.
-2*c*(c - 2)*(c - 1)*(c + 1)/7
Let s(z) = -5*z**4 - 10*z**3 + 11*z**2 + 4*z + 6. Let x(f) = -6*f**4 - 11*f**3 + 12*f**2 + 5*f + 7. Let u(d) = 7*s(d) - 6*x(d). Factor u(i).
i*(i - 2)*(i - 1)**2
Let s = -23 - -23. Let g(x) be the second derivative of 2/15*x**3 + 2/21*x**7 + x - 6/25*x**5 - 1/75*x**6 + 0 + s*x**2 + 1/30*x**4. Solve g(n) = 0 for n.
-1, -2/5, 0, 1/2, 1
Let c be (2/(-51))/((-2)/9). Let z = 26/51 - c. Suppose -z*i + 1/3 - 1/3*i**2 + 1/3*i**3 = 0. Calculate i.
-1, 1
Suppose -4*h - 2*f = -3*h + 10, -3*h = -3*f - 15. Let c(k) be the first derivative of h*k - 2 + 0*k**2 + 2/3*k**3 - 1/2*k**4. Suppose c(o) = 0. Calculate o.
0, 1
Let x be (-1)/((-10)/(-6) + -2). Factor 2*u**3 + 10*u**2 + 6*u**4 + 0*u - 2*u - 17*u**3 + u**x.
2*u*(u - 1)**2*(3*u - 1)
Suppose 3/4*k**4 + 3/4*k**3 + 3/2 - 3/4*k - 9/4*k**2 = 0. What is k?
-2, -1, 1
Let v = 164/255 + 2/85. What is g in -14/9*g**4 - 2/9*g**2 + 0 - 10/9*g**3 + 0*g - v*g**5 = 0?
-1, -1/3, 0
Let v(m) = 2*m**4 + 2*m**3 - 4*m. Let g be (-1)/(-4) + (-75)/(-20). Let f(q) = q**3 - q. Let h(s) = g*f(s) + v(s). Determine k so that h(k) = 0.
-2, 0, 1
Let c(k)