(g) be the second derivative of 2*g + 2*g**2 + 0 + 1/6*g**4 - g**3. Solve q(x) = 0 for x.
1, 2
Suppose -n = -6*n + 45. Let k = n - 4. Factor 19*w**3 - 4*w**2 + k*w**2 - 2*w + 4*w**3 + 20*w**4.
w*(w + 1)*(4*w - 1)*(5*w + 2)
Let k = 24/23 + -170/207. Factor 0 + k*o**2 - 4/9*o.
2*o*(o - 2)/9
Let y(j) be the second derivative of -j**7/168 + j**5/40 - j**3/24 - 2*j. Find k such that y(k) = 0.
-1, 0, 1
Let m(w) be the third derivative of -3*w**6/40 - 7*w**5/10 + 17*w**4/6 - 4*w**3 - 9*w**2 + 2. Factor m(j).
-(j + 6)*(3*j - 2)**2
Let q(h) be the third derivative of -h**8/13440 + h**7/1890 - 7*h**6/4320 + h**5/360 - h**4/4 - 5*h**2. Let u(t) be the second derivative of q(t). Factor u(v).
-(v - 1)**2*(3*v - 2)/6
Let z(g) be the first derivative of 0*g - 2*g**2 - 8/3*g**3 + 8 + 8/5*g**5 + 2/3*g**6 + 0*g**4. Factor z(q).
4*q*(q - 1)*(q + 1)**3
Let y(w) be the third derivative of -w**5/240 + w**4/48 - w**3/24 - 5*w**2. Factor y(a).
-(a - 1)**2/4
Let r(q) = q**2 - 1 + 23*q - 7*q + 0*q**2 - 5*q**2. Let g(n) = -n**2 + 5*n. Let j(w) = -7*g(w) + 2*r(w). Factor j(v).
-(v + 1)*(v + 2)
Let y(w) = 8*w**2 - 6. Let n(j) = 23*j**2 - 17. Let x(l) = -6*n(l) + 17*y(l). Factor x(p).
-2*p**2
Let u = 45 + -43. Let o(a) be the third derivative of 0*a**3 - 1/150*a**5 + 0 + 3*a**u + 0*a**4 - 1/600*a**6 + 0*a. Let o(w) = 0. Calculate w.
-2, 0
Suppose z + 3 + 0 = 0. Let k = z + 3. Factor k + 1/2*i**2 - 1/2*i.
i*(i - 1)/2
Suppose 0*o + 0*o**3 - 2/13*o**2 + 2/13*o**4 + 0 = 0. What is o?
-1, 0, 1
Suppose 0 = d + o + 18, 0 = 2*d - 3*d - 2*o - 20. Let g be 4/(-10)*10/d. Factor 0*v - g*v**3 + 1/4*v**2 - 3/4*v**5 - 5/4*v**4 + 0.
-v**2*(v + 1)**2*(3*v - 1)/4
Let c(g) = -g**3 + 3*g**2 + 3*g - 4. Let i be c(3). Let a = i + -5. Factor -2/7*y**3 + 0 + 2/7*y + a*y**2.
-2*y*(y - 1)*(y + 1)/7
Let w(c) be the first derivative of 114*c + 142*c - 2 + 230*c**3 + 480*c**2 + 170*c**3 + 125*c**4. Factor w(j).
4*(5*j + 4)**3
Let u = 97/64 - 1/64. Factor -9/4 - 1/4*l**2 - u*l.
-(l + 3)**2/4
Let f be ((-51)/48 + 1)/(39/(-234)). Factor 0 + 3/8*r + f*r**2.
3*r*(r + 1)/8
Let p = -9 + 9. Let k(l) be the first derivative of -1/2*l**4 - 2/9*l**3 + 0*l - 1/9*l**6 + p*l**2 - 2/5*l**5 + 2. Find n, given that k(n) = 0.
-1, 0
Let h(c) = -c**4 - c**3 + c**2 + 1. Let p be (2 - -4) + (-4)/2. Let z(n) = 2*n**4 + 8*n**3 - 6*n**2 - 4. Let u(y) = p*h(y) + z(y). Factor u(a).
-2*a**2*(a - 1)**2
Let v(d) be the third derivative of -41*d**5/150 + 43*d**4/60 - 2*d**3/15 - 17*d**2. Suppose v(j) = 0. Calculate j.
2/41, 1
Let d(a) be the second derivative of 0 - 141/4*a**4 - 49/5*a**6 + a - 6*a**2 - 20*a**3 - 609/20*a**5. What is v in d(v) = 0?
-1, -1/2, -2/7
Let f(g) be the first derivative of 8/9*g**3 - 1/36*g**6 + 1/5*g**5 + 1/3*g - 7/12*g**4 + 3 - 3/4*g**2. Factor f(k).
-(k - 2)*(k - 1)**4/6
Let j(h) = -h - 1. Let k be -3 - (-1 + 3 - 2). Let b be j(k). Factor -2*y**b + 3*y - 2*y + 3*y**2.
y*(y + 1)
Let z(b) be the third derivative of -1/60*b**6 + 3*b**2 - 1/105*b**7 - 1/672*b**8 + 0*b + 1/60*b**5 + 0 + 1/6*b**3 + 5/48*b**4. Factor z(w).
-(w - 1)*(w + 1)**3*(w + 2)/2
Let n = 15 - 10. Factor 13*q + 22*q**4 - 2 + 5 - 1 + 5*q**n + 38*q**3 + 32*q**2.
(q + 1)**4*(5*q + 2)
Let u = 35 + -31. Let a(d) be the third derivative of 1/90*d**5 + 0*d + 0*d**3 + 1/54*d**u + d**2 + 0. Let a(m) = 0. What is m?
-2/3, 0
Let u be ((-6)/(-15))/(4/50). Factor 0*w**3 + 3*w**2 + 1 - u + w**3 + 0.
(w - 1)*(w + 2)**2
Solve -144/7*h + 162/7*h**2 + 24/7 = 0.
2/9, 2/3
Let t = -91 - -96. Solve 0 + 3/7*i**2 - 1/7*i**t + 2/7*i - 3/7*i**4 - 1/7*i**3 = 0.
-2, -1, 0, 1
Let b(s) be the first derivative of -s**4/4 + 2*s**3/3 - s**2/2 + 6. Factor b(k).
-k*(k - 1)**2
Let h = 36 + -107/3. Let w = h - -1/6. Factor -1/2*u**2 + w - 1/4*u + 1/4*u**3.
(u - 2)*(u - 1)*(u + 1)/4
Let a be ((-10)/4)/(8/16*-20). Factor 1/2*i**3 + 0 - 1/2*i + a*i**4 - 1/4*i**2.
i*(i - 1)*(i + 1)*(i + 2)/4
Let h(m) = 7*m**4 + 3*m**3 - m**2 + 9*m - 6. Let f(z) = z**4 + z**3 + z - 1. Let p(s) = -6*f(s) + h(s). Factor p(t).
t*(t - 3)*(t - 1)*(t + 1)
Let o(q) be the first derivative of -6*q**2 - 5 - 20/3*q**3 - q**4 + 36*q. Solve o(k) = 0 for k.
-3, 1
Let b(s) = s - 7. Let l(j) = -6*j + 36. Let t(z) = 11*b(z) + 2*l(z). Let g be t(-7). Solve -1/3*k**g - 2/3*k + 0 = 0.
-2, 0
Let q = 19 - 15. Factor 0*c**4 + 4*c - 7*c**2 + 8*c**3 + c**2 - 2*c**q - 4*c**2.
-2*c*(c - 2)*(c - 1)**2
Let m(w) be the second derivative of 6*w**2 + 7/4*w**4 + 0 + 8*w**3 + 7*w. Suppose m(n) = 0. Calculate n.
-2, -2/7
Let u = -62 - -62. Let h(a) be the third derivative of -2/3*a**3 + 0*a + 1/12*a**4 + 1/30*a**5 + u + 4*a**2. Factor h(m).
2*(m - 1)*(m + 2)
Let g(z) = z**2 - 1. Let d(a) = 2*a**3 - 2*a. Let u(f) = d(f) + 4*g(f). Factor u(k).
2*(k - 1)*(k + 1)*(k + 2)
Let t be (0 + -12)*1/(-3). Let x(k) be the second derivative of 2*k**2 - 14/3*k**3 + 3*k + 0 + 49/12*k**t. What is b in x(b) = 0?
2/7
Let p be 1 + -4 - 6*-1. Factor 0*c**2 + 21*c - 12*c + 3*c**3 - p + c**2 - 10*c**2.
3*(c - 1)**3
Suppose 2*g = -1 + 11. Factor 2*c**4 + c**3 - g*c**5 - c**3 + 2*c**3 + c**4.
-c**3*(c - 1)*(5*c + 2)
Let s(v) = -v**2 + 5*v - 2. Let u be s(3). Let d be u/6 - 16/(-12). What is x in 2/5 + 8/5*x + 6/5*x**d = 0?
-1, -1/3
Suppose 5*h + 9 = -5*a + 24, 3 = h - a. Factor 2/5*d**4 + 0*d**h - 2/5*d**2 + 1/5*d**5 + 0 - 1/5*d.
d*(d - 1)*(d + 1)**3/5
Suppose -3*b = -0*b - 21. Find m, given that 2*m**2 - 2*m + b*m + 0*m**2 - 3*m = 0.
-1, 0
Let w(s) be the second derivative of -2*s + 0 - 1/2*s**2 - 1/24*s**4 - 1/4*s**3. Factor w(h).
-(h + 1)*(h + 2)/2
Let i = -86 + 89. Let f(c) be the first derivative of 2*c + 1/2*c**4 + 3*c**2 - i + 2*c**3. Factor f(q).
2*(q + 1)**3
Let j be (-36)/21 + (-1 - -3). Let u be (-2)/8 - (-15)/28. Let -u*w + j*w**2 + 0 = 0. What is w?
0, 1
Let k = 132 - 388/3. Factor 0*v - 2/3*v**3 + 0*v**2 + 0 + k*v**4.
2*v**3*(4*v - 1)/3
Suppose -22 + 6 = -4*s. Suppose 7*r - s*r - 11 = -4*k, -r + k + 6 = 0. Factor 15*p**3 - 75*p**r - 11*p**4 + 33*p**3 + 26*p**4 + 12*p**2.
-3*p**2*(p - 1)*(5*p + 2)**2
Factor 4*k + 6*k**4 + 3*k**3 - 2*k - 6*k**2 + 0*k**4 - 5*k**3.
2*k*(k - 1)*(k + 1)*(3*k - 1)
Factor 5*i**2 - 5*i**2 - 6*i**4 - 3*i**5 + i**2 + 5*i**2 + 3*i.
-3*i*(i - 1)*(i + 1)**3
Suppose -3*q - 30 = -36. Let b(f) be the first derivative of 1/5*f**q - 1/2*f**4 + 6/25*f**5 + 2/15*f**3 + 0*f + 4. Factor b(k).
2*k*(k - 1)**2*(3*k + 1)/5
Let y(o) be the third derivative of o**8/504 - 2*o**7/315 - o**6/30 + 2*o**5/45 + 13*o**4/36 + 2*o**3/3 + 21*o**2. Factor y(x).
2*(x - 3)*(x - 2)*(x + 1)**3/3
Let d be (5/(-4))/((-7)/28). Factor 3*r**3 - 4*r**3 + 2*r**4 - r**d + 0*r**4.
-r**3*(r - 1)**2
Factor -70*p + 6*p**2 - 21*p**2 - 40 + 0*p**2.
-5*(p + 4)*(3*p + 2)
Let p be 21/9 + 3/(-9). Suppose -3*n**2 + n**3 + 0*n**3 - p*n + 5*n + 3*n**4 - 4*n**3 = 0. What is n?
-1, 0, 1
Let k(u) = -3*u - 16. Let w be k(-6). Let m be (-1)/27*(-4 - w). Find p, given that -m*p + 0 - 8/9*p**2 - 2/9*p**5 - 8/9*p**4 - 4/3*p**3 = 0.
-1, 0
Let s(u) be the third derivative of 0*u**3 - 1/1512*u**8 + 1/180*u**6 + 0 + 0*u + 1/54*u**4 + 1/54*u**5 - u**2 - 1/945*u**7. Find f, given that s(f) = 0.
-1, 0, 2
Suppose 2*k = -3*i + 6*k - 12, i - k = -3. Find v such that i*v**3 + 0 + 0*v - 6/5*v**4 - 4/5*v**5 + 2/5*v**2 = 0.
-1, 0, 1/2
Let j(w) be the first derivative of 0*w - 7/2*w**4 + 2*w**5 + 0*w**2 + 3 + 4/3*w**3. Factor j(s).
2*s**2*(s - 1)*(5*s - 2)
Factor -1/3*w - 2/3 + 1/3*w**3 + 2/3*w**2.
(w - 1)*(w + 1)*(w + 2)/3
Let j(u) be the second derivative of 0*u**3 + 0*u**4 + 0 + 6*u - 1/105*u**7 - 1/50*u**5 + 2/75*u**6 + 0*u**2. Determine g so that j(g) = 0.
0, 1
Let x(j) be the first derivative of 1/18*j**4 + 8/9*j**3 + 128/9*j + 1 + 16/3*j**2. Find m, given that x(m) = 0.
-4
Let d(l) be the first derivative of -3*l**5/40 - l**4/4 - l**3/24 + l**2/2 + l/2 + 13. Determine r, given that d(r) = 0.
-2, -1, -2/3, 1
Let g(c) be the second derivative of 3/10*c**5 + 0 + 0*c**6 - 1/14*c**7 + 3*c + 0*c**4 + 0*c**2 - 1/2*c**3. Find u, given that g(u) = 0.
-1, 0, 1
Let j(n) be the first derivative of -n**2 - 4 - 2*n + 2/3*n**3 + 1/2*n**4. Determine t, given that j(t) = 0.
-1, 1
Determine v so that -3/5*v**2 - 4/5 - 8/5*v = 0.
-2, -2/3
Let v(n) = -12*n**4 + 3*n**3 - 9*n**2 + 3*n + 6. Let t(u) = u**4 + u**3 - u**2 + u - 1. Let h(w) = -9*t(w) - v(w). Determine f so that h(f) = 0.
1
Suppose 4*b = b +