 - m**5/30 - 7*m**4/48 + m**3/6 + 11*m**2. What is r in c(r) = 0?
-1, 2/7, 1
Let d(f) = 4*f**4 + 5*f**3 - 3*f**2 - 10*f + 4. Let g(r) = -5*r**4 - 5*r**3 + 3*r**2 + 11*r - 4. Let n(t) = -6*d(t) - 5*g(t). Factor n(c).
(c - 4)*(c - 1)**2*(c + 1)
Suppose 51 = 23*t - 6*t. Let p(k) be the second derivative of 0*k**t + 0 + 1/42*k**4 + 4*k - 1/7*k**2. Solve p(i) = 0.
-1, 1
Let a be 4/2 - (-16 + 18). Let q(d) be the first derivative of 1 + 1/18*d**6 - 1/24*d**4 + a*d + 1/6*d**3 - 1/10*d**5 - 1/12*d**2. Let q(n) = 0. What is n?
-1, 0, 1/2, 1
Let i = 1229/28 - 20191/462. Let p = 2/33 + i. Find y, given that 0 - 1/2*y - p*y**2 = 0.
-2, 0
Let h(m) be the third derivative of -m**8/26880 + m**6/2880 - m**4/24 + 3*m**2. Let s(x) be the second derivative of h(x). Factor s(y).
-y*(y - 1)*(y + 1)/4
Let v(m) be the second derivative of m**7/1120 - m**6/120 + m**5/40 + m**3/2 - 5*m. Let c(w) be the second derivative of v(w). Find z such that c(z) = 0.
0, 2
Let r(b) be the third derivative of b**7/105 + b**6/20 + b**5/10 + b**4/12 - 2*b**2. Factor r(q).
2*q*(q + 1)**3
Let n be (-119)/(-51) - ((-2)/3)/1. Factor 0*g**n + 0 - 1/2*g**4 - 1/4*g**5 + 1/2*g**2 + 1/4*g.
-g*(g - 1)*(g + 1)**3/4
Factor 3*j + 7/5*j**2 + 9/5 + 1/5*j**3.
(j + 1)*(j + 3)**2/5
Let g(t) = 5*t**4 - 7. Let m(l) = 2*l**4 - 3. Let d(n) = -4*n**2 + 3*n - 2. Let b be d(1). Let r(f) = b*g(f) + 7*m(f). Factor r(z).
-z**4
Suppose 4*g + 4 = d, 3*g - 2*g = 5*d - 20. Suppose d*k - 6 = k. Factor 6/5*c - 2/5 + 8/5*c**k.
2*(c + 1)*(4*c - 1)/5
Let c = 11 + -8. Let s(l) be the third derivative of -1/24*l**c + 1/240*l**5 - 2*l**2 + 0 - 1/96*l**4 + 0*l + 1/480*l**6. Factor s(o).
(o - 1)*(o + 1)**2/4
Let i(s) be the first derivative of s**6/15 - s**4/3 + s**2 - 6*s + 4. Let q(b) be the first derivative of i(b). Factor q(g).
2*(g - 1)**2*(g + 1)**2
Let h(a) be the third derivative of -a**8/33600 - a**7/4200 - a**5/30 - 3*a**2. Let n(l) be the third derivative of h(l). Factor n(p).
-3*p*(p + 2)/5
Let d = -64 - -44. Let l = -79/4 - d. Suppose -l*u**2 + 0 + 0*u = 0. What is u?
0
Let y(q) be the first derivative of 4*q**3/3 - 12*q**2 + 36*q - 1. Factor y(z).
4*(z - 3)**2
Let z(c) be the second derivative of -24*c**7/7 - 2*c**6/5 + 14*c**5/5 - c**4 + c - 1. Factor z(r).
-4*r**2*(3*r - 1)**2*(4*r + 3)
Let l be (-95)/(-57) + 8/6. Let m(p) be the first derivative of 1/12*p**4 - 1/3*p - l - 1/6*p**2 + 1/9*p**3. Suppose m(y) = 0. Calculate y.
-1, 1
Let d(x) be the first derivative of x**4 + 40*x**3/3 + 26*x**2 + 32*x + 2. Let i(m) = m**3 + 13*m**2 + 17*m + 11. Let j(f) = -3*d(f) + 8*i(f). Factor j(l).
-4*(l + 1)**2*(l + 2)
Factor 1/8*z**3 + 5/8*z**2 + 3/8*z - 9/8.
(z - 1)*(z + 3)**2/8
Let z(o) be the second derivative of 1/231*o**7 - 1/33*o**3 + 7*o - 1/33*o**4 + 0*o**2 + 0*o**5 + 0 + 2/165*o**6. Factor z(c).
2*c*(c - 1)*(c + 1)**3/11
Let r(b) be the first derivative of -b**7/105 + b**5/30 + b**2/2 + 2. Let g(f) be the second derivative of r(f). Suppose g(t) = 0. What is t?
-1, 0, 1
Let f(g) be the third derivative of -g**8/1344 + g**7/120 - g**6/60 - g**5/15 + 48*g**2. Factor f(r).
-r**2*(r - 4)**2*(r + 1)/4
Let w(s) be the third derivative of 1/39*s**3 + 0*s**5 + 0 - 1/78*s**4 + 1/390*s**6 + 0*s - 7*s**2 - 1/1365*s**7. Find c, given that w(c) = 0.
-1, 1
Suppose 3*v - 30 = -2*v. Let z = 10 - v. Let -3*c**3 + c**3 - 5*c**4 + 3*c**z = 0. What is c?
-1, 0
Let q be (-4)/(-3) + 2/3. Factor -3*m**3 - m**q - m**2 + 2*m**3 + 3*m**4.
m**2*(m - 1)*(3*m + 2)
Let c(i) = i**2 - 5*i + 4. Let q be c(4). Let k(h) = h**3 + h**2 + 2. Let l be k(q). Factor 0 + 14/11*d**l + 4/11*d.
2*d*(7*d + 2)/11
Let z be -5 - (-2)/36*94. Factor 2/9*r**2 - z*r + 0.
2*r*(r - 1)/9
Let o be (-18)/30*10/(-3). Factor -8*i - 15/2*i**o - 2.
-(3*i + 2)*(5*i + 2)/2
Let o(a) be the first derivative of -a**5/60 - a**4/12 + a**3/2 + 7*a**2/2 + 4. Let c(m) be the second derivative of o(m). Solve c(k) = 0.
-3, 1
Suppose -10 = -2*q + 2*y, -3*y - y + 4 = 2*q. Suppose q*s + 6 = 18. Suppose 1/2*m - 5/2*m**2 + 2*m**s + 0 = 0. What is m?
0, 1/4, 1
Let f(s) be the third derivative of s**9/1512 - s**8/840 - s**3/6 + s**2. Let c(x) be the first derivative of f(x). Factor c(d).
2*d**4*(d - 1)
Let f(p) be the first derivative of -2*p**3/27 - 2*p**2/3 - 2*p + 3. Determine l so that f(l) = 0.
-3
Let -3*f + 2*f**4 - 9*f**3 + f**4 + 10*f**2 - f**2 = 0. What is f?
0, 1
Let 1 + 2*m - 1/4*m**4 - 1/2*m**3 + 3/4*m**2 = 0. What is m?
-2, -1, 2
Let u(a) be the second derivative of a**5/130 - a**4/78 + 5*a. Factor u(t).
2*t**2*(t - 1)/13
Factor 8/5*t**2 + 11/5*t + 3/5.
(t + 1)*(8*t + 3)/5
Let p be -5 - -1 - (-3)/3. Let v be -3*(-4)/(-18)*p. Find z such that 5*z**3 - 2*z + v*z**3 - 3*z**2 - 2*z**3 = 0.
-2/5, 0, 1
Let s(x) be the second derivative of -x**4/18 + x**3/9 + 8*x. Let s(w) = 0. Calculate w.
0, 1
Let b(z) = -z**3 - z**2 + z - 4. Let k(w) = -w**3 - w**2 + w - 5. Let r(f) = 6*b(f) - 5*k(f). Find h, given that r(h) = 0.
-1, 1
Let u(h) be the third derivative of -4*h**2 + 0*h**6 + 1/315*h**7 + 0 + 0*h - 1/45*h**5 + 0*h**4 + 1/9*h**3. Factor u(v).
2*(v - 1)**2*(v + 1)**2/3
Let x be (8/(-32))/((-6)/(-40)). Let u = -17/12 - x. Find p, given that -u + 1/2*p - 1/4*p**2 = 0.
1
Let x(s) be the third derivative of -s**8/840 - s**7/525 + s**6/300 + s**5/150 + s**2. Let x(f) = 0. What is f?
-1, 0, 1
Let o(y) = 17*y**2 - 9*y + 13. Let h(m) = 8*m**2 - 4*m + 6. Let b(i) = 13*h(i) - 6*o(i). Factor b(j).
2*j*(j + 1)
Let k(u) be the second derivative of -u**5/110 - u**4/33 + u**3/33 + 2*u**2/11 + 5*u. Find c such that k(c) = 0.
-2, -1, 1
Let q(y) = 12*y**3 + 76*y**2 - 44*y - 12. Let b(p) = -p**3 - 7*p**2 + 4*p + 1. Let s(a) = 32*b(a) + 3*q(a). Factor s(v).
4*(v - 1)*(v + 1)**2
Let k be 5/(-5) - -1 - 0. Let j(l) be the first derivative of 3 + 2/3*l**3 + k*l - l**2. Factor j(u).
2*u*(u - 1)
Suppose 0 + 1/4*i**2 - 3/4*i = 0. What is i?
0, 3
Let i(l) = -l**2 + 15*l - 42. Let r be i(11). Suppose 0 - 26/7*g**r - 4/7*g - 48/7*g**3 - 18/7*g**4 = 0. Calculate g.
-2, -1/3, 0
Suppose 4*g = 9*g - 15. Let b(c) be the second derivative of 1/54*c**4 - 2/27*c**g + 2*c + 1/90*c**5 + 0 + 0*c**2. Factor b(x).
2*x*(x - 1)*(x + 2)/9
Suppose 2*o + 11 - 23 = 0. Suppose 14*h**2 + 4 - 3*h - 7*h - 2*h**3 - o*h**2 = 0. What is h?
1, 2
Suppose 2*a = -a. Suppose -6*p + 4*p**2 + 0*p + a*p - p**2 = 0. Calculate p.
0, 2
Let c(d) be the first derivative of -8*d**3/9 - 13*d**2/3 - 2*d + 17. Factor c(j).
-2*(j + 3)*(4*j + 1)/3
Factor -1 + 5/3*b - 2/3*b**2.
-(b - 1)*(2*b - 3)/3
Determine l, given that 42*l + 3*l**2 - 19*l**2 + 196 - 8*l**2 - 122*l**3 + 124*l**3 = 0.
-2, 7
Let x be ((-64)/(-12))/(28/6). Let f(r) be the first derivative of -x*r + 20/7*r**2 - 1 - 6/7*r**3. Solve f(i) = 0 for i.
2/9, 2
Let x(i) be the second derivative of 1/5*i**3 + 2/5*i**2 - 3/50*i**5 + 0 - 1/30*i**4 + 2*i - 1/75*i**6. Let x(s) = 0. Calculate s.
-2, -1, 1
Find x such that 3/4*x + 0 + 3/4*x**4 - 3/4*x**2 - 3/4*x**3 = 0.
-1, 0, 1
Let k be 9/15*(-10)/(-12). Factor -o - k - 1/2*o**2.
-(o + 1)**2/2
Let f(g) = g**3 + 13*g**2 - 33*g - 43. Let z be f(-15). Factor 3/2*l**z + 0*l + 0 - 3/2*l**3.
-3*l**2*(l - 1)/2
Find j such that 1/6*j**2 - 1/3*j + 1/6 = 0.
1
Let h(k) = -k**5 + 3*k**4. Let s(n) be the third derivative of -n**8/112 + n**7/21 - 2*n**2. Let v(o) = -7*h(o) + 2*s(o). Factor v(q).
q**4*(q - 1)
Let o(f) be the third derivative of f**6/660 - 7*f**5/165 + 49*f**4/132 - 19*f**2. Solve o(s) = 0 for s.
0, 7
Suppose -2*a = 2*x - 7*a + 10, 2*a = 2*x + 4. Let j(l) be the third derivative of 0*l**3 + 0*l + 1/60*l**5 - l**2 + x*l**4 + 0. Let j(v) = 0. What is v?
0
Let m(p) be the second derivative of 0*p**2 + 0*p**5 - 1/9*p**3 - 3*p - 2/45*p**6 + 1/63*p**7 + 1/9*p**4 + 0. Factor m(w).
2*w*(w - 1)**3*(w + 1)/3
Let w(r) = 10*r**2 + 16*r + 6. Let d(f) = -7*f**2 - 12*f - 4. Let v(k) = k. Let y(c) = -d(c) - v(c). Let m(h) = 5*w(h) - 7*y(h). Factor m(b).
(b + 1)*(b + 2)
Let k(l) be the first derivative of -3*l**4/4 + 5*l**3 - 25*l**2/2 + 125*l/9 - 55. Let k(w) = 0. What is w?
5/3
Suppose -4/5 - 2/5*w**3 + 2/5*w + 4/5*w**2 = 0. What is w?
-1, 1, 2
Suppose -9 = -3*l - 3*p, -l + 0*l = 2*p - 3. Factor -8*o**3 - o + 9*o**l + 4*o**2 - 2 - 2*o**2.
(o - 1)*(o + 1)*(o + 2)
Factor 0 - 25/2*w**2 + 15/2*w - 5*w**3.
-5*w*(w + 3)*(2*w - 1)/2
Let k(y) be the first derivative of 25*y**6/9 