 third derivative of -n**10/15120 + n**8/3360 + n**4/24 - 3*n**2. Let i(a) be the second derivative of u(a). Determine p so that i(p) = 0.
-1, 0, 1
Factor 6 + 196*q**2 - 22 + 258*q**3 - 16*q - 62*q**3.
4*(q + 1)*(7*q - 2)*(7*q + 2)
Let q(a) = 2*a - 1. Let h be q(2). Suppose 4*c = 9 + 11. Factor i**4 - i**c - h*i**4 - i**5.
-2*i**4*(i + 1)
Let w(z) be the first derivative of -z**7/70 + z**6/60 + z**5/9 + z**4/9 - z**2 - 3. Let k(p) be the second derivative of w(p). Find i such that k(i) = 0.
-2/3, 0, 2
Let x(t) be the second derivative of -2*t**7/21 - 4*t**6/5 - 9*t**5/5 - 4*t**4/3 - 33*t. Let x(s) = 0. What is s?
-4, -1, 0
Determine k, given that -2/3*k + 4/3 - 2/3*k**2 = 0.
-2, 1
Let q(x) be the third derivative of 1/3*x**3 + 5*x**2 + 0*x - 1/60*x**5 + 0 - 1/24*x**4. Factor q(w).
-(w - 1)*(w + 2)
Let z(i) be the third derivative of -i**5/90 + i**4/18 + i**3/3 - 3*i**2. Factor z(x).
-2*(x - 3)*(x + 1)/3
Let u(c) be the second derivative of -1/54*c**4 + 0 + c + 4/27*c**3 - 4/9*c**2. Factor u(k).
-2*(k - 2)**2/9
Let q(a) be the first derivative of 0*a**2 + 1 + 2/25*a**5 + 0*a**3 + 1/5*a**4 + 0*a. Let q(g) = 0. Calculate g.
-2, 0
Let p(r) be the second derivative of 0*r**2 - 1/189*r**7 + 0*r**3 + 1/90*r**5 + 0 + 0*r**6 + 0*r**4 - 3*r. Suppose p(k) = 0. What is k?
-1, 0, 1
Factor 432/7 - 72/7*k + 3/7*k**2.
3*(k - 12)**2/7
Let x(s) = -s**4 - 5*s**3 + 5*s**2 + s. Let i(a) = -a - 9. Let k be i(-5). Let c(f) = -2*f**4 - 4*f**3 + 4*f**2 + 2*f. Let p(h) = k*c(h) + 5*x(h). Factor p(v).
3*v*(v - 1)**3
Let v(n) = -n - 2. Let q be v(-7). Factor 2*g**2 + g - 2*g**4 - 5*g**3 - g**5 + q*g**3.
-g*(g - 1)*(g + 1)**3
Let l(w) be the second derivative of w**6/30 - w**5/15 - w**4/3 + 3*w**2/2 - w. Let s(m) be the first derivative of l(m). Factor s(u).
4*u*(u - 2)*(u + 1)
Let y(s) = s**3 + 10*s**2 + 10*s + 11. Let h be y(-9). Factor 2*n**h - 5 + 1 - 4*n**2 + 6*n.
-2*(n - 2)*(n - 1)
Let a(o) be the first derivative of -1/4*o - 2 - 1/6*o**3 - 1/8*o**4 + 3/20*o**5 + 3/8*o**2 - 1/24*o**6. What is d in a(d) = 0?
-1, 1
Let 2/3*y**4 - 2/3*y**5 + 4/3*y**3 - 4/3*y**2 + 2/3 - 2/3*y = 0. Calculate y.
-1, 1
Let o be 40/(-12) + (3 - (-1 - 0)). Solve -o*h - 4/3*h**2 + 4/3*h**4 + 0 + 2/3*h**5 + 0*h**3 = 0 for h.
-1, 0, 1
Let c(w) = 5*w + 15. Let o be c(-3). Suppose 3/2*p**3 + 3/2*p**4 + o*p + 0 + 1/2*p**2 + 1/2*p**5 = 0. Calculate p.
-1, 0
Let a(c) be the first derivative of -c**6/10 + 9*c**5/20 - c**4/2 + 2*c + 3. Let y(b) be the first derivative of a(b). Factor y(t).
-3*t**2*(t - 2)*(t - 1)
Let p be (-117)/(-420) - (-1)/(-4). Let x(g) be the third derivative of 1/5*g**5 + 0 + p*g**7 + 0*g**4 - 1/3*g**3 + g**2 + 0*g + 2/15*g**6. Factor x(q).
2*(q + 1)**3*(3*q - 1)
Factor -96 + 4*l - 4*l**2 - 4*l**3 + 4*l**4 + 96.
4*l*(l - 1)**2*(l + 1)
Let x(a) be the second derivative of a**6/240 - a**5/40 + a**4/16 + a**3/2 + a. Let d(f) be the second derivative of x(f). Determine s, given that d(s) = 0.
1
Let l(b) be the first derivative of -2*b**4 + 2*b**3 + b**2 + 4. Factor l(p).
-2*p*(p - 1)*(4*p + 1)
Let j(z) be the second derivative of z**5/20 - z**3/6 + 43*z. What is v in j(v) = 0?
-1, 0, 1
Let u(z) be the first derivative of z**6/90 - z**4/18 + z**2/6 - 2*z + 1. Let g(r) be the first derivative of u(r). Factor g(q).
(q - 1)**2*(q + 1)**2/3
Suppose 4*q + 0 = 4, -q = -4*y + 7. Suppose 15*m**y - 15*m**2 + 10*m**2 + 2*m**3 + 14*m + 6 = 0. Calculate m.
-3, -1
Let p be 2/(5/(445/(-4))). Let y = p - -627/14. Factor y*j + 2/7*j**3 + 0 + 4/7*j**2.
2*j*(j + 1)**2/7
Suppose -2*w = -3*i, -5*i - 4*w + 22 = -0*w. Factor 4/5*l**3 - 4/5*l - 2/5 + 2/5*l**4 + 0*l**i.
2*(l - 1)*(l + 1)**3/5
Suppose -14 + 6 = -4*o. What is s in 41/3*s**3 + 2/3 - 28/3*s**5 - 13/3*s**4 - 13/3*s + 11/3*s**o = 0?
-1, 1/4, 2/7, 1
Let d = 16/37 + -70/333. Factor -d*b**2 - 2/9*b**3 + 0 + 4/9*b.
-2*b*(b - 1)*(b + 2)/9
Let v(t) = 2*t + 3. Let n be v(0). Factor 4 - 1 - n + 10*u**2 - 2*u - 8*u**3.
-2*u*(u - 1)*(4*u - 1)
Let a = 3 + 0. Solve -12*n**3 + 19*n**3 - 6*n**a = 0.
0
Suppose -2*c - 2 = 2. Let y be -2*(-1 + 2 + c). Let 4/3*f + 0 + 10/3*f**2 + y*f**3 = 0. What is f?
-1, -2/3, 0
Determine g, given that -3*g + 8 + 6*g**5 - 21*g**2 + 15*g**4 + 3 - 3*g**3 - 5 = 0.
-2, -1, 1/2, 1
Factor g**2 - g**4 + 19*g**3 + 0*g**2 - 2*g + 0*g**2 - 17*g**3.
-g*(g - 2)*(g - 1)*(g + 1)
Factor 0 + 0*w - 2/5*w**2 + 1/5*w**3.
w**2*(w - 2)/5
Let h(y) be the second derivative of 5*y**4/12 - 5*y**3/2 - 17*y. Factor h(c).
5*c*(c - 3)
Let q be (-5)/6*((-652)/40 - -16). Let -1/4*d**2 + 0*d + q*d**3 - 1/4*d**5 + 1/4*d**4 + 0 = 0. What is d?
-1, 0, 1
Let v be -1 - 2/2*(-7)/7. Let r be -2*1 + 24/10. Find d, given that v + 2/5*d**2 - r*d = 0.
0, 1
Suppose m - 3*m = 0. Let d(b) be the second derivative of -1/12*b**3 + 0*b**4 + m + 1/40*b**5 - 1/120*b**6 - 2*b + 1/8*b**2. Solve d(f) = 0 for f.
-1, 1
Let t = 10 - 6. Suppose t = -a + 7. Suppose 3*g**4 - 5*g**4 + 6*g**5 - 1 + 8*g**2 - 6*g**a - 5*g**4 = 0. Calculate g.
-1, -1/3, 1/2, 1
Factor 4/5*m**2 + 1/5*m**3 + 0*m + 0.
m**2*(m + 4)/5
Let f = 17 - 8. Let v be (f/(-162))/(1/(-8)). Find m such that -v*m + 4/9*m**3 + 0 + 10/9*m**2 - 10/9*m**4 = 0.
-1, 0, 2/5, 1
Let q = -10 - -15. Let b = 4 + 0. Let a(y) = 3*y**3 + 2*y**2 - 5. Let z(o) = -3*o**3 - 2*o**2 + 4. Let t(k) = b*a(k) + q*z(k). Suppose t(x) = 0. What is x?
-2/3, 0
Let 8 + 26*z**2 - 10*z**3 + 2*z**4 - 2*z**3 - 41*z + 17*z = 0. Calculate z.
1, 2
Let u = 5 - 13/3. Factor u*y + 1/3*y**2 + 0.
y*(y + 2)/3
Let g(l) be the third derivative of -2*l**7/105 - 2*l**6/45 - l**5/45 - 9*l**2. Suppose g(b) = 0. What is b?
-1, -1/3, 0
Let w = -10 - -6. Let l = 6 + w. Factor -2/3 - 2*b - 2*b**l - 2/3*b**3.
-2*(b + 1)**3/3
Let y(m) be the second derivative of -5*m + 1/8*m**4 + 1/12*m**3 + 1/60*m**6 + 3/40*m**5 + 0*m**2 + 0. What is d in y(d) = 0?
-1, 0
Let b(f) = -2*f - 2. Let z be b(-2). Factor 6/5*h**z + 2/5 - 8/5*h.
2*(h - 1)*(3*h - 1)/5
Let h be (-4)/(-34) - 200/(-34). Let b(q) be the third derivative of q**2 + 0*q**3 + 0 + 1/60*q**h + 0*q + 1/6*q**4 + 1/10*q**5. Let b(f) = 0. What is f?
-2, -1, 0
Let o(g) be the first derivative of -g**5/30 + g**4/9 - g**3/9 + 3*g + 3. Let x(j) be the first derivative of o(j). Determine m, given that x(m) = 0.
0, 1
Let f(q) = q**3 + 6*q**2 - 9*q - 10. Let i(o) = -o**2 - 3*o + 3. Let k be i(-5). Let j be f(k). Factor 32/3*w**5 + 0 + 20/3*w**2 + 80/3*w**j + 22*w**3 + 2/3*w.
2*w*(w + 1)**2*(4*w + 1)**2/3
Let a(i) = i**2 - 20*i - 18. Let g be a(21). Let 6/7*c**g + 2/7*c**2 + 0 - 4/7*c - 2/7*c**4 - 2/7*c**5 = 0. Calculate c.
-2, -1, 0, 1
Suppose 0 = 3*l - 3, -h + 6 = 3*l + 1. Determine d, given that 0*d**3 + 0*d + 0*d**h + 0 + 0*d**4 - 2/3*d**5 = 0.
0
Suppose 3*p + 4*m - 31 - 6 = 0, 0 = p + 5*m - 27. Let t(k) = -k + 7. Let d be t(p). Determine x so that 1 - 3*x - 3 + d*x**2 - x**2 = 0.
-2, -1
Let k(s) be the third derivative of -1/300*s**6 + 0*s**4 + 0 - 2*s**2 + 0*s**5 - 1/840*s**8 + 0*s**3 + 2/525*s**7 + 0*s. Factor k(n).
-2*n**3*(n - 1)**2/5
Factor 0 + 1/8*p**4 - 3/8*p**3 - 1/8*p**2 + 1/4*p + 1/8*p**5.
p*(p - 1)**2*(p + 1)*(p + 2)/8
Factor -5/2*r**2 + 7/2*r - 3/2 + 1/2*r**3.
(r - 3)*(r - 1)**2/2
Find o such that 1/4*o**3 + 1/4*o**2 - 1/4 - 1/4*o = 0.
-1, 1
Let b = 8 - 6. Solve 2*f**b - 2 - 4*f**2 - 1 + 5 - 2*f**3 + 2*f = 0.
-1, 1
Let y(u) be the third derivative of -1/24*u**3 - u**2 + 0 - 1/48*u**4 - 1/240*u**5 + 0*u. Factor y(d).
-(d + 1)**2/4
Let q = -36 - -41. Let p be q*(-4)/(-20)*9. Factor -1/3*r**3 + 3*r**2 - p*r + 9.
-(r - 3)**3/3
Let f(d) be the first derivative of d**4/30 - d**2/5 + 3*d + 3. Let c(j) be the first derivative of f(j). Factor c(q).
2*(q - 1)*(q + 1)/5
Let p(g) = 13*g + 182. Let u be p(-14). Find b, given that -14/15*b**2 - 8/15*b**3 + 4/15*b + u = 0.
-2, 0, 1/4
Let t(q) be the third derivative of -3*q**2 + 1/60*q**6 + 0 - 1/84*q**7 - 1/120*q**5 + 0*q + 1/336*q**8 + 0*q**4 + 0*q**3. Factor t(m).
m**2*(m - 1)**2*(2*m - 1)/2
Let u = 4 - 2. Suppose 6*n**3 - u*n**2 + 2*n**4 + 2 + 2 - 6*n - 4*n**4 = 0. Calculate n.
-1, 1, 2
Let o(s) be the third derivative of -s**7/630 - s**6/360 - 4*s**2. Determine r so that o(r) = 0.
-1, 0
Let o = 368/561 + 2/187. Let k = o - 1/6. Factor 0 + 0*r + 0*r**3 + 0*r**2 - k*r**4.
-r**4/2
Let l be 1*(-1)/(-12)*(1 - 0). Let q(i) be the second derivative of 0*i**2 + 0 + l*i**4 - 1/30*i**6 - 1/20