 the second derivative of -h**4/3 + h**3/3 + 3*h**2 + 13*h. Solve g(u) = 0.
-1, 3/2
Let q(u) = u**3 - 9*u**2 + 14*u. Let n be q(7). Let 1/6*l - 1/6*l**4 - 1/6*l**3 + 1/6*l**2 + n = 0. What is l?
-1, 0, 1
Let m(q) = -q + 36. Let h be m(34). Let g(p) = p + 5. Let j be g(-5). Factor 3/5*a + j - 3/5*a**h.
-3*a*(a - 1)/5
Let f(x) be the first derivative of x**3 - 3*x**2 + 6. Let f(l) = 0. What is l?
0, 2
Let b(i) = 14*i**5 + 57*i**4 + 68*i**3 + 37*i**2 - 2*i - 9. Let o(l) = l**4 + l**2 - 1. Let d(f) = 2*b(f) - 10*o(f). Factor d(p).
4*(p + 1)**4*(7*p - 2)
Solve q**2 + 0 + 2/7*q + 5/7*q**4 + 1/7*q**5 + 9/7*q**3 = 0 for q.
-2, -1, 0
Suppose -10*d = 3*d - 52. Factor -1/3*j + 0 + 1/3*j**3 + 1/3*j**d - 1/3*j**2.
j*(j - 1)*(j + 1)**2/3
Let c(w) = -w**3 + 28*w**2 + w - 26. Let f be c(28). Solve -1/2*b**2 - f - 2*b = 0.
-2
Let r(t) = 2*t**2 + 36*t + 165. Let g(b) = -2*b**2 - 36*b - 166. Let n(s) = 3*g(s) + 4*r(s). What is a in n(a) = 0?
-9
Let k = -1 + 0. Let h(p) = p**2 + 9*p - 1. Let t(m) = -m**2 - 8*m + 1. Let u(o) = -5*h(o) - 6*t(o). Let n(x) = -x. Let c(a) = k*u(a) - 3*n(a). Factor c(d).
-(d - 1)*(d + 1)
Let o(y) be the third derivative of 4*y**7/1995 - 7*y**6/1140 - y**5/285 - 2*y**2. Find r such that o(r) = 0.
-1/4, 0, 2
Let u(d) be the first derivative of -d**6/27 + d**4/9 - d**2/9 - 24. Factor u(x).
-2*x*(x - 1)**2*(x + 1)**2/9
Determine a, given that 2*a**3 + 55*a**2 - 114*a**2 + 59*a**2 = 0.
0
Let t(k) be the second derivative of 0 + 3*k + 1/36*k**3 - 1/6*k**2 + 1/72*k**4. Determine h so that t(h) = 0.
-2, 1
Let n(r) be the first derivative of -7/5*r**5 + 41/12*r**4 + 2/9*r**6 - 2/3*r - 1 + 5/2*r**2 - 37/9*r**3. Factor n(x).
(x - 2)*(x - 1)**3*(4*x - 1)/3
Suppose 92 = 14*r + 22. Let v(n) be the second derivative of 0 - 1/90*n**r + 0*n**3 - 1/54*n**4 + 0*n**2 - 2*n. Determine p so that v(p) = 0.
-1, 0
Let y(p) be the second derivative of -5*p + 0 - 1/84*p**4 - 1/7*p**2 - 1/14*p**3. Suppose y(u) = 0. Calculate u.
-2, -1
Let o be 2*-1 - (-3 - 3). Suppose -o*g + 6 = -6*g. Let m(t) = -2*t**2 + 7*t - 1. Let q(f) = -f**2 + 4*f - 1. Let u(r) = g*m(r) + 5*q(r). Factor u(j).
(j - 2)*(j + 1)
Solve -m + 4*m**2 + 5*m - 11*m**2 - 6*m = 0 for m.
-2/7, 0
Let p(w) be the third derivative of -w**5/10 + w**4/18 - 40*w**2. What is g in p(g) = 0?
0, 2/9
Suppose 0*a = -2*a. Let g(y) be the third derivative of 4/945*y**7 + 0 - 2*y**2 + 0*y - 1/540*y**6 + 1/504*y**8 + a*y**3 - 1/135*y**5 + 0*y**4. Factor g(m).
2*m**2*(m + 1)**2*(3*m - 2)/9
Let v(m) = m**3 + 4*m**2 - 4*m + 5. Let d be v(-5). Solve -q**2 - 3 + d*q**2 - 3*q + 4*q**2 + 3*q**3 = 0.
-1, 1
Let s(u) = -4*u**2 - u + 1. Let t(v) be the first derivative of -v - 1. Let m(b) = s(b) - 2*t(b). Factor m(j).
-(j + 1)*(4*j - 3)
Determine s, given that -10*s**2 - 3*s**3 + 18*s + 0*s**3 - 18*s + s**4 = 0.
-2, 0, 5
Let j = -3085/9 - -343. Suppose j*z**2 - 8/9*z + 2/3 = 0. What is z?
1, 3
Factor -4 - 4*m**3 - 5 + 12*m - 1 + 2.
-4*(m - 1)**2*(m + 2)
Let m(p) be the second derivative of -5*p**4/12 + 18*p. Find b, given that m(b) = 0.
0
Factor -11 + 0 - 6*m + 5*m**2 - 2*m**2 + 2.
3*(m - 3)*(m + 1)
Let o = 34 + -32. Let h(s) be the first derivative of 0*s - 2 - s**o - 2/3*s**3. Find u, given that h(u) = 0.
-1, 0
Let v(h) be the first derivative of h**4/2 - 3*h**2 + 4*h + 1. Factor v(z).
2*(z - 1)**2*(z + 2)
Let g(o) be the second derivative of -o**6/30 + 3*o**5/20 - o**4/4 + o**3/6 - o. Factor g(t).
-t*(t - 1)**3
Let s(w) be the third derivative of w**6/1980 - w**4/132 - w**3/6 + 3*w**2. Let n(q) be the first derivative of s(q). Solve n(z) = 0 for z.
-1, 1
Suppose 10*i**3 + 40*i**4 - 24*i**5 + 85*i**3 + 30*i**2 + 2*i**5 - 3*i**5 = 0. Calculate i.
-1, -2/5, 0, 3
Suppose -21 = -2*x - 3*o, -3*o = x - 21 + 3. Factor x*r - 2*r + r**5 + 30*r**3 - 32*r**3.
r*(r - 1)**2*(r + 1)**2
Let z(n) = 5*n**2 + 4*n. Let o(q) = 3*q**2 - 9*q**2 - 8*q - 3*q**2. Let g(i) = -3*o(i) - 5*z(i). Let g(r) = 0. Calculate r.
-2, 0
Factor 3*q + q**3 + q - 25 + q + 27 + 4*q**2.
(q + 1)**2*(q + 2)
Suppose 4*z + 23 = s, -6*s + s + z = -39. Factor 2*v**2 - s*v**3 - v**3 + 2*v**3 + 7*v**3.
v**2*(v + 2)
Suppose r - 5*u = -2*u + 14, -4*r = 2*u. Suppose n - 2 = y, 4 = y + 3*y + r*n. Factor 1/2*s**4 + y*s + 1/4*s**3 + 0*s**2 + 0.
s**3*(2*s + 1)/4
Suppose -2*j + 4 = -0*j. Factor 5*v**2 + v**3 + 6*v + 2 + v**3 - 2*v**j + 3*v**2.
2*(v + 1)**3
Let i be (2 + 6)*110/(-2). Let v = i - -3090/7. Factor -8/7*p + 2/7 - v*p**2.
-2*(p + 1)*(5*p - 1)/7
Let u be 6/8*8/36. Let f(s) be the third derivative of 0 + 0*s + u*s**3 - 2*s**2 - 1/3*s**4 + 4/15*s**5. Suppose f(l) = 0. What is l?
1/4
Let l(a) be the first derivative of -1/3*a**3 + 2 - 1/12*a**4 + 0*a**2 + 1/180*a**6 + 0*a**5 + 0*a. Let n(s) be the third derivative of l(s). Factor n(w).
2*(w - 1)*(w + 1)
Let t = -25/3 + 76/9. Let g(l) be the first derivative of t*l**4 - 5/27*l**6 - 2/15*l**5 + 3 + 0*l + 0*l**3 + 0*l**2. Factor g(c).
-2*c**3*(c + 1)*(5*c - 2)/9
Factor -3 - 15/4*q**2 + 3/4*q**3 + 6*q.
3*(q - 2)**2*(q - 1)/4
Let s be 26/40 + 1/(-4). Factor 0 + 1/5*a**2 - s*a + 1/5*a**3.
a*(a - 1)*(a + 2)/5
Let z be 4*5/35*1. Factor -4/7 - 1/7*y**2 + z*y.
-(y - 2)**2/7
Let z(w) be the third derivative of w**7/6300 + w**6/450 + w**5/75 - w**4/6 + 5*w**2. Let g(j) be the second derivative of z(j). Factor g(f).
2*(f + 2)**2/5
Factor 3 + 8/3*g**2 - 2/3*g**3 + 6*g - 1/3*g**4.
-(g - 3)*(g + 1)**2*(g + 3)/3
Let j(u) be the third derivative of 4/21*u**3 + 0 + 0*u + 2/21*u**4 + 1/42*u**5 - 3*u**2 + 1/420*u**6. Solve j(y) = 0 for y.
-2, -1
Let o(x) = -4*x**2 - 8*x - 16. Let n(d) = -d**2. Let k(c) = -3*n(c) + o(c). Determine l, given that k(l) = 0.
-4
Let o(q) = -2*q**4 - 2*q**3 + 2*q**2 + 2*q. Let c(n) = 2*n**4 + 3*n**3 - 2*n**2 - 3*n. Let j(x) = 4*c(x) + 3*o(x). Let j(t) = 0. What is t?
-3, -1, 0, 1
Let i(f) be the first derivative of f**5 - 5*f**3 + 5*f**2 - 8. Factor i(m).
5*m*(m - 1)**2*(m + 2)
Let k = -1 + 4. Let j(h) be the second derivative of 0 - 1/3*h**3 - 1/10*h**5 + 0*h**2 + k*h + 1/3*h**4. Factor j(w).
-2*w*(w - 1)**2
Let r(o) be the first derivative of 2*o**3/33 + 4*o**2/11 - 20. Factor r(z).
2*z*(z + 4)/11
Let x(f) be the third derivative of 0*f + 0 + 0*f**5 + 0*f**4 + 1/105*f**7 + 5*f**2 + 0*f**6 + 0*f**3. Factor x(u).
2*u**4
Suppose -9*t = -14*t. Suppose 2/5*s**2 + 0*s + t = 0. What is s?
0
Let c = 6 - 3. Solve -2 + 6*x + 0 - 2*x**c - 2 = 0 for x.
-2, 1
Let p(r) = -3*r**5 - 8*r**4 + 7*r**3 + r**2 + 3*r - 7. Let s(x) = -2*x**5 - 4*x**4 + 4*x**3 + 2*x - 4. Let l(i) = -4*p(i) + 7*s(i). Factor l(j).
-2*j*(j - 1)**3*(j + 1)
Let l(q) be the second derivative of 0 - q + 1/4*q**2 - 1/6*q**3 + 1/24*q**4. Factor l(j).
(j - 1)**2/2
Let v(r) be the first derivative of -r**8/560 + r**6/20 - r**5/5 + 3*r**4/8 + 5*r**3/3 - 3. Let w(m) be the third derivative of v(m). Let w(x) = 0. Calculate x.
-3, 1
Let b(o) = -26*o**2 - 62*o - 36. Let n(z) = 9*z**2 + 21*z + 12. Let i(a) = -5*b(a) - 14*n(a). Factor i(p).
4*(p + 1)*(p + 3)
Let y(q) be the first derivative of 1/2*q**2 + 0*q - 4/3*q**3 + 4. Factor y(l).
-l*(4*l - 1)
Let t(j) = j**2 - j - 1. Let d(s) = -30*s**3 - 7*s**2 + 8*s + 5. Let m(r) = -d(r) - 6*t(r). Let z be m(1). Factor -8/3 - 50/3*y**3 - z*y**2 - 16*y.
-2*(y + 1)*(5*y + 2)**2/3
Let l(m) be the first derivative of m**4/3 + 8*m**3/3 + 8*m**2 - 11*m + 10. Let g(z) be the first derivative of l(z). Let g(x) = 0. What is x?
-2
Let n(i) be the second derivative of 0 + i**3 + 1/4*i**4 + 0*i**2 - 5*i. Find r such that n(r) = 0.
-2, 0
Let z be (-11)/(-5) - 2/10. Determine p, given that -3/5 + 3/5*p**3 - 9/5*p**z + 9/5*p = 0.
1
Let v(y) = y**2 - 2*y + 1. Let a be v(3). Suppose h - a = 0, 16 = 5*o + h + 3*h. Factor 1/3*d**2 + o + 0*d + 1/3*d**4 - 2/3*d**3.
d**2*(d - 1)**2/3
Let z(k) be the first derivative of -3*k**5/10 + k**3/2 - 7. Factor z(o).
-3*o**2*(o - 1)*(o + 1)/2
Let t(i) be the second derivative of -i**6/120 - 3*i**5/80 + i**4/16 + 11*i**3/24 + 3*i**2/4 + i + 12. Let t(j) = 0. What is j?
-3, -1, 2
Find m, given that -14*m - 249/2*m**3 - 163*m**2 + 20 + 63/2*m**4 = 0.
-2/3, 2/7, 5
Let r(f) = -3*f**5 + 3*f**4 - 3*f**3 - 3*f**2. Suppose 2*n - 9 = 1. Let s(g) = -6*g**5 + 0*g**5 + 5*g**n. Let i(p) = -r(p) + 6*s(p). Factor i(b).
-3*b**2*(b - 1)*(b + 1)**2
Let m(o) be the second derivative of -1/48*o**4 + 0*o**2 - 1/80*o**5 + 0 + 1/120*o**6