lve -7*c**2 + 16*c**2 - 1 - 9*c - 3 - 3*c**3 + 7 = 0 for c.
1
Let u(o) be the second derivative of o**5/5 - o**4/3 - 4*o**3/3 + 40*o. Let u(v) = 0. Calculate v.
-1, 0, 2
Let s(m) be the first derivative of -m**3/18 - m**2/4 - m/3 - 5. Factor s(l).
-(l + 1)*(l + 2)/6
Let j be 36/5 + (-3)/15. Suppose -12*w - 5*w**2 + j + 5 + 8*w**2 = 0. What is w?
2
Let z(i) be the first derivative of -12*i**5/5 + 21*i**4/4 + 30*i**3 + 69*i**2/2 + 12*i + 28. Suppose z(c) = 0. What is c?
-1, -1/4, 4
Let d(n) = -10*n**3 + n**2. Let h be d(-1). Let p**2 - p**4 + p**3 + p**2 + 19*p**4 + h*p**3 = 0. Calculate p.
-1/3, 0
Solve -174 - 208 - 7*j**2 + 62 - 80*j + 2*j**2 = 0 for j.
-8
Factor -5*v**2 + 5*v**2 - 2*v**4 + 7*v**3 - 4 + 14*v + 3*v**3 - 18*v**2.
-2*(v - 2)*(v - 1)**3
Factor -5/8*d + 0 + 1/8*d**2.
d*(d - 5)/8
Factor -6*o**2 + 4*o + 65 - 65 + 2*o**4.
2*o*(o - 1)**2*(o + 2)
Let l(k) be the third derivative of -k**5/510 + k**4/51 - 4*k**3/51 + 15*k**2. Suppose l(r) = 0. Calculate r.
2
Let o(i) = 13*i**5 - 17*i**4 - 5*i**3 - 9. Let x(v) = -3*v**5 + 4*v**4 + v**3 + 2. Let s(a) = -2*o(a) - 9*x(a). Factor s(z).
z**3*(z - 1)**2
Let j(c) = 2*c + 18. Let m be j(-9). Let l(w) be the second derivative of m*w**2 + 1/70*w**5 + 0 + 0*w**3 + 2*w + 0*w**4. Factor l(f).
2*f**3/7
Let j(h) be the first derivative of 4/21*h**3 + 2*h + 1/42*h**4 + 4/7*h**2 - 1. Let w(b) be the first derivative of j(b). Find i, given that w(i) = 0.
-2
Let k(o) = -9*o**5 - 34*o**4 - 26*o**3 - 6*o - 6. Let t(a) = 10*a**5 + 35*a**4 + 25*a**3 + 5*a + 5. Let v(d) = -5*k(d) - 6*t(d). Let v(p) = 0. What is p?
-2, -2/3, 0
Let x(q) = q**4 + q + 1. Let j(p) = -2*p**4 + 10*p**3 + 18*p**2 + 10*p. Let z(k) = j(k) + 4*x(k). Find y, given that z(y) = 0.
-2, -1
Let t(x) be the second derivative of -x**6/6 + x**5/4 + 5*x**4/12 - 5*x**3/6 + 9*x. Suppose t(v) = 0. What is v?
-1, 0, 1
Suppose n - 5*f + 0 = -8, 5*n - 2*f = 6. Let o = 269/2 + -134. Factor 1/4*w**3 + 0 + 1/4*w + o*w**n.
w*(w + 1)**2/4
Let y be (-9)/((-27)/(-102)) - 3. Let h = -110/3 - y. Factor -1/3*r**3 + 0*r + 1/3*r**5 + 0 + h*r**2 - 1/3*r**4.
r**2*(r - 1)**2*(r + 1)/3
Let j = -3221/7 + 461. Factor -6/7*y - 2/7*y**3 - j*y**2 - 2/7.
-2*(y + 1)**3/7
Let o(a) be the third derivative of a**6/60 - a**5/10 + a**4/6 + 2*a**2. Factor o(v).
2*v*(v - 2)*(v - 1)
Suppose 127*z - 129*z = 0. Let m(w) be the third derivative of 0 + 0*w**3 + w**2 + 0*w**5 + z*w + 0*w**4 + 1/420*w**6. Determine t so that m(t) = 0.
0
Let g be (-1 - 2) + 7*66/77. Determine b so that -8/3 + 8*b + 10/3*b**4 - 2/3*b**2 - 8*b**g = 0.
-1, 2/5, 1, 2
Suppose -5*s + 3*f - 142 + 973 = 0, 2*s - 321 = 5*f. Let l be s/245 - 4/14. Factor -l - 2/5*h**2 + 4/5*h.
-2*(h - 1)**2/5
Let d(z) be the first derivative of 5*z**4/16 - 5*z**3/6 + 5*z**2/8 + 18. Solve d(l) = 0 for l.
0, 1
Let k(z) be the second derivative of -z**6/45 + z**5/15 + z**4/6 - 39*z. Factor k(c).
-2*c**2*(c - 3)*(c + 1)/3
Suppose -4*y = i + 2, 9*i - 4*i = 2*y - 10. Factor -1/4*n**2 + y*n + 1/4*n**3 + 0.
n**2*(n - 1)/4
Suppose -h + 33 = 4*m + 2, 5*h = -2*m + 137. Solve 9*o + 8*o - h + 0*o**2 - 3*o**2 + o = 0 for o.
3
Let j(v) be the third derivative of v**2 - 1/6*v**3 - 1/40*v**6 + 0 - 1/24*v**4 + 0*v + 1/12*v**5. Solve j(d) = 0.
-1/3, 1
Factor 3/4*n**2 - 1/4*n**4 + 0 - 1/2*n + 0*n**3.
-n*(n - 1)**2*(n + 2)/4
Let y be (9/(-6))/(-2 + (-15)/(-12)). Let -y*f + 2 + 1/2*f**2 = 0. What is f?
2
Let -2/9*g**2 + 2/9*g + 0 = 0. Calculate g.
0, 1
Let t(s) = -s. Let f(y) = -3*y + 9. Let x(u) = -f(u) + 5*t(u). Let j be x(-7). Let 2*d**3 - 3*d**4 - d**5 + 3*d**j - d**4 = 0. Calculate d.
0, 1
Suppose -d - 10 = -2*d + 4*z, 3*d + 5*z + 21 = 0. Let q be (d - -1)*10/(-35). Suppose 0*t + 0 - q*t**2 = 0. What is t?
0
Suppose -9 = -i - 4. Let f = i - 3. Solve -b + 3*b - 2*b**4 - 2*b**3 - 2*b**4 + 4*b**f = 0 for b.
-1, -1/2, 0, 1
Factor -4/9*r**2 - 20/9*r + 8/3.
-4*(r - 1)*(r + 6)/9
Let y(z) = z - 3. Let x be y(8). Let v be (-17)/(-3) - x/(-15). Determine p, given that -3/2 - v*p + 9*p**3 - 3/2*p**2 = 0.
-1/2, -1/3, 1
Let z(h) = -113*h**3 + 36*h**2 + 2*h - 5. Let t(n) = -114*n**3 + 36*n**2 + 3*n - 6. Let l(u) = 5*t(u) - 6*z(u). What is d in l(d) = 0?
0, 1/6
Suppose 21 = 6*w - 3. What is p in 9/4*p**w - 9/4*p**2 - 3*p**5 - 3/4*p + 0 + 15/4*p**3 = 0?
-1, -1/4, 0, 1
Let f be (0/(-1 + 4))/((-6)/(-3)). Let s(u) be the third derivative of -4*u**2 + 1/270*u**5 + 1/3*u**3 + f*u - 1/18*u**4 + 0. Determine m so that s(m) = 0.
3
Suppose -3*u = -4*w - 1, 0 = 4*w + u - 4 - 7. Factor -3/5*r**4 - 3/5*r**3 + 3/5*r + 0 + 3/5*r**w.
-3*r*(r - 1)*(r + 1)**2/5
Let g = -145/12 - -1039/84. Let g*h**2 + 12/7*h + 18/7 = 0. What is h?
-3
Let t(x) be the second derivative of x**8/3360 + x**4/4 + 4*x. Let s(o) be the third derivative of t(o). Factor s(k).
2*k**3
Let t(l) be the second derivative of l**4/3 + 2*l**3 + 4*l. Factor t(g).
4*g*(g + 3)
Let a(q) be the first derivative of q**4/16 - q**3/6 + 3. Let a(o) = 0. Calculate o.
0, 2
Let n(q) be the first derivative of -5*q**4/4 - 35*q**3/3 - 55*q**2/2 - 25*q + 72. What is p in n(p) = 0?
-5, -1
Let z = 296/231 + 4/77. Let l(i) be the second derivative of -1/6*i**4 - 4*i**2 - i + 0 - z*i**3. Solve l(n) = 0 for n.
-2
Let z = 2918/547 - 2/1641. Factor 8/3*c - z*c**2 + 0 - 2/3*c**4 + 10/3*c**3.
-2*c*(c - 2)**2*(c - 1)/3
Suppose -4*t + 11 = -3*c, -c + 4*t - 12 = t. Factor 47*a - 3*a**2 + 2*a**c + a**2 - 47*a.
2*a**2*(a - 1)
Factor r**5 + 2*r**2 - 2 - 4*r**4 + 0*r**5 - 5*r + 4*r**3 + 2 + 2.
(r - 2)*(r - 1)**3*(r + 1)
Let m = 2 - 0. Let q be 11/(-66)*(-3)/m. Find f, given that -1/4*f**3 + 0 + 1/4*f**2 - q*f**4 + 1/4*f = 0.
-1, 0, 1
Let h(u) be the second derivative of 1/189*u**7 + 3*u - 1/27*u**4 + 1/27*u**3 - 1/45*u**5 + 0 + 1/135*u**6 + 1/9*u**2. Factor h(q).
2*(q - 1)**2*(q + 1)**3/9
Let q(o) be the third derivative of o**6/120 - 13*o**5/60 + o**4/2 + o**3/3 - o**2. Let f be q(12). Let 0*g - 1/2 + 1/2*g**f = 0. What is g?
-1, 1
Suppose 13 = 5*q - 7. Factor -2*a - 3*a**3 + a**3 + q*a**2 + 0*a.
-2*a*(a - 1)**2
Suppose j = 3*m + 5*j, -27 = -3*m + 5*j. Let y(d) be the third derivative of 1/48*d**m + d**2 + 0*d + 1/12*d**3 + 0 - 1/60*d**5. What is b in y(b) = 0?
-1/2, 1
Let v(l) = l**2 - 6*l - 1. Let x be v(5). Let o be 2/(-3) - 8/x. Determine u so that -2/3*u**2 - 2/9 + o*u + 2/9*u**3 = 0.
1
Let w be 7 + 6 + -5 - 6. Factor 0 + 0*d + 2/3*d**w + 2/3*d**5 - 2/3*d**3 - 2/3*d**4.
2*d**2*(d - 1)**2*(d + 1)/3
Let z(p) be the second derivative of p**4/12 + p**3/6 - p**2 - 2*p. Factor z(g).
(g - 1)*(g + 2)
Let d(n) be the second derivative of -n**4/24 - n**3/3 - n**2 - 7*n. Factor d(p).
-(p + 2)**2/2
Let d be (-1024)/12*(-2)/14. Let y = d - 76/7. Factor -y - 12*x - 27*x**2.
-(9*x + 2)**2/3
Let s(d) be the first derivative of d**8/560 + d**7/140 + d**6/120 + d**3 - 7. Let p(w) be the third derivative of s(w). Factor p(n).
3*n**2*(n + 1)**2
Determine q, given that -2/7*q**3 + 6/7*q - 4/7 + 0*q**2 = 0.
-2, 1
Let x(t) be the first derivative of t**5/10 - t**4/8 - t**3/2 + t**2/4 + t - 1. Factor x(z).
(z - 2)*(z - 1)*(z + 1)**2/2
Let z = -6 + 8. Suppose b**3 - z*b**3 + 0*b**3 + 2*b - b**3 = 0. What is b?
-1, 0, 1
Let m = 7/20 + 1/20. Let a be -4 + (-51)/(-15) + 1. Factor 6/5*g**2 + m*g**3 + 6/5*g + a.
2*(g + 1)**3/5
Let n = 5882/19 + 72706/209. Let v = 658 - n. Factor -2/11*g + v*g**4 - 14/11*g**3 + 10/11*g**2 + 0.
2*g*(g - 1)**2*(3*g - 1)/11
Let m be (-1)/(-3) - (-35)/(-150). Let w(l) be the first derivative of 0*l**2 + 0*l**4 + 1/6*l**3 - m*l**5 - 2 + 0*l. Determine h, given that w(h) = 0.
-1, 0, 1
Let g(m) = -m**3 - m - 1. Let a(h) = -30*h**3 - 6*h**2 - 9. Let i(z) = a(z) - 15*g(z). Factor i(y).
-3*(y - 1)*(y + 1)*(5*y + 2)
Let 16*w**2 - w**3 + 4 - 44*w + 2 + 21*w**3 + 2 = 0. What is w?
-2, 1/5, 1
Let p(l) be the third derivative of l**8/280 - 2*l**7/525 - 11*l**6/900 + 2*l**5/225 + l**4/45 - 3*l**2. Factor p(u).
2*u*(u - 1)**2*(3*u + 2)**2/15
Factor -25 + 74*q + 27*q**2 - 20*q**3 - 7 + 41*q**2 - 18*q.
-4*(q - 4)*(q + 1)*(5*q - 2)
Let w(s) be the first derivative of 3*s**4/2 - 4*s**3/3 - 7*s**2 - 4*s + 8. Factor w(v).
2*(v - 2)*(v + 1)*(3*v + 1)
Let i(k) = 11*k**3 - 10*k**2 + 2*k + 2. Let l(y) = -5*y**3 + 5*y**2 - y - 1. Let p(h) = -2*i(h) - 5*l(h). Factor p(o).
(o - 1)**2*(3*o + 1)
Let z(r) = r**3 + 3*r**2 - 3*r + 1. Suppose 6*k = 4*k - 2. Let m(x) = -x*