at is v in -10*v**4 - 75*v**2 + 4*v**5 - 12 - 11*v**4 + 48*v - v**5 + 57*v**3 = 0?
1, 2
Let p(n) = 32*n**3 + 32*n**2 + 12*n. Let m(z) = -13*z**3 - 13*z**2 - 5*z. Let v(w) = 12*m(w) + 5*p(w). Factor v(y).
4*y**2*(y + 1)
Let 0*c + 2/3*c**2 - 10/3*c**4 + 0 + 2/3*c**3 + 2*c**5 = 0. What is c?
-1/3, 0, 1
Let c(i) be the third derivative of -i**6/160 - i**5/80 - 7*i**2. Suppose c(t) = 0. What is t?
-1, 0
Let a(z) be the first derivative of -z**6/360 - z**5/120 - 2*z**3/3 + 1. Let l(w) be the third derivative of a(w). Suppose l(u) = 0. Calculate u.
-1, 0
Let f(m) be the third derivative of m**5/20 - 5*m**4/4 + 25*m**3/2 - 13*m**2. Determine i, given that f(i) = 0.
5
Let v(p) be the first derivative of -9*p**4/10 + 4*p**3/15 + 1. Factor v(c).
-2*c**2*(9*c - 2)/5
Suppose -5 + 4*v**3 + 73*v**2 + 48 + 38 + 342*v = 0. Calculate v.
-9, -1/4
Suppose -4*r + 0*u = -2*u, -26 = -3*r - 5*u. Find s, given that 13*s**3 + 2*s**4 + 28*s + 25*s**2 + 5*s**r + 0 + 8 = 0.
-2, -1/2
Find v, given that -9/4*v + 3/4 + 9/4*v**2 - 3/4*v**3 = 0.
1
Let k(z) be the first derivative of 3 + 0*z + 0*z**2 - 1/3*z**3. Factor k(u).
-u**2
Let f(n) = -n**3 + n**2 - 1. Let s be f(0). Let c be s*1*16/(-8). Determine g so that 2*g**4 - 8*g**5 - 4*g**3 + 5*g**5 - 4*g**2 + 10*g**3 - 3*g + c = 0.
-1, 2/3, 1
Let 183 - 64*c + 86 + 2*c**2 + 243 = 0. Calculate c.
16
Let s(z) = 2*z**3 + 7*z**2 + 9*z + 3. Let r(g) = -g**3 - g**2 + 1. Let v(m) = r(m) + s(m). Factor v(q).
(q + 1)**2*(q + 4)
Let q(d) be the first derivative of -1/18*d**4 + 0*d**2 + 3*d + 0*d**3 + 3 - 1/60*d**5. Let u(w) be the first derivative of q(w). Let u(t) = 0. What is t?
-2, 0
Let k(d) be the third derivative of d**5/60 - d**4/4 + 3*d**3/2 + 16*d**2. Determine q, given that k(q) = 0.
3
Let k(a) be the second derivative of -7/3*a**3 + 0 - a**2 + 2*a - 49/24*a**4. Suppose k(g) = 0. What is g?
-2/7
Let v(i) = i**2 - 17*i + 5. Let p be v(17). Let r(f) be the second derivative of f**2 + f**3 + 1/2*f**4 + 0 + 4*f + 1/10*f**p. Suppose r(z) = 0. What is z?
-1
Factor 4*f - 2*f**2 - 5*f**2 + 3*f**2 - 2*f**2 + 2*f**3.
2*f*(f - 2)*(f - 1)
Let n = -2 + 4. Determine t so that -t + t**3 + 2 - 4*t**2 - 2*t**n + 3*t**2 + t**4 + 0*t**3 = 0.
-2, -1, 1
Solve 3/7*g**2 + 6/7*g + 3/7 = 0 for g.
-1
Suppose -c - 4*f = 4*c - 27, 2*c - 4*f + 6 = 0. Factor 0 + 1/3*t**4 - 1/3*t**5 + 1/3*t**c - 1/3*t**2 + 0*t.
-t**2*(t - 1)**2*(t + 1)/3
Suppose -5*w + 100 = -0*b + 5*b, -w - 112 = -5*b. Factor 175*x**4 + 4 + 7*x - b*x - 25*x + 145*x**2 - 235*x**3 - 49*x**5.
-(x - 1)**3*(7*x - 2)**2
Let z(i) be the second derivative of 0 - 1/7*i**3 + i - 1/42*i**4 - 2/7*i**2. Let z(p) = 0. What is p?
-2, -1
Let x(k) be the first derivative of 2*k**3/21 + 5*k**2/7 - 4. Let x(z) = 0. What is z?
-5, 0
Suppose -4*p + 33 + 0 = -5*o, 10 = p - 3*o. Suppose 3*j - 6 = -j - n, p = 3*j + 2*n. Factor -5*v + 5*v**3 + 0*v**2 - v**2 - 1 + 3*v**4 - j.
(v - 1)*(v + 1)**2*(3*v + 2)
Let l = 0 - 0. Let j be (-11)/((-693)/45)*4/10. Factor 0 + l*f - 4/7*f**3 + j*f**2.
-2*f**2*(2*f - 1)/7
Solve -4*i**3 + 104*i - 106*i + i**2 + 3*i**2 + 2*i**3 = 0.
0, 1
Let i(n) be the first derivative of n**4/28 - n**3/7 - 38. Factor i(k).
k**2*(k - 3)/7
Determine h so that 25*h**3 - 14*h**4 - 20*h - h**4 + 48*h**2 - 28*h**2 = 0.
-1, 0, 2/3, 2
Suppose 5*h = 12 + 28. Suppose 0 = -4*u + h, 3*u - 3 = 5*i - 7. Factor -5*x**i + 5*x**2 - 2*x**2.
-2*x**2
Suppose 4 = -3*n - 2, -2*j + 5*n = -14. Let o(y) be the third derivative of -y**j + 0*y**4 + 0 - 1/15*y**3 + 1/75*y**5 - 1/525*y**7 + 0*y + 0*y**6. Factor o(z).
-2*(z - 1)**2*(z + 1)**2/5
Suppose 2*x - 8*x - 6 = 0. Let n be x + (-8)/(-18) + 1. Determine o so that 2/9 + n*o + 2/9*o**2 = 0.
-1
Let x(b) be the first derivative of -b**6/80 + b**2 - 4. Let g(q) be the second derivative of x(q). Factor g(f).
-3*f**3/2
Suppose -3*i - 4 + 1 = 0. Let c(n) = -n**2 - 1. Let t(w) = 6*w**2 + 3. Let g(a) = i*t(a) - 3*c(a). Factor g(d).
-3*d**2
Let d(p) be the first derivative of p**6/10 - 3*p**5/20 - p**4/4 + p**3/2 - 3*p + 2. Let o(b) be the first derivative of d(b). Let o(y) = 0. What is y?
-1, 0, 1
Let f(u) be the second derivative of 0*u**3 + 1/21*u**7 + 3*u + 0 + 0*u**4 + 1/10*u**5 - 2/15*u**6 + 0*u**2. Factor f(c).
2*c**3*(c - 1)**2
Let y(m) be the third derivative of -m**6/30 - m**5/3 - m**4 - 4*m**2. Suppose y(g) = 0. Calculate g.
-3, -2, 0
Let q be (1 - (2 - 0))*-5. Suppose -4*s - 3*a + 23 = 0, 35 = q*s - 2*a + 7*a. Factor 4*n + 12*n**3 + s*n**5 + 8*n**2 + 8*n**4 - 3*n + n.
2*n*(n + 1)**4
Suppose 5*c - h = -6*h - 5, 11 = -2*c - 5*h. Factor -3/2*s + 0 - 1/2*s**c.
-s*(s + 3)/2
Determine m, given that 10/7*m + 8/7 + 2/7*m**2 = 0.
-4, -1
Let b be ((3 - 3)/(-6))/(-1). Determine m, given that b*m + 1/2*m**3 + 1/4 - 3/4*m**2 = 0.
-1/2, 1
Let x(r) be the second derivative of -3*r**5/10 - r**4/3 + r**3 + 2*r**2 + 14*r. Factor x(u).
-2*(u - 1)*(u + 1)*(3*u + 2)
Suppose l - 4*u + 15 = u, 3*l - u = -3. Suppose 1/2*n - 1/2*n**2 + l = 0. Calculate n.
0, 1
Let h(g) be the second derivative of -1120*g**7/3 - 5264*g**6/15 - g**5 + 374*g**4/3 + 200*g**3/3 + 16*g**2 - 6*g. Find q such that h(q) = 0.
-2/7, -1/4, 2/5
Suppose 0 = -5*j - 0*j + 1530. Let z = j + -910/3. Find w such that 2/3*w**2 + 0 + 4/3*w - 2*w**4 - z*w**3 = 0.
-1, 0, 2/3
Let q(j) be the second derivative of -j**4/66 + j**3/11 - 2*j**2/11 - j. Solve q(r) = 0.
1, 2
Let p(v) = 2*v + 6. Let l be p(5). Let g be (l/6)/((-6)/(-9)). Factor o + g*o**2 - 5*o**2 + 0*o.
-o*(o - 1)
Factor 0*c + 5/4*c**3 - 1/2*c**2 + 0.
c**2*(5*c - 2)/4
Let l = 65/18 - 28/9. Factor j**3 + 0*j**2 - 1/2 + l*j**4 - j.
(j - 1)*(j + 1)**3/2
Let m(n) = n**2. Let a(d) = 13*d**2 + 2*d. Let q(v) = -12*v**2 - v. Let p(x) = 4*a(x) + 5*q(x). Let y(f) = 5*m(f) + p(f). What is w in y(w) = 0?
0, 1
Suppose -2*y = y - p - 17, 13 = -y + 5*p. Factor 11*r**4 - y*r**4 + 2*r**2 - 1 - 5*r**4.
-(r - 1)**2*(r + 1)**2
Let b(s) be the second derivative of -s**5/110 + s**4/33 - s**3/33 + s. Factor b(z).
-2*z*(z - 1)**2/11
Let -8 - 40*l**2 - 275*l**3 - 272*l**3 - 34*l + 539*l**3 = 0. Calculate l.
-4, -1/2
Suppose 0*i + i - 5 = 0. Let k(l) = l**2 - 4*l - 5. Let p be k(i). Factor 2/7*n**4 + 2/7*n**3 + 0*n + 0*n**2 + p.
2*n**3*(n + 1)/7
Let t(b) be the first derivative of -b**3/18 - b**2/12 + 40. Factor t(n).
-n*(n + 1)/6
Let p(i) be the first derivative of 5*i**4/2 + 2*i**3 - 2*i**2 - 9. Solve p(d) = 0.
-1, 0, 2/5
Suppose 8 = 4*u + w + 2, -9 = -5*u - 2*w. Factor 0*q**2 + 3/2*q - u - 1/2*q**3.
-(q - 1)**2*(q + 2)/2
Suppose 0 = -t + 2*a + 11, -5*t + 3*t + 26 = -5*a. Factor 0*w + 0 + 2/7*w**t - 2/7*w**4 + 0*w**2.
-2*w**3*(w - 1)/7
Suppose -14 = -3*g - 5. Let s(z) be the second derivative of 0 - 2/3*z**4 - 1/15*z**6 + 0*z**g - 2/5*z**5 + 0*z**2 + z. Factor s(t).
-2*t**2*(t + 2)**2
Let s(q) be the first derivative of -3 + 0*q + 1/9*q**3 + 1/12*q**4 - 1/3*q**2. Solve s(j) = 0 for j.
-2, 0, 1
Let a = -405 - -155. Let i = -2248/9 - a. Factor -4/9 + i*m**2 - 2/9*m.
2*(m - 2)*(m + 1)/9
Solve 43*h**2 + h**3 - 2*h + h**3 + 2*h**4 - 45*h**2 = 0.
-1, 0, 1
Let t(a) be the second derivative of -a**6/60 + a**4/12 + a**2 + 2*a. Let m(j) be the first derivative of t(j). Factor m(l).
-2*l*(l - 1)*(l + 1)
Let g(q) be the second derivative of -q**6/14 + 39*q**5/140 - 9*q**4/28 - q**3/14 + 3*q**2/7 + 3*q. Let g(z) = 0. Calculate z.
-2/5, 1
Let k(i) = i**3 - 11*i**2 + 10*i + 2. Suppose 12 = -3*d + 42. Let o be k(d). Determine n so that -o*n**3 + 0*n + 0 - 4/5*n**2 = 0.
-2/5, 0
Suppose -4*o + 3 = -3*o. Find d such that -3*d - d - 28*d**3 - 2*d**4 + 2 + 32*d**o = 0.
-1, 1
Let a(y) be the second derivative of -y**7/231 + 2*y**6/165 - y**5/110 + 7*y - 3. Find q, given that a(q) = 0.
0, 1
Let r be (-6)/(-30)*(-10)/(-8). Find u, given that r*u**2 + 1/2*u - 1/4 - 1/2*u**3 = 0.
-1, 1/2, 1
Let q(f) = -f**2 - f + 7. Let s be q(-3). Let o(c) be the first derivative of -2*c + 3*c**3 + c**5 - 13/4*c**4 + 1/2*c**2 + s. Factor o(k).
(k - 1)**3*(5*k + 2)
Factor -4/5*g**5 + 0 + 16/5*g**2 + 12/5*g**3 - 16/5*g - 8/5*g**4.
-4*g*(g - 1)**2*(g + 2)**2/5
Let q(l) be the first derivative of -l**8/1680 + l**6/180 - l**4/24 - l**3 + 8. Let z(f) be the third derivative of q(f). Factor z(g).
-(g - 1)**2*(g + 1)**2
Suppose -2*t - 1 + 9 = 4*y, t + 5*y - 7 = 0. Let u(f) be the third derivative of 0*f - 1/120*f**5 + 0*f**3 - 1/240*f**6 + 0 - 