4/7*y**2 = 0.
0, 1
Let s(k) = -2*k + 10. Let b be s(6). Let x be (-84)/(-40) + b/4. Factor 2/5*w**3 + 6/5*w**2 - x + 0*w.
2*(w - 1)*(w + 2)**2/5
Let o be ((-12)/(-42)*7/3)/16. Let d(v) be the first derivative of 0*v + 0*v**2 + 1/5*v**5 + 13 - 5/16*v**4 - o*v**6 + 1/6*v**3. Solve d(u) = 0 for u.
0, 1, 2
Determine v, given that 2*v**3 - 10/7*v - 4/7*v**5 + 2/7*v**4 - 4/7 + 2/7*v**2 = 0.
-1, -1/2, 1, 2
Suppose -4*f + 5*t + 136 = -13, 0 = 3*t - 9. Suppose 5*m = 136 - f. Factor 2*b + m - 19 - 2*b**2.
-2*b*(b - 1)
Suppose 2*r + 5*q - 7 = 4, 5*q = -3*r + 14. Let u be (4/14)/(12/(-14) + r). Factor u*x**5 + 0 + 8/15*x + 26/15*x**3 - 8/5*x**2 - 4/5*x**4.
2*x*(x - 2)**2*(x - 1)**2/15
Suppose 9 = -3*m, 2*a - 3 = -5*m - 14. Let o be (-3)/(3/a) + 2 + 2. Factor -3/5*b + 0*b**o + 3/5*b**3 + 0.
3*b*(b - 1)*(b + 1)/5
Let x(a) = -a**2 + 3*a + 7. Let t = -5 + 2. Let o be (-15*12/18)/((-4)/(-2)). Let q(r) = 2*r**2 - 5*r - 13. Let k(l) = o*x(l) + t*q(l). Solve k(z) = 0 for z.
-2, 2
Let i(p) be the first derivative of -p**5/25 - 9*p**4/20 - 4*p**3/3 - 6*p**2/5 + 166. Factor i(n).
-n*(n + 1)*(n + 2)*(n + 6)/5
Let k(p) be the second derivative of 4*p**6/105 - 67*p**5/10 + 6123*p**4/14 - 80613*p**3/7 + 59319*p**2/7 + 9*p - 39. What is m in k(m) = 0?
1/4, 39
Let h(u) be the first derivative of -2*u**3/27 - 4*u**2/9 + 8*u/3 + 85. Factor h(v).
-2*(v - 2)*(v + 6)/9
Let k(h) = h**4 - 6*h**3 - h**2 - 10. Let z(g) = -g**4 + 7*g**3 + 12. Let d(w) = 6*k(w) + 5*z(w). Let d(m) = 0. Calculate m.
-2, 0, 3
Let q = -94 - -92. Let i be (q/6)/(3/(-4)). Let i*u**3 + 0*u + 0 + 2/9*u**4 + 2/9*u**2 = 0. What is u?
-1, 0
Suppose -960*k = -952*k. Let q(m) be the third derivative of 0*m + 1/240*m**6 + 0*m**5 + 0*m**3 + k + 7*m**2 + 0*m**4. Factor q(j).
j**3/2
Determine n, given that 6/7*n**2 - 6/7*n**4 + 6/7*n + 0 - 6/7*n**3 = 0.
-1, 0, 1
Determine y so that 40*y**2 - 17*y**3 - 40*y**4 - 5*y + 4*y**3 + 18*y**3 = 0.
-1, 0, 1/8, 1
Suppose 3*r = -16 + 10. Let g be 2 + (-11)/r + -6. Factor 3*z**2 - 3/2*z**4 + 0*z - g + 0*z**3.
-3*(z - 1)**2*(z + 1)**2/2
Let m = 8 + -22. Let w be 16/6 + (-3 - m/6). Factor -1/3*n**w + 0 + 1/3*n.
-n*(n - 1)/3
Suppose 47*l = -14*l. Suppose l - 2/11*o**3 + 0*o + 2/11*o**4 - 4/11*o**2 = 0. What is o?
-1, 0, 2
Let z(r) be the third derivative of -r**6/30 - 4*r**5/15 - 60*r**2. Suppose z(d) = 0. Calculate d.
-4, 0
Let u(a) = 5*a + 9. Let x be u(3). Solve -78*b**2 - 48*b**3 - 25*b**2 - 17*b**2 - 51*b - x*b = 0.
-5/4, 0
Let l(s) = s**3 + 2*s - 1. Let n be l(1). Let t(z) be the third derivative of -4*z**n - 1/36*z**3 - 1/144*z**4 + 1/180*z**5 + 0*z + 0. Factor t(g).
(g - 1)*(2*g + 1)/6
Let a(f) = -f**3 + 13*f**2 + 14*f + 4. Let v be a(14). Factor -20 - v*p**2 + 16 - 5*p + p - 4*p.
-4*(p + 1)**2
Suppose 1 + 5 = 2*m. Let j be (-4 - -3)/(4/(-8)). What is b in -19*b**2 - b**m - 3*b**3 + 17*b**j - 2*b**4 = 0?
-1, 0
Factor -98*d**4 + 80*d**4 - 5*d + 18*d**2 + 15*d**3 - 4*d - 6*d.
-3*d*(d - 1)*(d + 1)*(6*d - 5)
Suppose -3*a**3 + 0 + 0*a - 1/6*a**5 + 11/6*a**4 + 0*a**2 = 0. What is a?
0, 2, 9
Factor 8*w + 4*w**4 + 40 - 4*w**4 + 4*w**3 - 11*w**4 - 30*w**2 + 13*w**4.
2*(w - 2)**2*(w + 1)*(w + 5)
Let t = -2/427 + 431/854. Let s(a) be the first derivative of 3 + 0*a**2 - 3/4*a**4 - 3/10*a**5 - t*a**3 + 0*a. Determine b, given that s(b) = 0.
-1, 0
Let s(f) = 8*f**2 - f. Let r(m) = -2*m**2. Suppose 4*l + 4 = c, -5*c + 29 = -4*l + 9. Suppose l = 2*b + 6 - 24. Let a(d) = b*r(d) + 2*s(d). Factor a(t).
-2*t*(t + 1)
Let k be (-57)/7 - (0 + -7 - 4). Factor -50/7*l**2 - 2/7 + k*l.
-2*(5*l - 1)**2/7
Let j(c) = 6*c**2 + 7. Let v(q) be the first derivative of -5*q**3/3 - 6*q - 57. Let o(m) = 6*j(m) + 7*v(m). Factor o(r).
r**2
Let l = 2/653 - 11109/2612. Let g = -4 - l. Factor 0 - 1/4*o**2 + g*o**3 + 0*o.
o**2*(o - 1)/4
What is u in -146/5*u**2 + 2/5*u**3 - 2592/5 + 2736/5*u = 0?
1, 36
Let p(b) be the third derivative of 1/60*b**5 + 0*b + 0 - 2/3*b**3 + 0*b**4 + 6*b**2. Suppose p(r) = 0. Calculate r.
-2, 2
Let i(m) be the third derivative of m**7/105 - m**6/20 - 13*m**5/30 + 5*m**4/4 + 2*m**2 - 57*m. Determine h so that i(h) = 0.
-3, 0, 1, 5
Let p(j) be the first derivative of 0*j + 3/8*j**4 - 4 + 1/40*j**6 - 1/4*j**5 + 0*j**2 + 10/3*j**3. Let q(h) be the third derivative of p(h). Factor q(y).
3*(y - 3)*(3*y - 1)
Let f(t) = 2*t**4 + 190*t**3 + 5774*t**2 + 53246*t - 131070. Let c(i) = i**3 + 7*i**2 - i + 1. Let n(r) = -2*c(r) + f(r). Find u, given that n(u) = 0.
-32, 2
Let f(l) = 3*l**3 - 7*l**2 + 2*l. Let q(g) = 2*g**3 + 2*g - 8*g**2 + 4*g**3 - 2*g**3. Let d(h) = -7*f(h) + 6*q(h). Determine p so that d(p) = 0.
-1, 0, 2/3
Let w(z) be the second derivative of 1/12*z**4 + 0 - 1/80*z**5 - 5/24*z**3 + 1/4*z**2 - 14*z. Determine o, given that w(o) = 0.
1, 2
Let a(q) be the third derivative of q**6/30 - 12*q**5/5 - 7*q**2 - 6*q. Factor a(h).
4*h**2*(h - 36)
Let v(i) be the first derivative of -i**6/3 + 4*i**5/5 + 9*i**4/2 - 44*i**3/3 - 4*i**2 + 48*i + 180. What is q in v(q) = 0?
-3, -1, 2
Let y(p) = -23*p + 25. Let l be y(1). Determine z, given that -8/15*z - 2/5 - 2/15*z**l = 0.
-3, -1
Suppose 3*z + 31 = 5*s, -35 + 20 = 3*s + 3*z. Find c, given that -4/3 - 1/3*c**s - 5/3*c = 0.
-4, -1
Let i(k) be the first derivative of -k**3/15 + 3*k**2/5 - k + 41. Factor i(g).
-(g - 5)*(g - 1)/5
Let q(h) be the second derivative of h**6/120 - 3*h**5/40 + h**4/4 - h**3/3 - 51*h. Find r, given that q(r) = 0.
0, 2
Let b(a) be the third derivative of -a**8/672 + a**7/420 + 7*a**6/120 + 13*a**5/60 + 19*a**4/48 + 5*a**3/12 - 2*a**2 - 59*a. Determine z, given that b(z) = 0.
-1, 5
Let c(t) = -t**3 + 6*t**2 - 232*t + 671. Let b be c(3). Find h, given that 0 + 3/5*h**5 + 0*h**b - 6/5*h**3 + 3/5*h + 0*h**4 = 0.
-1, 0, 1
Let l(c) = c**2 + 294*c - 4310. Let a be l(14). Determine x, given that 3*x**4 + 0 - 3/2*x + 0*x**3 - 3*x**a + 3/2*x**5 = 0.
-1, 0, 1
Let y(q) be the first derivative of -q**4/12 - 68*q**3/9 - 578*q**2/3 + 128. Let y(u) = 0. What is u?
-34, 0
Let b be 6 + 5 - 14 - (-23)/7. Factor -b*i**2 - 6/7*i - 4/7.
-2*(i + 1)*(i + 2)/7
Let b(n) be the third derivative of -n**6/24 - n**5/2 - 55*n**4/24 - 5*n**3 + 344*n**2. Let b(i) = 0. Calculate i.
-3, -2, -1
Suppose -81*c = 14*c - 13*c - 164. Factor -8/7*u + 2/7*u**3 + 8/7*u**c - 2/7*u**4 + 0.
-2*u*(u - 2)*(u - 1)*(u + 2)/7
Let b be 5 - 6 - (-1 - 3). Find k such that -3*k**4 - 3*k**b + 39*k**2 - 33*k**2 + 0*k**4 = 0.
-2, 0, 1
Let m be -4 + (-1 - (-63)/9). Let q(k) be the third derivative of -6*k**m - 1/90*k**5 + 0 + 1/9*k**4 + 0*k - 1/3*k**3. Find o such that q(o) = 0.
1, 3
Suppose -5*c = -4*z + 44, -z - 6 + 0 = 3*c. Suppose -4*l + 6*l - z = 0. Solve 4*u**l + 2/3*u**5 + 0 + 8/3*u**2 + 2/3*u + 8/3*u**4 = 0.
-1, 0
Suppose 18/7*i**3 - 402/7*i - 45 - 72/7*i**2 + 3/7*i**4 = 0. Calculate i.
-7, -3, -1, 5
Suppose 76*h + 138 = 79*h. Find z, given that -15 - 41*z**2 + 22*z**2 - 65*z - h*z**2 - 15*z**3 = 0.
-3, -1, -1/3
Let v(z) be the third derivative of -z**6/300 - 2*z**5/15 - 5*z**4/3 - 39*z**2 + 3*z. Suppose v(u) = 0. What is u?
-10, 0
Suppose 2*t - 17 = j, 23 = 3*t - 0*j - 2*j. Factor t*b + b**2 - 4*b**2 + 27 + 13*b.
-3*(b - 9)*(b + 1)
Let r be (-8)/20*-45*1. Let i = r + -13. Solve 4*s - 9*s**3 + 7*s**5 - 2*s**i + s**3 - s**5 = 0.
-1, 0, 1
Let u(s) = -4*s**5 + 16*s**4 - 8*s**2 - 4*s. Let c(o) = o**4 + 2*o - 6*o + 3*o. Let i = 414 - 422. Let d(n) = i*c(n) + u(n). Factor d(m).
-4*m*(m - 1)**3*(m + 1)
Let r = -214 - -218. Suppose -4*a - r + 18 = 5*q, 4*q + a - 9 = 0. Let 6/7*u + 4/7 + 2/7*u**q = 0. Calculate u.
-2, -1
Let u(q) = q**2 - 7*q - 6. Let f(y) = -5*y**2 - 46*y + 14 + 75*y + 10. Let a(m) = 2*f(m) + 9*u(m). Suppose a(w) = 0. What is w?
-3, -2
Determine q so that 8/7*q**2 + 16/7*q**3 + 4/7*q**5 - 20/7*q - 16/7*q**4 + 8/7 = 0.
-1, 1, 2
Let f(z) be the first derivative of -15 - 1/24*z**6 - 1/16*z**4 + 1/2*z**2 + 2*z - 5/6*z**3 + 1/5*z**5. Factor f(s).
-(s - 2)**3*(s + 1)**2/4
Factor -d**3 - 16*d - 16 - 14*d + 3*d**3 - 12*d**2 + 0*d**3.
2*(d - 8)*(d + 1)**2
Suppose 7*i - 15 = 4*i. Let f(u) be the second derivative of -1/9*u**4 + 10*u + 0*u**3 + 0*u**2 - 1/30*u**i + 0. Factor f(g).
-2*g**2*(g + 2)/3
Let t be 1/5 + (-3)/15. Suppose -5*f = -c - t*f, 3*c - 4*f = 0. Solve c*w**5 - w**5 + 5*w**5 + 20*w**2 - 5*w**4 - 12*w**3 - 8*w + w**4 = 0 for w.
-2, 0, 1
Determine a so that 0*a 