at is u?
0
Let l be -5 - ((-160)/70 + -3). Let 2/7 - 4/7*y + l*y**2 = 0. What is y?
1
Let d(r) be the second derivative of -r**7/840 - r**6/40 - r**5/8 - 7*r**4/24 - 11*r**3/2 + 14*r. Let a(v) be the second derivative of d(v). Factor a(h).
-(h + 1)**2*(h + 7)
Suppose -235*k + 237*k = 8. Let t(j) be the second derivative of -1/15*j**6 - 1/2*j**k + 2*j + 3/10*j**5 + 0 + 0*j**2 + 1/3*j**3. Suppose t(h) = 0. Calculate h.
0, 1
Let w(h) = -h + h + 3*h**2 + 13 - 16. Let n(g) = g**2 - 1. Suppose -2*m - 2 + 0 = 0. Let y(v) = m*w(v) + 4*n(v). Determine o, given that y(o) = 0.
-1, 1
Suppose y - 8 = -3. Suppose c - 10 = -2*k + 4*c, -y*k + 12 = -c. Factor v**k + v**2 - 12 + 10.
2*(v - 1)*(v + 1)
Suppose 2*g + o - 3*o + 4 = 0, 0 = 4*g - 3*o + 3. Let d be g/(-9) + (-8)/36*-15. Factor -2*h**d - 8/3 + 16/3*h - 2/3*h**2.
-2*(h - 1)*(h + 2)*(3*h - 2)/3
Let v(l) be the first derivative of l**6/8 + 9*l**5/20 + 3*l**4/8 + 83. Solve v(b) = 0 for b.
-2, -1, 0
Determine r so that -4/5*r**2 - 152/5*r - 1444/5 = 0.
-19
Determine y so that 6*y**3 - 27/2*y**2 - 15/4 - 3/4*y**4 + 12*y = 0.
1, 5
Suppose -7*c = -24 - 25. Suppose -9*o + 8 = -c*o. Solve 0 + 1/7*w**o - 1/7*w**2 + 1/7*w**3 - 1/7*w = 0.
-1, 0, 1
Let g = -3125/2 + 1564. Factor 3/4*s**5 + 0 - 3/2*s**2 + 0*s**3 + g*s**4 - 3/4*s.
3*s*(s - 1)*(s + 1)**3/4
Let b(d) be the first derivative of -d**5/20 + d**4/16 + 5*d**3/12 + 3*d**2/8 - 18. What is k in b(k) = 0?
-1, 0, 3
Let j(f) be the second derivative of -f**7/126 + f**6/45 + f**5/10 - 2*f**4/9 - 5*f**3/18 + f**2 - f + 59. Solve j(g) = 0 for g.
-2, -1, 1, 3
Let t = 22 + -37. Let v be (-30)/t + 1/(-4). Factor -1/4*z**3 - 15/4*z - 9/4 - v*z**2.
-(z + 1)*(z + 3)**2/4
Let f(i) be the first derivative of -11/6*i**3 + 18*i - 1/8*i**4 + 19 - 6*i**2. Determine g, given that f(g) = 0.
-6, 1
Let g(d) be the second derivative of d**5/60 + 103*d**4/18 + 10609*d**3/18 + 489*d. Suppose g(b) = 0. What is b?
-103, 0
Suppose 0 = 211*b - 195*b. Let p(q) be the first derivative of -2/5*q**5 + b*q**2 + 0*q**3 + 0*q**4 - 1/3*q**6 + 11 + 0*q. Determine t so that p(t) = 0.
-1, 0
Let f(n) = -3*n**5 - 6*n**4 + 6*n**3 + 17*n**2 + 2*n - 1. Let h(g) = -g**2 - g - 1. Let w = 15 - 20. Let l(a) = w*h(a) - f(a). Let l(m) = 0. What is m?
-2, -1, 1
Suppose 132*o**4 - 2*o**3 - 160*o - 20 + 245*o**4 + 127*o**3 + 71*o**5 + 9*o**5 - 305*o**2 - 97*o**4 = 0. Calculate o.
-2, -1/4, 1
Let x(d) = -d**2 + 12*d + 30. Let b be x(-2). Let z(h) be the first derivative of 2/3*h**6 + 0*h**5 + 0*h**3 + 2*h**b - 7 - 2*h**4 + 0*h. Factor z(a).
4*a*(a - 1)**2*(a + 1)**2
Let p(g) = -7*g**2 + 12*g + 12. Let c(y) = y**2 + y - 2. Let u(t) = -6*c(t) - p(t). Find b such that u(b) = 0.
0, 18
Let 4*k + 12 + k**5 - 7*k + 18*k**4 - 4*k**5 - 6*k**4 + 21*k**3 - 15*k**3 - 24*k**2 = 0. What is k?
-1, 1, 4
Let u = 15 - 29. Let j be ((-16)/6)/(u/21). Determine c so that -8*c**2 - 9*c**2 + 19*c**2 + j*c + 2 = 0.
-1
Factor -3 - 30*o - 34 + 195*o**2 - 192*o**2 + 4.
3*(o - 11)*(o + 1)
Suppose 2*r + r + 5*n + 4 = 0, -5*r = 2*n - 6. Factor 3 + 0*m**2 - 6*m**2 + 6*m**r - 3*m**2.
-3*(m - 1)*(m + 1)
Let f(i) = -2*i**3 + 2*i**2 - 4*i - 5. Let y be f(-1). Let l(v) be the first derivative of 3*v**y - 9/2*v**2 - 3/4*v**4 + 3*v + 6. Factor l(x).
-3*(x - 1)**3
Let h(c) be the first derivative of -c**7/945 + c**6/270 + 4*c**5/135 - 7*c**2 + 5. Let n(p) be the second derivative of h(p). Factor n(g).
-2*g**2*(g - 4)*(g + 2)/9
Let r = -8/2997 - -12028/14985. Factor -13/5*z**2 - 2/5 - r*z**3 - 11/5*z.
-(z + 1)*(z + 2)*(4*z + 1)/5
Let v(g) = 6*g**2 + 18*g. Let p(k) = 31*k**2 + 89*k. Let n = 82 - 71. Let t(y) = n*v(y) - 2*p(y). Factor t(q).
4*q*(q + 5)
Let z(t) = 3*t**3 - 16*t**2 - 21*t + 58. Let q be z(6). Solve 1/5*j**q + 4/5*j - 6/5*j**2 - 1/5*j**3 + 8/5 = 0.
-2, -1, 2
Suppose -7*x + 3 = -2*g, -55*g - 3 = 5*x - 57*g. Factor 1/5*l**x + l**2 + 0 + 0*l.
l**2*(l + 5)/5
Suppose 7*l = l + 60. Let v be (-12)/(-21)*7/l. Factor -4/5*q**2 + v*q**4 + 0 + 0*q + 2/5*q**3.
2*q**2*(q - 1)*(q + 2)/5
Let c(i) be the first derivative of i**5/10 + i**4/2 + i**3 + i**2 - 8*i + 3. Let r(m) be the first derivative of c(m). Let r(b) = 0. Calculate b.
-1
Let k(r) = 2*r**3 - 2*r**2 + r + 1. Let g(u) = -12*u**3 + 28*u**2 - 45*u - 5. Let s(p) = g(p) + 5*k(p). Factor s(o).
-2*o*(o - 5)*(o - 4)
Let y be 5*(36/(-675))/((-22)/(-177)). Let n = -17/11 - y. Factor 0 + 3/5*g**2 + 0*g + n*g**3.
3*g**2*(g + 1)/5
Let j(y) be the third derivative of 0 + 1/24*y**6 - 1/42*y**7 + 26*y**2 + 0*y**3 + 1/3*y**5 + 0*y - 5/6*y**4. Factor j(u).
-5*u*(u - 2)*(u - 1)*(u + 2)
Let g(m) be the first derivative of m**8/7560 - m**6/1620 - m**3 + 3. Let q(b) be the third derivative of g(b). Factor q(i).
2*i**2*(i - 1)*(i + 1)/9
Let r be 0/(2 - 3) - -27. Let m be -1 - (-1 - -3*(-6)/r). Factor 1/3*x**4 + 0*x**3 + 1/3 + 0*x - m*x**2.
(x - 1)**2*(x + 1)**2/3
Factor -8/5*h**2 + 16/5 + 28/5*h + 4/5*h**5 - 32/5*h**3 - 8/5*h**4.
4*(h - 4)*(h - 1)*(h + 1)**3/5
Suppose -6*q - 3*q = -27. Find d, given that 7 - 8 - q*d + 3*d**2 - 5 = 0.
-1, 2
Factor -185*f - 50 - 153*f + 383*f + 5*f**2.
5*(f - 1)*(f + 10)
Determine c, given that 9*c - 48/5 + 3/5*c**2 = 0.
-16, 1
Let m(l) be the second derivative of -l**8/3360 - l**7/252 - 7*l**6/360 - l**5/20 - 11*l**4/12 + 11*l. Let q(c) be the third derivative of m(c). Factor q(b).
-2*(b + 1)**2*(b + 3)
Let z(c) = -c**2. Let y(j) = 3*j**2 + 490*j + 12005. Let w(i) = -y(i) + 2*z(i). Determine u so that w(u) = 0.
-49
Let f(h) be the first derivative of 0*h - 3 + 4/3*h**3 + 2*h**2. Let f(k) = 0. What is k?
-1, 0
Let p(h) be the third derivative of -h**5/12 + 5*h**4/6 + 25*h**3/6 + 35*h**2 - 5. Factor p(v).
-5*(v - 5)*(v + 1)
Suppose 278 - 78 = 5*z. Factor -z*t**2 + 37*t**2 - 6*t + 3*t.
-3*t*(t + 1)
Let b(u) = -4*u**3 + 1. Let h be b(-1). Let y be h/((-70)/(-46)) - 3. Factor -y*w**3 + 0 + 2/7*w + 0*w**2.
-2*w*(w - 1)*(w + 1)/7
Let w = -2111 + 6337/3. Factor 0*n + 0 - w*n**3 + 8/3*n**2.
-4*n**2*(n - 2)/3
Let d = -5023/3 - -10055/6. What is u in -3*u**2 + 0*u + 0*u**4 + 9/2*u**3 - d*u**5 + 0 = 0?
-2, 0, 1
Let v(a) be the second derivative of a**5/60 + a**4/18 - 808*a. Let v(r) = 0. What is r?
-2, 0
Let x(q) be the third derivative of 0 - 16*q**2 - 8/9*q**3 + 13/18*q**4 + 7/90*q**5 + 0*q. Factor x(l).
2*(l + 4)*(7*l - 2)/3
Let 72/5 - 42/5*i**3 - 69/5*i**2 - 3/5*i**4 + 42/5*i = 0. What is i?
-12, -2, -1, 1
Let o(f) be the first derivative of 7*f**4/4 + 5*f**3/3 - 8*f**2 + 4*f - 152. Factor o(a).
(a - 1)*(a + 2)*(7*a - 2)
Let j = -14430 - -14433. Factor -4/3*w**j + 0 - 4/3*w - 8/3*w**2.
-4*w*(w + 1)**2/3
Let 60/7*s - 123/7*s**2 - 3/7*s**4 + 66/7*s**3 + 0 = 0. What is s?
0, 1, 20
Let x = -3873 - -3878. Factor -2/15*a**x - 6/5*a**3 + 0 + 2/3*a**4 - 4/15*a + 14/15*a**2.
-2*a*(a - 2)*(a - 1)**3/15
Let m(a) be the second derivative of 0 - 1/8*a**4 - 3/2*a**3 - 6*a**2 + 10*a. Solve m(f) = 0.
-4, -2
Suppose 120 = 31*j + 9*j. Let g(a) be the second derivative of 0*a**j + 0 + 0*a**5 - 1/75*a**6 + 0*a**2 - 8*a + 1/30*a**4. Factor g(u).
-2*u**2*(u - 1)*(u + 1)/5
Suppose 4*c + 29 - 49 = 0. Suppose -c*s = -10, -s - 5 - 3 = -5*x. Factor x + 2/9*i**2 + 4/3*i.
2*(i + 3)**2/9
Let i(o) be the second derivative of 3*o**5/20 + 5*o**4/12 + 17*o. Factor i(s).
s**2*(3*s + 5)
Let f(x) be the first derivative of -2*x**3/3 + 217*x**2/2 - 108*x + 43. Factor f(c).
-(c - 108)*(2*c - 1)
Factor -8/11*f + 0 - 18/11*f**3 + 2*f**2 + 2/11*f**4 + 2/11*f**5.
2*f*(f - 1)**3*(f + 4)/11
Suppose 1 = 4*r - 11. Factor 39*i + 4*i**2 + 40*i + 2*i**r - 74*i - 3*i**3.
-i*(i - 5)*(i + 1)
Let i(t) be the first derivative of t**8/840 - t**7/980 - 11*t**3/3 + 19. Let h(u) be the third derivative of i(u). Solve h(w) = 0.
0, 3/7
Let b be ((-182)/(-26))/(-1*1) - -10. Find n such that -7/4*n + 3/2*n**b + 5/4*n**4 - 3/4 + 1/4*n**5 - 1/2*n**2 = 0.
-3, -1, 1
Let l = 19 + -23. Let q be (-3 - l)*(-2 + 5). Find v such that 24*v + 29*v**3 + 3*v**5 + 21*v**4 + 22*v**3 + q*v**3 + 60*v**2 = 0.
-2, -1, 0
Find v, given that 5*v**3 + 7*v**3 + 2*v**4 + 2*v**2 - 3*v - 5*v**3 = 0.
-3, -1, 0, 1/2
Let z(y) = -2*y - 2. Let j be 3 + (3 - 6) - 1. Let v be z(j). What is l in v*l - 3*l - 12*l**2 - 12*l**3 - l - 2*l**4 - 2*l**4 = 0?
-1, 0
Suppose 16*i - 33 - 31 = 0. Let w(x) be the third derivative of 1/6*x**i + 0*x**3 + 1/60*x**6 + 0 + 0*x + 1/10*x**5 - x**2. Factor 