h**4 + 10*h**3 - 18 - 4 + 3*h**4 + 2 - x*h + 15*h**2 = 0. What is h?
-1, 2
Let y be (-12)/(-108)*-3*0. Let b(q) be the third derivative of 0*q - 9*q**2 - 1/140*q**5 + 1/280*q**6 + y + 0*q**4 + 0*q**3. Factor b(w).
3*w**2*(w - 1)/7
Factor q**4 - 4*q**3 - 3*q**3 + 5*q**4 - 10 - q**4 + 25*q + 2*q**3 - 15*q**2.
5*(q - 1)**3*(q + 2)
Let s(h) be the first derivative of -48*h - 4/3*h**3 - 33 - 16*h**2. Solve s(x) = 0.
-6, -2
Let t(i) be the second derivative of i**7/2016 - i**6/192 - 23*i**4/12 - 11*i. Let o(k) be the third derivative of t(k). Find x, given that o(x) = 0.
0, 3
Suppose -16*n = -22*n. Let k(b) be the second derivative of 2/3*b**6 - 3*b + 1/3*b**4 - 4/3*b**3 + 8/5*b**5 + n*b**2 + 0. What is y in k(y) = 0?
-1, 0, 2/5
Let g(y) be the third derivative of -25/24*y**4 - 5*y**3 + 0*y + 12*y**2 + 1/12*y**5 + 0. Factor g(p).
5*(p - 6)*(p + 1)
Let -h - 14/9 + 2/3*h**2 + 1/9*h**3 = 0. Calculate h.
-7, -1, 2
Let t(a) be the first derivative of -5*a**4/4 + 250*a**3/3 + 255*a**2/2 + 97. Determine s so that t(s) = 0.
-1, 0, 51
Let p be (-13 - 2)/3 + 9. Factor 5*r**p - 2*r**4 - 12*r**3 + 1607*r + 15*r**2 - 1613*r.
3*r*(r - 2)*(r - 1)**2
Let q(u) be the first derivative of u**3/3 + 3*u**2/2 - 69. Factor q(d).
d*(d + 3)
Let h(k) be the second derivative of -k**5/20 + 23*k**4/12 - 71*k. Let h(v) = 0. What is v?
0, 23
Let b(t) be the third derivative of -2/21*t**3 + 0 + 0*t - 2/35*t**5 - 5/42*t**4 - 26*t**2. Let b(i) = 0. What is i?
-1/2, -1/3
Let n(y) = y**2 + 16*y + 20. Let v be n(-15). Suppose 0 = v*u - 4*i - 27, 18 = 4*u - 3*i - 2*i. Solve -11 + 12*a**2 - 8 + 32*a + u = 0.
-3, 1/3
Let w(r) be the third derivative of r**8/221760 + r**7/18480 + r**6/3960 + 23*r**5/60 - 8*r**2. Let d(i) be the third derivative of w(i). Factor d(c).
(c + 1)*(c + 2)/11
Let v(c) be the second derivative of -c**7/14 + 7*c**6/5 - 27*c**5/5 + 17*c**4/2 - 11*c**3/2 + 28*c. Factor v(h).
-3*h*(h - 11)*(h - 1)**3
Let k(l) be the second derivative of l**3 + 11*l + 0*l**2 + 0 + 3/4*l**4 + 3/20*l**5. Factor k(z).
3*z*(z + 1)*(z + 2)
Let v be (((-32)/(-3))/4)/(4/18). Let y be (v/15)/((-14)/35) + 4. Factor 0 + 4*k**y - 2/3*k - 6*k**3 + 8/3*k**4.
2*k*(k - 1)**2*(4*k - 1)/3
Let l be -5 + ((-34)/25)/((-26)/130). Let h(p) be the first derivative of 2 + l*p - 3/5*p**2 + 1/15*p**3. Let h(j) = 0. What is j?
3
Let r**3 + 1/2 - 1/6*r - 5/3*r**2 - 5/6*r**5 + 7/6*r**4 = 0. Calculate r.
-1, -3/5, 1
Let k(r) be the third derivative of -25/8*r**3 - 5/16*r**4 + 0 - 5*r**2 + 0*r - 1/80*r**5. Factor k(d).
-3*(d + 5)**2/4
Let w(i) = -i**3 - i**2 + 1. Let s(b) = 22 - 7 + 15*b**2 - 20*b**3 - 30*b + 5*b**2 + 0*b**2. Let v(g) = -s(g) + 15*w(g). Factor v(c).
5*c*(c - 6)*(c - 1)
Let i(y) = 132*y + 662. Let j be i(-5). Let -1/3 - 1/3*l**3 + 1/3*l + 1/3*l**j = 0. Calculate l.
-1, 1
Let r(h) be the second derivative of 3*h**5/20 - 11*h**4/4 + 5*h**3 + 26*h + 6. Factor r(d).
3*d*(d - 10)*(d - 1)
Let z(i) be the third derivative of i**5/20 - 17*i**4/8 - 9*i**3 - 360*i**2. Suppose z(r) = 0. Calculate r.
-1, 18
Let h = 116 - 108. Let u be 2 - -1 - 2/2. Suppose -13 + h*k - 2*k**2 + 7 - u = 0. What is k?
2
Factor -9*p**2 - 1125 - p**2 + 5*p**2 + 150*p.
-5*(p - 15)**2
Let s(g) = -3*g + 37. Let d(f) = f - 12. Let w(x) = -7*d(x) - 2*s(x). Let b be w(8). Let 2*c**2 + 4*c**2 - 3*c - 3*c**2 + 0*c**b + 3*c**3 - 3 = 0. What is c?
-1, 1
Factor -695*j**4 + 698*j**4 - 3*j**3 - 10*j**2 - 5*j**2 - 9*j.
3*j*(j - 3)*(j + 1)**2
Suppose 4*c = u + 38, c - 1 - 3 = 3*u. Suppose 18*d + 3*m = 14*d + 15, -4*d - 2*m = -c. Factor -2/11*o**3 + 2/11*o**2 + 0 + d*o.
-2*o**2*(o - 1)/11
Let z(b) be the third derivative of 2*b**2 - 1/4*b**5 + 1/16*b**6 + 25/48*b**4 + 0*b - 1/168*b**7 + 0 - 5/8*b**3. Factor z(l).
-5*(l - 3)*(l - 1)**3/4
Let v(b) = 9*b**2 - 10*b - 71. Let x(d) = -11*d**2 + 10*d + 69. Let j(f) = 3*v(f) + 2*x(f). Suppose j(u) = 0. Calculate u.
-3, 5
Let v be 1351/182*-2 + (-4)/26. Let b be (5*(-4)/(-50))/((-3)/v). What is i in -1/2*i**3 - i**b + 0 - 1/2*i = 0?
-1, 0
Let u be 0 + (-6)/(-10) + (-319)/715. Determine p, given that 4/13*p**3 + 0 + 0*p - u*p**2 - 2/13*p**4 = 0.
0, 1
Suppose -10 = -5*v + 2*n, n - 62 + 58 = -2*v. Let k be -1 + 46/10 + -3. Suppose 1/5*p**3 + 2/5*p + 0 - k*p**v = 0. Calculate p.
0, 1, 2
Let p(w) be the third derivative of -w**8/16 - w**7/14 + 37*w**6/40 - 31*w**5/20 + 3*w**4/4 + 106*w**2. What is x in p(x) = 0?
-3, 0, 2/7, 1
Let l = 38 + -36. Let y be (0 + -3)/(3/(-4)). Factor 2*k**5 + y*k**4 + 3*k**3 + 2*k**2 - 7*k**3 - 6*k**l + 2*k**3.
2*k**2*(k - 1)*(k + 1)*(k + 2)
Let l(o) be the second derivative of -o**6/420 - o**5/42 - o**4/21 + 13*o**2 + o. Let a(f) be the first derivative of l(f). Factor a(g).
-2*g*(g + 1)*(g + 4)/7
Let i(p) be the third derivative of 1/84*p**8 + 0*p**3 + 0 - 5*p**2 + 0*p + 1/6*p**4 + 0*p**7 - 1/15*p**6 + 0*p**5. Factor i(v).
4*v*(v - 1)**2*(v + 1)**2
Let x = 145/6 + -59/3. Let q be (-23)/(-18) - (90/(-81))/5. Solve 0*t + x*t**2 - q*t**4 - 2 + t**3 = 0.
-1, 2/3, 2
Let r be (-150)/2475 + (-184)/(-132). Factor r*b**3 - 2/3*b**4 - 2/3*b**2 + 0*b + 0.
-2*b**2*(b - 1)**2/3
Let c be 40/300 + 43/15. Factor 73 - 20*y - 53 + 2*y**2 + c*y**2.
5*(y - 2)**2
Suppose -32 + 11 = 3*n. Let l(x) = x**3 + 7*x**2 - 4*x - 16. Let j be l(n). Factor -4*o**2 + 12*o - j + 3 - 2 + 3.
-4*(o - 2)*(o - 1)
Let y(r) = -r**2 - 4. Let f(c) = c**2 + 1. Let a(x) = -4*f(x) - 2*y(x). Let i(g) = -6*g**2 - g + 11. Let v(o) = -11*a(o) + 4*i(o). Suppose v(k) = 0. What is k?
-2, 0
Suppose -3 + 9/4*s**2 - 1/2*s - 1/8*s**4 - 3/8*s**3 = 0. Calculate s.
-6, -1, 2
Let w(x) be the third derivative of -1/210*x**5 - 3/7*x**3 + 0*x + 8*x**2 + 0 - 1/14*x**4. Factor w(l).
-2*(l + 3)**2/7
Let k(h) be the second derivative of h**4/12 + 2*h**3/3 + 3*h**2 + 5*h. Let n be k(-4). Factor 5 + 7 + 3*z**2 - 6*z - n*z + 0*z**2.
3*(z - 2)**2
Let g = 10 - -14. Let k = g + -10. Factor 14*o + o**4 - k*o + 2*o**4.
3*o**4
Factor 8*m**2 + 18*m**2 + 4*m + 5*m**3 + 7*m**3.
2*m*(m + 2)*(6*m + 1)
Let i(t) be the first derivative of t**4 + 148*t**3/3 - 76*t**2 + 56. Factor i(l).
4*l*(l - 1)*(l + 38)
Factor 192*p**2 - 3 + 1076*p + 7*p**3 + 3 - 3*p**3 + 1228*p.
4*p*(p + 24)**2
Let u be 14/(-36)*4*12/(-224). Let w(g) be the second derivative of 0 + g + 1/2*g**2 - 1/24*g**4 - u*g**3. Factor w(a).
-(a - 1)*(a + 2)/2
Let z be (3*4/(-8))/((-795)/6). Let u = 13491/2120 + z. What is m in 15/8*m**3 + 3/2 + 6*m + u*m**2 = 0?
-2, -1, -2/5
Let a(u) be the second derivative of u**10/10080 + u**9/7560 - u**8/6720 - 11*u**4/12 + 10*u. Let f(q) be the third derivative of a(q). Factor f(t).
t**3*(t + 1)*(3*t - 1)
Let b(r) be the second derivative of r**6/30 - r**4/2 - 4*r**3/3 - 23*r**2/2 + 8*r. Let y(q) be the first derivative of b(q). Suppose y(x) = 0. What is x?
-1, 2
Let r(i) = i**3 + 10*i**2 + 13*i - 102. Let v(a) = -5*a**3 - 60*a**2 - 79*a + 610. Let j(y) = -34*r(y) - 6*v(y). Factor j(c).
-4*(c - 4)**2*(c + 3)
Let m = 19 + -12. Let f = 10 - m. Factor -4*b**4 + 4*b**2 + 8*b**3 + f*b**4 - 2*b**4 - 8*b - b**4.
-4*b*(b - 2)*(b - 1)*(b + 1)
Suppose 4*v - 25 = 5*s, 0*s - 2*s = -v + 10. Let f(j) be the first derivative of 4 + 0*j**3 + 1/18*j**4 + 0*j + v*j**2. Let f(i) = 0. What is i?
0
Let v = -175 - -178. Factor -4*g**2 + 4*g + 4/3*g**v - 4/3.
4*(g - 1)**3/3
Let o = 2590/3 + -863. Factor 1/3*m**3 + m + m**2 + o.
(m + 1)**3/3
Factor -156/7*r**2 + 130/7*r - 12/7 + 38/7*r**3.
2*(r - 3)*(r - 1)*(19*r - 2)/7
Suppose a**5 - 9*a**4 + 8*a**2 - a**4 + 2*a**4 - 5*a**5 + 4*a**3 = 0. What is a?
-2, -1, 0, 1
Let g(c) be the second derivative of -c**4/42 - 4*c**3/7 - 11*c**2/7 - 19*c. Solve g(u) = 0 for u.
-11, -1
Let j be (-102)/4*10/(-15). Solve -u**2 + j + u + 0*u**2 - 15 = 0 for u.
-1, 2
Let b(y) be the second derivative of 0 + 1/5*y**3 + 3/20*y**4 - 2/25*y**6 + 35*y - 3/10*y**2 - 3/25*y**5. Determine h, given that b(h) = 0.
-1, 1/2
Determine o so that -40*o - 72*o**5 + 35*o**2 + 15*o**2 + 67*o**5 - 20*o**4 + 15*o**3 = 0.
-4, -2, 0, 1
Let y(m) = 6*m**3 - 6*m + 2. Suppose -2*z = 1 - 5. Let t(d) = -d**4 + 12*d**3 + d**2 - 12*d + 5. Let n(u) = z*t(u) - 5*y(u). Find v, given that n(v) = 0.
-3, -1, 0, 1
Let r(n) be the first derivative of 5/8*n**4 - 3*n**3 + 0*n - 14 - 2*n**2. Factor r(t).
t*(t - 4)*(5*t + 2)/2
Let n(z) = -5*z + 35. Suppose -8*a + 63 = a. Let p be n(a). Factor 0*j + p + 