**3.
2*j*(j + 1)*(7*j + 2)/5
Factor -108/5*u - 2/5*u**3 - 16 - 6*u**2.
-2*(u + 1)*(u + 4)*(u + 10)/5
Let o(g) = -14*g - 98. Let i = 151 + -158. Let t be o(i). Find c such that t - 4/3*c - 2*c**2 - 2/3*c**3 = 0.
-2, -1, 0
Suppose 4*r = -r + 115. Suppose 15 = -4*q + r. Let 4*p**2 + 4*p - 12*p**2 + 4*p**q = 0. Calculate p.
0, 1
Suppose -23*l - 3689 = -3781. Solve -8/5 + 24/5*n**3 - 14/5*n**l + 22/5*n**2 - 24/5*n = 0.
-1, -2/7, 1, 2
Let m(x) be the first derivative of x**5/20 - 11*x**4/16 + 2*x**3 + x**2/2 - 8*x + 204. Factor m(n).
(n - 8)*(n - 2)**2*(n + 1)/4
Let w = 3/2320 - -7421/2320. Let -w*j - 64/5 - 1/5*j**2 = 0. Calculate j.
-8
Let u(w) be the first derivative of -1/9*w**2 + 3 + 2/27*w**3 - 1/54*w**4 + w. Let q(h) be the first derivative of u(h). Factor q(g).
-2*(g - 1)**2/9
Suppose 97*k = 95*k + 5*q - 34, 2*k + q = 14. Find m, given that -24/7*m - 2/7*m**k - 16/7 - 12/7*m**2 = 0.
-2
Find h such that 0 + 2/21*h**2 - 58/21*h = 0.
0, 29
Let r be (3 - (-246)/(-84))/(5/(-2078)). Let z = r - -212/7. Solve 1/5*v**3 + 0 - 2/5*v**2 - z*v = 0.
-1, 0, 3
Let b(t) = -t - 15. Let s(n) = n - 23. Let z be s(6). Let i be b(z). Factor -3/2*a**3 + 0 + 0*a + 3/4*a**i + 3/4*a**4.
3*a**2*(a - 1)**2/4
Let t(m) = 4*m**3 - 3 - 2*m**2 - 1 + 3*m**3 - 907*m + 912*m. Let d(u) be the first derivative of u**4/4 - u**3/3 - u + 1. Let j(k) = 6*d(k) - t(k). Factor j(y).
-(y + 1)**2*(y + 2)
Suppose 6 = -f + 8. Factor 4*n**2 - f*n**3 - 5*n + 13*n + 0*n**3 - 2*n**3.
-4*n*(n - 2)*(n + 1)
Let v(d) be the first derivative of d**5/15 - 25*d**4/6 + 172*d**3/3 + 459*d**2 + 729*d - 31. Factor v(m).
(m - 27)**2*(m + 1)*(m + 3)/3
Let z(i) be the first derivative of 1/16*i**4 + 6 + 2*i + 1/8*i**3 + 0*i**2. Let q(b) be the first derivative of z(b). Factor q(n).
3*n*(n + 1)/4
Let o(l) be the second derivative of 1/60*l**4 + 0 - 1/2*l**2 - 1/300*l**6 - 1/75*l**5 + 2*l + 2/15*l**3. Let t(u) be the first derivative of o(u). Factor t(j).
-2*(j - 1)*(j + 1)*(j + 2)/5
Let m(x) be the third derivative of -4*x**3 + 0*x - 9/40*x**6 + 0 - 7/2*x**4 - 3/2*x**5 + 33*x**2. Determine q so that m(q) = 0.
-2, -2/3
Let u be (-2 - -3)/((-2)/(-6)). Let v = u + 6. Factor 2 + 0 - d**2 + 4*d**2 + v*d + 4.
3*(d + 1)*(d + 2)
Let j(z) be the second derivative of -z**5/20 - z**4/12 - z**3/3 + 2*z**2 - 5*z. Let y be j(-3). Factor 12*v**3 - 43 - y*v**2 + 4*v + 21*v + 39 - 5*v.
4*(v - 1)**2*(3*v - 1)
Let a(s) be the third derivative of -1/12*s**5 + 0*s + 5/12*s**4 - 5*s**2 - 5/6*s**3 + 0. Find z, given that a(z) = 0.
1
Factor 42 - 117/2*m - 3/2*m**3 + 18*m**2.
-3*(m - 7)*(m - 4)*(m - 1)/2
Factor 474*m**2 - 608/5*m + 8 - 90*m**3.
-2*(m - 5)*(15*m - 2)**2/5
Find z such that -107*z - 194*z**2 + 2*z**4 - 154*z - 27*z - 128 - 4*z**4 - 36*z**3 = 0.
-8, -1
Let h(s) be the first derivative of 7 - 1/20*s**5 - 1/8*s**4 + 1/4*s**2 + 1/12*s**3 + 0*s. Suppose h(u) = 0. What is u?
-2, -1, 0, 1
Suppose 2*o = 7*o + 3*p - 45, -5*p - 5 = -5*o. Factor 48*u**2 - 10*u - 12*u - 10*u**3 + o*u - 26*u**3.
-4*u*(3*u - 2)**2
Let h be 27/5 - 20/50. Suppose h*b + 4 = 6*b. Determine p, given that -3*p**2 + 3*p**b - 2*p**5 + 3*p**3 + 0*p**5 - p**5 = 0.
-1, 0, 1
Suppose -3*o - u = -14, -2*u + 16 = o + 3*o. Factor -49*j - o*j**3 - 3*j**3 + 3*j**4 - 3*j**2 + 58*j.
3*j*(j - 3)*(j - 1)*(j + 1)
Determine k so that -108*k - 962 - 948 - 2*k**2 + 452 = 0.
-27
Let y be (-16*15/(-400))/1. Factor -21/5*f**2 + y*f + 21/5 - 3/5*f**3.
-3*(f - 1)*(f + 1)*(f + 7)/5
Let r(w) be the first derivative of 4*w**4/15 + 26*w**3/9 + 8*w**2/15 - 9. Factor r(t).
2*t*(t + 8)*(8*t + 1)/15
Let h = 1825 - 1823. Factor -1/4 + 1/2*w**3 + 3/4*w**4 - 3/4*w - 1/2*w**h + 1/4*w**5.
(w - 1)*(w + 1)**4/4
Suppose -3*w - p = -8, 4*w - 5*p - 15 = 2. Let r be (-3 + 18)*(w + 73/(-25)). Let -12/5*v**3 - 3/5 + 21/5*v**2 - r*v = 0. Calculate v.
-1/4, 1
Let x be (-6)/9 + (-20)/(-21). Suppose -4*z + 78 - 70 = 0. Factor 0 - x*d**z + 0*d.
-2*d**2/7
Let k(r) be the second derivative of 10*r**4/3 - 38*r**3/3 - 4*r**2 - 268*r. Determine l so that k(l) = 0.
-1/10, 2
Let k(b) be the third derivative of -b**6/40 + 4*b**5/5 - 29*b**4/8 + 7*b**3 + b**2 - 4*b. Factor k(h).
-3*(h - 14)*(h - 1)**2
Let q(u) be the third derivative of u**6/420 - 2*u**5/105 + u**4/28 + 125*u**2. Let q(n) = 0. What is n?
0, 1, 3
Let h(a) = 8*a**2 + 17*a - 3. Let p(k) = 14*k**2 + 35*k - 5. Let x(t) = 5*h(t) - 3*p(t). Determine c so that x(c) = 0.
-10, 0
Let q be -1*(-70)/(-21)*24/10. Let h be (-5)/((-60)/q)*1*-3. Factor 4*y**3 + 3*y**4 - 4*y - 5/3*y**h - 4/3.
(y - 1)*(y + 1)*(3*y + 2)**2/3
Let t(k) be the second derivative of 0*k**2 - 2/3*k**3 + 0 - 1/3*k**4 - 3*k + 1/10*k**6 + 1/4*k**5. Suppose t(y) = 0. Calculate y.
-2, -2/3, 0, 1
Let k be (0 + (-40)/(-25))*15. Factor -24*o + o**3 + 3*o**2 + 51*o - 9 + 2*o**2 - k*o.
(o - 1)*(o + 3)**2
Let c(v) = v**3 + 14*v**2 + 12*v - 10. Let h be c(-13). Determine f so that -19*f + 32 + f**3 - 29*f + 24*f**2 - f**h - 4*f**3 = 0.
2
Find d, given that 4/3 + 10/9*d**2 + 22/9*d = 0.
-6/5, -1
Let b(j) be the second derivative of -j**5/60 - 7*j**4/18 - 159*j. Find r such that b(r) = 0.
-14, 0
What is c in -26*c**2 - 1014 + 9*c**3 - 15*c**2 + 1677*c - 199*c**2 = 0?
2/3, 13
Let i(q) be the third derivative of q**9/20160 + q**8/840 + q**7/80 + 3*q**6/40 - 11*q**5/30 - 14*q**2. Let l(h) be the third derivative of i(h). Factor l(z).
3*(z + 2)*(z + 3)**2
Let s(d) = d**2 - d - 1. Let q(j) = 2*j**2 + 2*j - 9. Let i(o) = -o**2 + 2*o - 3. Let h be i(3). Let g(t) = h*s(t) + 2*q(t). Factor g(x).
-2*(x - 3)*(x - 2)
Let i(a) be the second derivative of -2*a**2 + 1/6*a**4 - a**3 + 0 + 3/10*a**5 + 1/15*a**6 + 11*a. Suppose i(t) = 0. Calculate t.
-2, -1, 1
Let d(s) be the second derivative of 2/21*s**7 + 0*s**2 + 11*s + 0 + 0*s**4 + 1/5*s**5 + 4/15*s**6 + 0*s**3. Solve d(r) = 0 for r.
-1, 0
Let o(m) be the first derivative of m**6/14 + 6*m**5/35 - 3*m**4/7 - 2*m**3/7 + 9*m**2/14 - 364. Suppose o(r) = 0. Calculate r.
-3, -1, 0, 1
Let d = -172 - -100. Let w = -214/3 - d. Solve 2/3*f + 2/3*f**2 - w - 2/3*f**3 = 0 for f.
-1, 1
Let f be 4/(-12) - (-1)/3. Suppose f = -3*z - 2*z. Suppose z + 2*g**3 + 2*g - 1 + g**4 - 4*g**3 + 0 = 0. What is g?
-1, 1
Suppose -2*v - 2*c + 28 = 0, 5 = 3*c - 2*c. Suppose 5*u = -5*w, u + v = 6*u + 2*w. Let 0 + 2*a - 4*a + 3*a**u - a - 3*a**2 + 3 = 0. Calculate a.
-1, 1
Let x(w) be the first derivative of -3*w**7/280 + 11*w**6/60 - 4*w**5/5 - 4*w**4 - 20*w**3/3 - 10. Let y(m) be the third derivative of x(m). Factor y(q).
-3*(q - 4)**2*(3*q + 2)
Suppose -9*k = -11*k + 6. Let p(b) be the second derivative of 0*b**4 + 0*b**k - 1/4*b**6 + 1/4*b**7 - 3/20*b**5 + 0*b**2 - b + 0. Determine m so that p(m) = 0.
-2/7, 0, 1
Let v(w) = -1345*w**3 + 3945*w**2 - 3095*w + 680. Let j(z) = 79*z**3 - 232*z**2 + 182*z - 40. Let x(n) = -35*j(n) - 2*v(n). Solve x(d) = 0 for d.
2/5, 2/3, 2
Let q(n) be the second derivative of 5*n + 4/75*n**6 + 0*n**2 + 1/50*n**5 + 0*n**3 + 0 + 0*n**4. Factor q(h).
2*h**3*(4*h + 1)/5
Let 0*s - 6/13*s**2 + 8/13*s**3 - 2/13*s**4 + 0 = 0. What is s?
0, 1, 3
Suppose -63*b - 199 + 514 = 0. Let y(p) be the second derivative of 2/63*p**7 + 0 + 1/3*p**b + 8/45*p**6 + 0*p**3 - 10*p + 0*p**2 + 2/9*p**4. Factor y(t).
4*t**2*(t + 1)**2*(t + 2)/3
Suppose 2*u = -q + 2, -3*q - 19 = -6*q + 7*u. Let g(a) be the second derivative of 2*a + 5/12*a**q + 5*a**2 + 0 + 5/2*a**3. Suppose g(o) = 0. What is o?
-2, -1
Let s(m) be the first derivative of -5*m**3/3 + 25*m**2/2 + 30*m + 56. Factor s(l).
-5*(l - 6)*(l + 1)
Let l(y) be the first derivative of -y**4/24 + y**3/4 - y**2/2 + 3*y - 4. Let v(t) be the first derivative of l(t). Factor v(o).
-(o - 2)*(o - 1)/2
Solve 21/5*a - 12/5*a**2 + 6 - 3/5*a**3 = 0 for a.
-5, -1, 2
Let f = 2/4101 + 32786/45111. Let c be ((-10)/(-33))/(2/6). Solve 24/11*m + c*m**2 + f = 0.
-2, -2/5
Factor 668*k**4 - 5*k**5 - 361*k**4 - 332*k**4.
-5*k**4*(k + 5)
Let t(b) = -23*b + 27. Let m be t(4). Let u = m + 65. Let 4*r**2 - 4/5*r**4 + 12/5*r**3 + u + 8/5*r - 4/5*r**5 = 0. What is r?
-1, 0, 2
Let i(c) = -c**3 + c**2 - 2*c - 2. Let y(k) = 5*k**3 - 9*k**2 + 12*k + 12. Let d(r) = 6*i(r) + y(r). Let d(g) = 0. Calculate g.
-3, 0
Suppose -5*g - 2*u = 2*u, -3*u = -5*g. Let k(r) be the second derivative of g*r**3 + 3/8*r**5 - 1/4*r**4 - 1/5*r**6 + 0 - 7*r + 0*r**2 + 1/28*r**7. Factor k(a)