 -20 = 4*p, -2*n + 12 + 13 = -3*p. Suppose -7*k + 5*k + 2*a + 2 = 0, 3*k - 1 = n*a. What is b in 3 + 3/2*b**k + 9/2*b = 0?
-2, -1
Let b(p) = -95*p**3 + 740*p**2 - 1055*p + 515. Let j(a) = 8*a**3 - 62*a**2 + 88*a - 43. Let t(z) = 3*b(z) + 35*j(z). Factor t(h).
-5*(h - 8)*(h - 1)**2
Let x(z) be the first derivative of -13*z**4/30 + 74*z**3/45 + 2*z**2/5 - 92. Solve x(f) = 0.
-2/13, 0, 3
Let q(j) be the third derivative of -j**8/336 - 5*j**7/168 - 7*j**6/72 - j**5/8 - j**3 + 12*j**2. Let k(y) be the first derivative of q(y). Solve k(x) = 0.
-3, -1, 0
Let u(b) = -480*b + 1 - b**2 + 479*b + b**3 - 4*b**2. Let t(g) = -g**3 + g**2 - g - 1. Let r(n) = -2*t(n) - u(n). Determine s, given that r(s) = 0.
-1
Factor -24/5*f**2 - 5*f**3 - 1/5*f**4 + 0*f + 0.
-f**2*(f + 1)*(f + 24)/5
Let a = 260/7 - 891/14. Let r = -25 - a. Factor -r*m + 1/2 + 3/2*m**2 - 1/2*m**3.
-(m - 1)**3/2
Let u = -9 - -7. Let c(a) = -14*a - 3. Let g be c(u). Factor 27*b**2 - 25*b - 5*b + 58*b**2 - g*b**3.
-5*b*(b - 3)*(5*b - 2)
Suppose -5*f + 87 = -3*b, -f + 4*b + 14 = -17. Factor -f*t**4 + 8*t**3 - 34*t**5 - t**3 + 39*t**5 + 3*t**3.
5*t**3*(t - 2)*(t - 1)
Let o(g) be the third derivative of -g**6/300 - 16*g**5/75 - 19*g**4/4 - 30*g**3 - 94*g**2. Solve o(v) = 0.
-15, -2
Suppose 0 = n + 3*c + 1 - 0, 2*c = -3*n + 11. Let g(t) = -45*t**2 + 26*t - 1. Let f(p) = -45*p**2 + 25*p. Let l(o) = n*g(o) - 4*f(o). Factor l(u).
-5*(3*u - 1)**2
Let g(i) be the first derivative of -3*i**6/4 + 33*i**5/10 - 45*i**4/8 + 9*i**3/2 - 3*i**2/2 + 3. Factor g(m).
-3*m*(m - 1)**3*(3*m - 2)/2
Suppose 15 = -16*y + 21*y. Suppose 312*p - 98*p**2 + 28*p**3 - 18 - 20*p**y - 54 = 0. Calculate p.
1/4, 6
Let b(h) be the second derivative of -h**6/75 + h**5/25 + h**4/10 - 540*h. Suppose b(w) = 0. Calculate w.
-1, 0, 3
Let a(y) = 10*y - 24*y**2 - 12*y**3 + 21 + 72*y + 18*y - 85. Let h(u) = -4*u**3 - 8*u**2 + 33*u - 21. Let t(d) = 5*a(d) - 16*h(d). Solve t(x) = 0.
-4, 1
Let v = 723 + -15182/21. Let b(k) be the first derivative of -18/35*k**5 + 48/7*k**2 - 16/3*k**3 + 16/7*k**4 + 12 + v*k**6 - 32/7*k. Factor b(r).
2*(r - 2)**4*(r - 1)/7
Suppose 2*z - 4*p - 25 - 17 = 0, 0 = -5*z - 5*p + 45. Factor 15 + 11*t + 5*t - 10*t**2 + z*t - 4*t.
-5*(t - 3)*(2*t + 1)
Let r be -10*((-187)/(-22))/(-17). Let g(l) be the third derivative of 0*l + 1/600*l**6 + 1/100*l**r + 1/30*l**3 + 0 + 5*l**2 + 1/40*l**4. Factor g(m).
(m + 1)**3/5
Let d(v) = v**2 - 66*v - 132. Let i be d(-2). Let q(g) be the first derivative of -2/5*g**2 + 2/5*g**3 + 9 - 1/10*g**i + 0*g. Determine f so that q(f) = 0.
0, 1, 2
Let w(k) be the first derivative of 3*k**6/16 - 19*k**5/8 + 20*k**4/3 - 25*k**3/3 + k**2 + 13. Let h(y) be the second derivative of w(y). Solve h(m) = 0.
2/3, 5
Factor 103*d**4 - 4*d - 2*d + 101*d**4 + 6*d**3 - 3*d**2 - 201*d**4.
3*d*(d - 1)*(d + 1)*(d + 2)
Let m(h) be the second derivative of -h**7/21 - h**6/3 - h**5 - 5*h**4/3 - 5*h**3/3 - h**2 - 207*h. Factor m(l).
-2*(l + 1)**5
Let k(h) be the second derivative of h**7/10080 - h**4/6 + 4*h. Let u(l) be the third derivative of k(l). Determine p so that u(p) = 0.
0
Suppose 0 = m - 26 + 23. Factor 40*r - 31*r**4 + 17*r**2 + 46*r**4 + m*r**2 - 50*r**3.
5*r*(r - 2)**2*(3*r + 2)
Let w(f) = f**2 + f. Let i = 1 + -3. Let a(g) = -g**2 + g. Let q(u) = -9*u**2 - 15*u + 6. Let z(r) = 2*a(r) + q(r). Let t(l) = i*z(l) - 18*w(l). Factor t(h).
4*(h - 1)*(h + 3)
Let g(f) be the second derivative of f**5/10 - 11*f**4/2 + 96*f**3 - 256*f**2 - 109*f. Factor g(a).
2*(a - 16)**2*(a - 1)
Let o(n) be the first derivative of 4*n**5 - 8*n**4 - 16*n**3/3 + 45. Factor o(u).
4*u**2*(u - 2)*(5*u + 2)
Let i(y) be the third derivative of 0 + 1/60*y**6 + 0*y**4 - 1/30*y**5 - 2*y**2 + 0*y + 0*y**3. Find m, given that i(m) = 0.
0, 1
Suppose 0 = -m + 3*m. What is z in -3*z**4 + m*z**4 + 2*z**4 + z**5 = 0?
0, 1
What is k in 2*k**2 - 37*k - 16 + 56 - 48*k + 48*k**2 - 5*k**3 = 0?
1, 8
Let z = -1468 - -1472. Factor -3/2*y**2 + 0 + 3/2*y - 3/2*y**3 + 3/2*y**z.
3*y*(y - 1)**2*(y + 1)/2
Let s(f) = -f**2 + f - 1. Let i be s(0). Let c be i + (-3 - (-20)/6) + 2. Find u such that 1/3*u**2 + 0*u - c = 0.
-2, 2
Let k = 1471/960 + 13/192. Suppose 0 - 44/5*w**3 + 56/5*w**4 + k*w - 4*w**2 = 0. Calculate w.
-1/2, 0, 2/7, 1
Let l(c) be the first derivative of -c**5/3 - 65*c**4/24 - 5*c**3/2 + 7*c**2 + 7. Let m(q) be the second derivative of l(q). Determine k so that m(k) = 0.
-3, -1/4
Let s(k) be the first derivative of -8 + 0*k - 1/3*k**3 + 1/5*k**5 + 1/2*k**2 - 1/4*k**4. Solve s(q) = 0 for q.
-1, 0, 1
Let p(s) be the third derivative of s**9/37800 - s**8/16800 - s**7/3150 - s**4/24 - 2*s**2. Let g(j) be the second derivative of p(j). Factor g(u).
2*u**2*(u - 2)*(u + 1)/5
Factor -232*z**3 + 468*z**3 - 234*z**3 + 22*z - 12*z**2 - 12.
2*(z - 3)*(z - 2)*(z - 1)
Let l(p) be the first derivative of -p**3/12 - 3*p**2/8 - p/2 - 26. Factor l(u).
-(u + 1)*(u + 2)/4
Let o(l) be the first derivative of 4*l**3/3 - 56*l**2 - 240*l + 398. Determine d so that o(d) = 0.
-2, 30
Let x(t) be the first derivative of -4*t**5/35 + 6*t**4/7 + 64*t**3/21 - 29. Factor x(c).
-4*c**2*(c - 8)*(c + 2)/7
Suppose t = -3*t + 28. Let j be (6/t)/(2/7). Let -j*d**2 - d + 4 - 3*d**2 - d + 0 = 0. Calculate d.
-1, 2/3
Let p(q) be the second derivative of 0 + 1/4*q**4 - 5/42*q**3 - 2*q + 0*q**2 - 19/140*q**5 + 1/70*q**6. Factor p(d).
d*(d - 5)*(d - 1)*(3*d - 1)/7
Factor 74/7*r - 20/7*r**2 - 52/7 - 2/7*r**3.
-2*(r - 2)*(r - 1)*(r + 13)/7
Let n(w) = -w**3 - 7*w**2 - 209*w - 786. Let r be n(-4). Factor 16/5 - 2/5*q**r - 14/5*q.
-2*(q - 1)*(q + 8)/5
Factor 8*r**2 + 2*r - 11*r + 58*r**2.
3*r*(22*r - 3)
Let l be ((-1408)/(-33) - 25) + -17. Factor 4/3*m**2 + l - 1/3*m**3 - 5/3*m.
-(m - 2)*(m - 1)**2/3
Factor 2028 + 1/3*v**2 + 52*v.
(v + 78)**2/3
Let d(m) be the second derivative of -m**4/4 + 17*m**3 - 139*m. Solve d(l) = 0 for l.
0, 34
Let r(o) be the third derivative of o**7/70 - 7*o**6/40 + 13*o**5/20 + 3*o**4/8 - 9*o**3 - o**2 - 100. Factor r(m).
3*(m - 3)**2*(m - 2)*(m + 1)
Let g(r) = 2*r**2 - 3*r + 1. Let i be g(1). Factor -5*t**3 - t**3 - 2*t**2 + 10*t**3 + 2*t**4 + i*t**3 - 4*t.
2*t*(t - 1)*(t + 1)*(t + 2)
Let i = -338 - -340. Determine w so that -5 + 1/2*w**i + 3/2*w = 0.
-5, 2
Suppose 5*k - 2*j - 166 = 0, 0*k + 4*j + 152 = 5*k. Factor 6*u - k - 1/4*u**2.
-(u - 12)**2/4
Let u(y) = y**3 - 34*y**2 + 226*y - 5. Let j be u(9). Determine q so that -8/3 - 2/3*q**j + 2*q**2 - 8/3*q + 4/3*q**3 = 0.
-1, 2
Let x(q) be the first derivative of q**6/80 + 9*q**5/160 - q**3/4 - 16*q + 8. Let s(b) be the first derivative of x(b). Let s(z) = 0. What is z?
-2, 0, 1
Factor -79*u - u - 1044 - u**2 - 556.
-(u + 40)**2
Let d(l) = l**2 + 8*l - 15. Let p be d(-10). Let r be (((-8)/52)/2)/(24/(-156)). Factor 0*a + 0*a**2 - a**3 + 1/2*a**p + r*a**4 + 0.
a**3*(a - 1)*(a + 2)/2
Let h(t) be the first derivative of -t**6/12 - 26*t**5 - 22705*t**4/8 - 340345*t**3/3 - 323575*t**2 - 318028*t + 385. Find i such that h(i) = 0.
-86, -1
Let b be (-8 + 6)/((-3)/(18/4)). Let q be (-1*3/b)/(-5)*3. Factor -6/5*v + q - 9/5*v**2.
-3*(v + 1)*(3*v - 1)/5
Suppose -12*u**5 - 24*u + 377*u**2 - 6*u**4 - 367*u**2 + 16*u**3 + 8 + 8*u**5 = 0. What is u?
-2, 1/2, 1
Let c(d) be the first derivative of d**3/12 - 143*d**2/8 + 71*d/2 - 226. Factor c(f).
(f - 142)*(f - 1)/4
Let y be (4/46 + (-1862)/(-4508))*1. Factor 0 + 0*j + 1/2*j**5 - j**4 + y*j**3 + 0*j**2.
j**3*(j - 1)**2/2
Suppose 3*h = 6*h - 18. Suppose 5*u - 31 = 4*r, 4*r = r - 12. Determine w, given that -5*w**2 - h - 4*w**2 + 7*w**2 + u*w + 5*w = 0.
1, 3
Let y(z) = -z**3 + 21*z**2 - 40*z + 43. Suppose -2*k - 7*k = -171. Let r be y(k). Factor -60*w**3 - 50/3*w**4 + 250/3*w**r + 0 - 16/3*w + 104/3*w**2.
2*w*(w + 1)*(5*w - 2)**3/3
Let b be (0 - (-28)/8)*-2. Let a be (-6 - -4) + b/(-1). Solve -5*z**2 + 18*z**3 - z**2 - 2*z - 22*z**4 + 8*z**a + 0*z**2 + 4*z**2 = 0.
-1/4, 0, 1
Factor p**4 - 1/6*p**5 + 0 - 2*p**3 + 5/3*p**2 - 1/2*p.
-p*(p - 3)*(p - 1)**3/6
Let i(k) = -k**2 - 5*k - 1. Let t be i(-4). Determine v, given that -5*v**t + 35*v**4 + 3*v**2 + 3*v**5 - 38*v**4 + 2*v**3 = 0.
-1, 0, 1
Factor -48 - 4/3*d**3 + 20*d + 8/3*d**2.
-4*(d - 3)**2*(d + 4)/3
Suppose -4*c - 4 = -3*c. Let k(z) = -2*z - 4. Let b be k(c). Factor -7*x**3 - 2*x**4 + b*x**4 + 9*x**3 - 2*x**5 + 0*x**2 - 2*x**2.
-2