-3*k*(k - 1)
Let p be (-34)/(-136) - (-382)/8. Factor -37*q**2 + 56 - 3*q**3 - 506 - 615*q + p*q**2 + 77*q**2.
-(q - 15)**2*(3*q + 2)
Suppose 3*h = x + 19, -2*h - 17*x - 10 = -12*x. Let f be -4*(-23)/(-4)*-2. Factor h*c**2 + 20 + 6*c + 8*c**3 - 5*c**4 - 5*c**5 + 17*c**3 - f*c.
-5*(c - 1)**3*(c + 2)**2
Let u = -359 - -362. Find o, given that -56*o**4 + 13*o**u - 26*o**4 + 79*o**4 - 4*o**2 = 0.
0, 1/3, 4
Let l(t) be the second derivative of -t - 17 + 19/15*t**6 - 13/10*t**5 + 0*t**2 + 4/3*t**3 - 2/7*t**7 - 2/3*t**4. Solve l(p) = 0.
-1/2, 0, 2/3, 1, 2
Let u be -2*(-42)/(-12)*(-6)/(-14). Let x be (16/(-12))/2*u. Let 3 - 92*t + 29 + 7*t + 8 + 10*t**x = 0. What is t?
1/2, 8
Let d(z) be the second derivative of -200*z + 0*z**2 + 0 + 1/80*z**5 - 5/24*z**4 - 11/24*z**3. Determine u so that d(u) = 0.
-1, 0, 11
Let p be (-46)/230 - 1242/(-10). Let z = p + -1112/9. Determine u so that -z*u**4 - 2/9*u + 0 + 2/9*u**5 + 0*u**3 + 4/9*u**2 = 0.
-1, 0, 1
Let p(c) = 4*c**4 - 24*c**3 + 20*c**2 + 120. Let q(v) = 2*v**3 - v**2 - 6. Let k(o) = p(o) + 20*q(o). Factor k(j).
4*j**3*(j + 4)
Let r(u) be the second derivative of 7/3*u**4 - u + 68*u**2 - 13 + 242/3*u**3. Factor r(k).
4*(k + 17)*(7*k + 2)
Let i = 86 - 84. Suppose -20*c**2 - 3*c**4 + 5 + 8*c**4 + 10*c**i + 5*c**5 - 10*c**3 + 5*c = 0. Calculate c.
-1, 1
Let b(a) be the first derivative of a**4/16 + 101*a**3/12 - 205*a**2/8 + 103*a/4 - 384. Factor b(s).
(s - 1)**2*(s + 103)/4
Let v(n) = 2*n**3 - 2*n**2 - 8*n + 11. Let f be v(2). Factor -653*w**4 + 325*w**4 - 341*w**2 + 324*w**4 + 64*w**f + 85*w**2.
-4*w**2*(w - 8)**2
Factor 4077*t**3 - 32*t**2 + 8*t**2 - 4075*t**3.
2*t**2*(t - 12)
Find m, given that 859/3 - 860/3*m + 1/3*m**2 = 0.
1, 859
Let v(n) be the first derivative of 3*n**4/4 + 19*n**3/3 - 9*n**2/2 + 37*n + 155. Let r be v(-7). Factor 8 - 14/3*p**r - 80/3*p.
-2*(p + 6)*(7*p - 2)/3
Let g be (-6 + 2481/9)/(3/(-9)). Let b = 813 + g. Factor -4*i**b - 4/3*i**2 + 0 + 0*i + 4*i**3 + 4/3*i**5.
4*i**2*(i - 1)**3/3
Suppose 0 = -5*u - 2*y + 3*y + 16, -3*u = y - 16. Suppose -171*k + 172*k = s - 10, -20 = -s + 3*k. Factor -2*a**s - 2*a**3 + 4*a**3 - 5*a**u - 6*a**3 - a**2.
-a**2*(a + 1)**2*(2*a + 1)
Let b(r) be the second derivative of -r**7/70 + 11*r**6/50 + 9*r**5/100 - 31*r**4/20 - 11*r**3/5 + r - 153. What is k in b(k) = 0?
-1, 0, 2, 11
Suppose 0 = -43*d + 11*d + 160. Let q(l) be the third derivative of -1/24*l**4 + 1/3*l**3 + 0*l + 0 - 1/60*l**d + 33*l**2. Solve q(m) = 0.
-2, 1
Let l be (-6 - (-56)/12)/(2/720). Let d = -1430/3 - l. Solve -5/3*w**2 + d*w**3 + 0 + 0*w = 0 for w.
0, 1/2
Factor -1/2*o**2 + 83*o - 805/2.
-(o - 161)*(o - 5)/2
Let c(s) = -s**3 - s**2 - 12*s + 8. Let d be c(0). Let t(b) be the first derivative of 10/3*b**3 + d*b**2 + 8*b + 1/2*b**4 - 3. Factor t(q).
2*(q + 1)*(q + 2)**2
Factor -1/4*n**2 + 0 - 237/2*n.
-n*(n + 474)/4
Let c(b) = -b**3 - 13*b**2 - 44*b - 10. Let a be c(-7). Suppose 65*l**3 + 0*l**a - 5*l**4 + 3*l**2 - 50*l**3 - 13*l**2 = 0. Calculate l.
0, 1, 2
Let n(c) be the first derivative of -24 - 9/5*c + 1/5*c**3 + 3/5*c**2. Suppose n(l) = 0. Calculate l.
-3, 1
Let s(y) = -100*y**4 - 22480*y**3 - 1272336*y**2 - 1007098*y - 200704. Let c(d) = -d. Let x(l) = 6*c(l) + s(l). Factor x(q).
-4*(q + 112)**2*(5*q + 2)**2
Let r = 2557/3 - 89491/105. Let c(i) be the second derivative of 0*i**2 + 1/140*i**5 + 0*i**3 + 12*i + 0 + 1/42*i**4 - r*i**6 + 5/294*i**7. Factor c(v).
v**2*(v - 1)**2*(5*v + 2)/7
Let z(g) be the second derivative of g**5/25 - 16*g**4/15 + 26*g**3/15 + 12*g**2 + 159*g - 1. Solve z(t) = 0.
-1, 2, 15
Let t(z) be the first derivative of 1/2*z**4 - 50 + 1/12*z**6 - 2/5*z**5 + 0*z**3 + 0*z + 0*z**2. Suppose t(r) = 0. Calculate r.
0, 2
Let k be (-583 + ((-24)/(-6) - 4))/1. Let l = k + 1753/3. Find r such that -2/3 + 2/3*r**4 - 4/3*r + 0*r**2 + l*r**3 = 0.
-1, 1
Let b(y) be the third derivative of -y**9/52920 - y**8/11760 - y**7/8820 + 25*y**4/8 - 3*y**2 - 3*y. Let t(g) be the second derivative of b(g). Factor t(v).
-2*v**2*(v + 1)**2/7
Let y be 1*(4/(-16) + 20/16) + 4. Let h(z) = -2 + z**2 - 12*z - 2 + 9. Let l(k) = -k**2 + 6*k - 3. Let r(w) = y*l(w) + 3*h(w). Find g such that r(g) = 0.
-3, 0
Let i be (3/4 + -1)*-116 + -8 + 5. Let f(u) be the second derivative of 0 + 1/8*u**3 + i*u + 0*u**2 - 1/16*u**4. Solve f(y) = 0 for y.
0, 1
Let o(u) be the third derivative of u**6/90 + 541*u**5/90 + 202*u**4/9 + 269*u**3/9 + 1725*u**2 + 2*u. Find q, given that o(q) = 0.
-269, -1, -1/2
Factor 56 - 19/2*a**2 - 185/4*a - 1/4*a**3.
-(a - 1)*(a + 7)*(a + 32)/4
Let b(h) be the third derivative of -h**5/270 + 11*h**4/36 + 328*h**3/27 + 888*h**2 + 3. Factor b(k).
-2*(k - 41)*(k + 8)/9
Suppose 4 = x - 0. Let l = 1699/3703 - 16/529. Solve 0*g**2 + 0*g**3 + l*g**5 + 0*g + 0 - 3/7*g**x = 0 for g.
0, 1
Let t(x) be the second derivative of x**4/8 - 65*x**3 + 12675*x**2 - 286*x + 2. Let t(w) = 0. What is w?
130
Let o(x) be the third derivative of 1/18*x**5 - 3/8*x**4 - 1/360*x**6 - 8 + x**3 + 11*x**2 + 0*x. Suppose o(d) = 0. What is d?
1, 3, 6
Let q(p) = 60*p + 4107. Let y be q(-68). Let v(z) be the first derivative of 9/8*z**4 - 9*z**2 + 6*z + y - 1/2*z**3. Factor v(h).
3*(h - 2)*(h + 2)*(3*h - 1)/2
Let c(i) be the third derivative of 1/30*i**5 - 1/36*i**4 + 1/180*i**6 - 4 + 0*i - 2*i**2 - 1/3*i**3. Determine v, given that c(v) = 0.
-3, -1, 1
Let m(w) be the third derivative of -w**3 + 0 + 3/40*w**4 - 47*w**2 + 0*w + 1/100*w**5. Suppose m(z) = 0. Calculate z.
-5, 2
Let o = 1 + 3. Let i = -422/221 + 3396/1547. Let 12/7*a**o + 24/7*a - 22/7*a**3 - i*a**5 - 16/7 + 4/7*a**2 = 0. Calculate a.
-1, 1, 2
Let a(b) = -110*b**3 + 1495*b**2 - 5720*b + 6535. Let q(y) = 5*y**3 - 68*y**2 + 260*y - 297. Let d(k) = -3*a(k) - 65*q(k). Factor d(v).
5*(v - 6)*(v - 5)*(v - 2)
Let n = -333 + 350. Let o be 28/238 + (15/n)/1. Suppose 1/2*g**2 + 3/2*g + o = 0. What is g?
-2, -1
Let x(b) = b**3 + 10*b**2 + 14*b - 1. Let r be x(-9). Let t = 281/6 + r. What is n in -5/3 + 5/6*n**2 + t*n = 0?
-2, 1
Let a be (-14)/(-4)*(-2028)/(-17745)*(-2 - -7). Factor -2/11*w**5 + 6/11*w**3 + 0*w - 4/11*w**a + 0*w**4 + 0.
-2*w**2*(w - 1)**2*(w + 2)/11
Let t(h) be the third derivative of h**5/3 - 4525*h**4/24 + 565*h**3/3 + 2040*h**2. Suppose t(v) = 0. Calculate v.
1/4, 226
Let l(g) be the third derivative of -2*g**7/735 + 3*g**6/35 + 53*g**5/35 + 194*g**4/21 + 200*g**3/7 - 825*g**2. Find x, given that l(x) = 0.
-3, -2, 25
Let y = -6/2323 - -2743/162610. Let v(b) be the second derivative of -y*b**5 + 0 - 9/7*b**2 - 20*b + 5/42*b**4 - 1/7*b**3. Find s, given that v(s) = 0.
-1, 3
Suppose 3*f + 60 - 247 = 4*g, 5*f - 4*g = 317. Suppose f*j = 35*j. Suppose j*h + 3/5*h**4 + 0*h**2 + 3/5*h**3 + 0 = 0. What is h?
-1, 0
Let p = 7679491/7 + -1100301. Let j = p - -3240. Factor -96/7*m**2 - 32/7*m**3 - 128/7*m - j - 4/7*m**4.
-4*(m + 2)**4/7
Let l = 97 - 95. Suppose 0 = -6*q + 2*q + l*o + 68, -o - 82 = -5*q. Factor 4*c + 15*c**2 + 3*c**2 - q*c**2.
2*c*(c + 2)
Let c(f) be the first derivative of -2/9*f**3 + 6*f - 95 - 8/3*f**2. Determine m, given that c(m) = 0.
-9, 1
Let t = 3615 - 10841/3. Let l(c) be the first derivative of 0*c - t*c**3 + 4*c**4 + 2 + 0*c**2. Let l(a) = 0. Calculate a.
0, 1/4
Let m be 665/133 - 19/4. Let v(j) be the second derivative of 0 + 0*j**2 + 18*j + m*j**3 + 1/24*j**4 - 3/40*j**5 - 1/60*j**6. Find x, given that v(x) = 0.
-3, -1, 0, 1
Let l(q) be the third derivative of q**6/450 + 3*q**5/200 + q**4/60 + 7*q**3 - 44*q**2. Let n(c) be the first derivative of l(c). Find a such that n(a) = 0.
-2, -1/4
Let n(b) be the second derivative of 1/14*b**7 + 1/5*b**6 + 0 - 1/2*b**3 + 70*b + 0*b**2 - 1/2*b**4 + 0*b**5. Factor n(z).
3*z*(z - 1)*(z + 1)**3
Let z = 24694 + -24692. Factor 3/5*o**z + 21/5*o + 6.
3*(o + 2)*(o + 5)/5
Let h(f) be the second derivative of -f**5/100 + 53*f**4/12 + 134*f**3/15 - 266*f**2/5 + 298*f - 2. Factor h(t).
-(t - 266)*(t - 1)*(t + 2)/5
Suppose 5*c + 162 = 41*s - 36, 4*s + c + 3 = 0. Factor -125/2*j**s - 79507/2 - 27735/2*j - 3225/2*j**2.
-(5*j + 43)**3/2
Let v = 8599 - 8566. Let r(i) be the third derivative of 0 - 1/280*i**6 + 9/140*i**5 - v*i**2 - 3/7*i**4 + 0*i + 8/7*i**3. Factor r(q).
-3*(q - 4)**2*(q - 1)/7
Let v be (-3 - 264/(-77)) + 198/28 - 77/22. Determine i so that -38/7*i**3 - 2/7*i**5 - 8/7 - 50/7*i**2 - 2