992/5 + 976/5*o - 244/5*o**3 - 4/5*o**4 = 0. Calculate o.
-62, -2, 1, 2
Let h = -103829 + 103833. Determine d, given that -10/21*d**h - 16/21*d**3 + 0 + 38/21*d**2 - 4/7*d = 0.
-3, 0, 2/5, 1
Suppose -c + 14 = -4. Let g be -7*(-6)/c - (-1)/(-3). Find p, given that p**2 + 0*p**2 - 5*p**g = 0.
0
Let v(q) = q**3 + 6*q**2 - 150*q - 767. Let y be v(-5). Factor -72/5 - 2/5*p**2 + y*p.
-2*(p - 18)*(p - 2)/5
Suppose -2*t = 88*c - 87*c - 707, -3*t = 4*c - 2853. Let u = -4297/6 + c. Factor -u + 2/3*p + 1/6*p**2.
(p - 1)*(p + 5)/6
Suppose -33377 - 607 = -6*z. Factor 105*p**2 - 6*p**3 + 37211 + 3675*p + 7*p**3 + z.
(p + 35)**3
Let k = 140843/18 + -7827. Let z = -31/18 - k. Factor -z + 2/9*n + 2/3*n**2 - 2/9*n**3.
-2*(n - 3)*(n - 1)*(n + 1)/9
Let o(v) be the second derivative of -2*v**6/15 + 8*v**5 - 98*v**4 + 944*v**3/3 - 434*v**2 + 2046*v + 2. Factor o(h).
-4*(h - 31)*(h - 7)*(h - 1)**2
Let j(z) be the first derivative of z**4/28 + 334*z**3/21 - 337*z**2/14 - 670*z/7 - 3390. Factor j(i).
(i - 2)*(i + 1)*(i + 335)/7
Let c(x) be the third derivative of x**7/280 - x**6/40 - 19*x**5/40 - 15*x**4/8 - 27*x**3/8 + 8*x**2 + 24*x. Let c(w) = 0. Calculate w.
-3, -1, 9
Let r = 3604 + -43241/12. Let v(u) be the first derivative of -1/24*u**6 - 9/16*u**4 - r*u**3 - 1/4*u**5 - 1/4*u**2 - 3 + 0*u. Factor v(s).
-s*(s + 1)**3*(s + 2)/4
Let k(f) = f**2 + 9*f - 6. Let i(a) = -8*a**2 - 35*a + 22. Let p(r) = r**2. Let v(o) = -i(o) - 5*p(o). Let b(y) = 22*k(y) - 6*v(y). Factor b(n).
4*n*(n - 3)
Suppose 5*b - 1853 = -3*w - 535, -8 = 2*w. What is l in l**2 - l**5 - 3*l**3 - 2*l**2 + b*l**4 - 269*l**4 = 0?
-1, 0
Suppose d - g = 7, -482*d + 11 = -481*d + 3*g. Let k(j) be the first derivative of 0*j - 5*j**2 + d + 5/3*j**3. Factor k(l).
5*l*(l - 2)
Suppose 36*t - 160 + 216 = -3*t + 173. Factor 0 + 66/7*i**2 + 0*i - 3/7*i**t.
-3*i**2*(i - 22)/7
Let g(s) be the first derivative of 2*s**3/21 + 3434*s**2/7 + 5896178*s/7 - 3622. Factor g(i).
2*(i + 1717)**2/7
Let g(a) be the second derivative of a - 1/4*a**5 + 0*a**2 + 5/6*a**3 - 8 + 0*a**4. Factor g(b).
-5*b*(b - 1)*(b + 1)
Let z(r) = -2*r**2 - r**3 + 17*r + 9 - 13*r**2 + 13 + 0*r**2. Let n be z(-16). Determine l so that 2*l**4 - 7*l**4 + 16*l**3 + 4*l**3 - n*l + 5*l**2 - 14*l = 0.
-1, 0, 1, 4
Let c = -6178 + 197713/32. Let s(m) be the first derivative of -5 + 0*m - c*m**4 - 1/4*m**2 + 1/8*m**5 + 2/3*m**3. Determine o, given that s(o) = 0.
0, 2/5, 1, 2
Let j(l) be the third derivative of 0*l**3 - 7*l**2 + 0*l**6 + 0 + 1/840*l**8 + l + 0*l**4 - 2/525*l**7 + 0*l**5. Factor j(v).
2*v**4*(v - 2)/5
Let c be (0 + 578)/((7 - 4) + -2). Find l, given that -2*l**4 + 2*l**2 - c + 578 + 4*l**3 - 30*l**3 + 26*l = 0.
-13, -1, 0, 1
Let q(w) be the second derivative of -17/110*w**5 - 64/33*w**3 + 0 + 0*w**2 + 143*w + 40/33*w**4 + 1/165*w**6. Factor q(c).
2*c*(c - 8)**2*(c - 1)/11
Let q be (-6)/(-21) + -45 + (-48949)/(-1085). Suppose 0 + 0*v - q*v**2 = 0. What is v?
0
Solve 33/2*k**4 - 3*k**5 - 3/2*k**2 + 0 - 18*k**3 + 6*k = 0 for k.
-1/2, 0, 1, 4
Suppose -2/19*m**4 + 0*m - 192/19*m**2 + 0 - 40/19*m**3 = 0. What is m?
-12, -8, 0
Let t(n) = 11*n**2 + 2*n - 2. Let p(k) = 325*k**2 - 6410*k - 2093105. Let s(v) = p(v) - 30*t(v). Factor s(g).
-5*(g + 647)**2
Suppose -370 - 372 = -7*z. Let t = -199/2 + z. Determine v so that 33/4*v**2 - 77/8*v**3 + t*v - 49/8*v**4 + 1 = 0.
-2, -2/7, 1
Factor -56*z**3 - 46*z**2 - 466*z - 60*z**2 + 25*z**3 + 32*z**3 + 1250*z.
z*(z - 98)*(z - 8)
Let r(q) = -q**3 - 5*q**2 + 93*q + 465. Let d be r(-5). Let c(i) be the second derivative of 0*i**2 + 17*i + 1/60*i**4 + 1/10*i**3 + d. Factor c(p).
p*(p + 3)/5
Let w(o) be the first derivative of -13*o**7/5040 + o**6/40 - o**5/12 + o**4/18 + 4*o**3/3 + 9. Let t(c) be the third derivative of w(c). Factor t(b).
-(b - 2)**2*(13*b - 2)/6
Let a(f) be the first derivative of 2*f**3/15 - 392*f**2/5 - 786*f/5 - 1271. Factor a(b).
2*(b - 393)*(b + 1)/5
Factor -671460*u**2 - 17352/7*u - 16/7 + 336350*u**3.
2*(u - 2)*(1085*u + 2)**2/7
Let l(z) be the second derivative of 5*z**7/42 + z**6/2 - 3*z**5/2 - 10*z**4/3 - z - 12. Factor l(c).
5*c**2*(c - 2)*(c + 1)*(c + 4)
Let h = -718 - -4309/6. Let b = h + 1/18. Suppose -2/9*j + 2/9*j**3 - 2/9*j**2 + b*j**4 + 0 = 0. Calculate j.
-1, 0, 1
Let t(n) be the second derivative of -3*n**2 + 3/20*n**5 - 3/10*n**6 - 3*n + 9/4*n**4 + 3/2*n**3 + 1. Find a such that t(a) = 0.
-1, 1/3, 2
Suppose 0 = -46*l + 35*l + 55. Factor -88*o**3 - 30*o**4 + 11*o**3 + 7*o**3 - 10 + 55*o**l - 45*o - 80*o**2 - 60*o**5.
-5*(o + 1)**4*(o + 2)
Let b be 232/16 + (-805)/70. Let 8*r - 16/3 - b*r**2 + 1/3*r**3 = 0. What is r?
1, 4
Let s be 5 - -19 - (-111300)/(-4823). Solve -10/13*v + 0 - 2/13*v**3 - s*v**2 = 0 for v.
-5, -1, 0
Let j(p) be the first derivative of 3*p**5/10 + 21*p**4/8 + 3*p**3 - 1955. Factor j(d).
3*d**2*(d + 1)*(d + 6)/2
Let x(z) be the second derivative of -37*z + 0 + 0*z**3 + 1/160*z**5 - 5/64*z**4 + 37/2*z**2. Let l(t) be the first derivative of x(t). Let l(v) = 0. What is v?
0, 5
Factor 6*j**3 + 2*j**3 + 3*j**4 - 22*j**3 + 150*j - 75*j**2 + 6*j**3 + 2*j**3.
3*j*(j - 5)*(j - 2)*(j + 5)
Suppose 5*l = 439 - 274. Solve 0*u**5 - 8*u**4 - 32 - l*u + 4*u**5 + 83*u + 40*u**2 - 34*u - 20*u**3 = 0 for u.
-2, -1, 1, 2
Let m = 2/58617 - -1524008/996489. Find a such that 0 + m*a**4 + 30/17*a**3 + 8/17*a**5 + 14/17*a**2 + 2/17*a = 0.
-1, -1/4, 0
Let c(t) be the second derivative of -t**5/180 + t**4/6 - 2*t**3 - 58*t**2 + 31*t. Let d(f) be the first derivative of c(f). Factor d(k).
-(k - 6)**2/3
Let h(i) be the second derivative of -2/5*i**6 - i**5 - i - 2/3*i**4 + 0*i**2 + 0*i**3 + 72. Factor h(p).
-4*p**2*(p + 1)*(3*p + 2)
Let i be (5/(-1))/(2/(-12)*-3). Let r(f) = 3*f**3 + 30*f**2 + f + 13. Let s be r(i). Suppose 5 + 5*z**4 + 3794*z**3 - 10*z**2 - 3794*z**s = 0. What is z?
-1, 1
Let q(i) be the third derivative of -i**6/24 - 197*i**5/3 - 260035*i**4/8 - 257415*i**3 - 3*i**2 + 2*i + 3. Factor q(m).
-5*(m + 2)*(m + 393)**2
Let l = 33881 - 1287553/38. Let p = 1583/494 + l. Factor p + 2/13*n**2 + 18/13*n.
2*(n + 1)*(n + 8)/13
Let b be (0 + 90)*11/330. Factor 0*d + 0 - 5/4*d**b - 15/4*d**2.
-5*d**2*(d + 3)/4
Let y(i) be the first derivative of 0*i + 0*i**2 + 3*i**4 - 16/9*i**3 - 100 + 2/3*i**5. Determine f so that y(f) = 0.
-4, 0, 2/5
Let j be (-316)/(-1503) - 3532/(-294922). What is m in j*m**3 + 16/9*m + 8/9 + 10/9*m**2 = 0?
-2, -1
Let z(r) be the first derivative of 5/9*r**3 - 1/2*r**2 + 51 - 3*r - 1/12*r**4. Suppose z(p) = 0. What is p?
-1, 3
Let v(b) = -6*b**5 + 38*b**3 - 132*b**2 + 180*b - 84. Let d(g) = -5*g**5 + g**4 + 37*g**3 - 134*g**2 + 181*g - 83. Let s(n) = -4*d(n) + 3*v(n). Factor s(r).
2*(r - 2)**3*(r - 1)*(r + 5)
Let x(t) be the second derivative of t**5/60 + t**4/6 - 5*t**3/6 + 4*t**2/3 - 970*t. Factor x(q).
(q - 1)**2*(q + 8)/3
Suppose -144*m**2 - 85*m**3 + 2254*m - 421 - 398*m - 91 - 187*m**3 - 28*m**4 = 0. Calculate m.
-8, -4, 2/7, 2
Let t(a) = 2*a**2 - 216*a - 236. Let y(s) = 2*s**2 - 222*s - 236. Let j(n) = -2*t(n) + 3*y(n). Factor j(m).
2*(m - 118)*(m + 1)
Let y = 11058 + -22103/2. Factor y*s - 1/2*s**3 - 5 - s**2.
-(s - 2)*(s - 1)*(s + 5)/2
Suppose -49 + 277*p + 722*p**2 - 3 - 1440*p**2 - 288 + 714*p**2 = 0. What is p?
5/4, 68
Let b(h) = h**3 + h - 7. Let y(x) = -2*x**4 + 142*x**3 + 140*x**2 - 130*x - 180. Let m(i) = -12*b(i) + 2*y(i). Factor m(u).
-4*(u - 69)*(u - 1)*(u + 1)**2
Suppose -7420*b = -7443*b + 41 + 5. Let c(g) be the first derivative of -9 - 1/6*g**3 + 0*g - 1/24*g**4 - 1/6*g**b. Factor c(a).
-a*(a + 1)*(a + 2)/6
Let i be (73 - 61)*1/6. Let h(b) be the second derivative of 1/6*b**6 + b - 1/4*b**5 - 5/12*b**4 + 0 + 0*b**i + 5/6*b**3. Let h(g) = 0. Calculate g.
-1, 0, 1
Factor 143/2 + 71*u - 1/2*u**2.
-(u - 143)*(u + 1)/2
Suppose -22 = 5*u - 3*o - 53, -2*u - 5*o = 0. Determine s so that 22*s**5 - 2*s**4 + 13*s**3 + 5*s**4 - 40*s**3 - 19*s**u - 9*s - 3*s + 33*s**2 = 0.
-4, 0, 1
Let m(y) = -8*y**3 + 4*y**2 + 63*y + 6. Let h(t) = 58*t**3 - 28*t**2 - 446*t - 44. Let d(k) = -6*h(k) - 44*m(k). Factor d(u).
4*u*(u - 6)*(u + 4)
Let t(i) be the second derivative of -i**5/10 - 559*i**4/6 + 1121*i**3/3 - 561*i**2 - 6363*i. Suppose t(r) = 0. What is r?
-561, 1
Suppose -80*r + 75*r + 5*y - 55 = 0, -33 = -31*r - 3*y. Solve r - 4/3*u**2 + 28/3*u = 0 for u.
0