5
Let g be (-4)/26 + 576*(-46)/(-16744). Suppose -2*q**2 - 12/7*q - g*q**4 + 36/7*q**3 + 0 = 0. Calculate q.
-2/5, 0, 1, 3
Let c be (192/20)/(1461/12175*(-190)/(-4)). Factor -62/19*o + c + 28/19*o**2 + 2/19*o**3.
2*(o - 1)**2*(o + 16)/19
Let g(z) be the second derivative of 14/15*z**6 - 96*z**2 - 416/3*z**3 - 48*z**4 - 12/5*z**5 - 2*z - 101. Determine s so that g(s) = 0.
-2, -2/7, 6
Let d(y) be the second derivative of -77/3*y**4 + 2/5*y**5 + 224/3*y**3 - 74*y**2 + 29 + 2*y. Factor d(b).
4*(b - 37)*(b - 1)*(2*b - 1)
Let o(m) = -28*m**3 - 440*m**2 - 768*m - 80. Let x(p) = 9*p**3 + 146*p**2 + 256*p + 25. Let v(q) = -5*o(q) - 16*x(q). Factor v(f).
-4*f*(f + 2)*(f + 32)
Let k(l) = -l**3 + 37*l**2 - 26*l + 5. Let q(g) = -g**3 + 19*g**2 - 14*g + 2. Let p(u) = 2*k(u) - 5*q(u). Factor p(m).
3*m*(m - 6)*(m - 1)
Let j(f) be the second derivative of 3*f**5/70 - 2*f**4/3 + 4*f**3/7 + 288*f**2/7 - 406*f. What is h in j(h) = 0?
-8/3, 6
Let g be ((-30)/(-99))/(174/638). Suppose -5/9*j**3 - 1/3*j**2 + 17/9*j - g + 1/9*j**4 = 0. Calculate j.
-2, 1, 5
Let t be ((-125)/(-100))/((-25)/8 + 3) + 10. Suppose 1/2*k**3 + t*k**2 - 1 - 3/2*k = 0. Calculate k.
-1, 2
Let i(t) = -7*t + 1. Let o(z) = 2*z**2 + 124*z - 612. Let b(v) = -12*i(v) - o(v). Factor b(h).
-2*(h - 10)*(h + 30)
What is o in -468*o**2 + 484 + 536*o**2 - 87*o - 2*o**3 - 463*o = 0?
1, 11, 22
Let l = 1007 - 1004. Suppose -l*c - h = -3*h + 2, c - 3*h + 10 = 0. Determine m so that 3 - 3/2*m**c - 3/2*m = 0.
-2, 1
Factor -70/3*w**2 - 1/3*w**4 - 48*w + 0 + 73/3*w**3.
-w*(w - 72)*(w - 2)*(w + 1)/3
Suppose 0 = -13*c + 1126 - 216. Suppose -c*u**2 + 4 - 98*u**3 + 160*u + 216*u**2 + 92*u**2 + 20 = 0. What is u?
-2/7, 3
Let m(o) be the first derivative of o**4 + 392*o**3/3 + 2234*o**2 + 4080*o - 12788. Factor m(a).
4*(a + 1)*(a + 12)*(a + 85)
Suppose -p + 2*u = -17, 0 = 2*p + 17*u + 110 + 3. Suppose 0 + 3*q - 13/2*q**2 + 4*q**p - 1/2*q**4 = 0. Calculate q.
0, 1, 6
Let c(w) be the second derivative of 45/2*w**2 + 5*w**3 + 5/12*w**4 - 26*w + 0. Suppose c(v) = 0. What is v?
-3
Factor -9/7*t**3 + 3/7*t**4 + 3*t - 9/7*t**2 + 18/7.
3*(t - 3)*(t - 2)*(t + 1)**2/7
Factor -233/2*c - 7/2*c**2 - 33.
-(c + 33)*(7*c + 2)/2
Let b(q) be the second derivative of -q**4/132 + 53*q**3/33 - 105*q**2/22 - 38*q - 9. Factor b(s).
-(s - 105)*(s - 1)/11
Let v(g) = g**2 + 31 - 52 + g + 21. Let k(l) = -l**3 - 5*l**2 - 20*l - 16. Let b(o) = k(o) - 6*v(o). Solve b(r) = 0.
-8, -2, -1
Let x(l) be the third derivative of -l**6/24 - 1159*l**5/6 - 6716405*l**4/24 - 5*l**2 - 25*l - 1. Factor x(n).
-5*n*(n + 1159)**2
Let g(j) = -7*j**3 - 12*j**2 + 3*j + 16. Let o = 84 + -81. Let q(w) = 1 + 41*w**3 - 90*w**3 + 48*w**o. Let d(p) = g(p) - 4*q(p). Find t such that d(t) = 0.
-4, -1, 1
Let p(s) be the second derivative of -3*s**5/35 - 1109*s**4/2 - 7531080*s**3/7 + 11302443*s**2/7 - 10602*s. Factor p(d).
-6*(d + 1941)**2*(2*d - 1)/7
Let 2/19*k**4 - 3054207776/19 - 5480/19*k**3 + 263232*k**2 - 1517079136/19*k = 0. Calculate k.
-2, 914
Suppose 17*y - 34 + 0 = 0. Factor 16 + 70*c - 12*c**y - 138*c + 4*c**3 + 68*c.
4*(c - 2)**2*(c + 1)
Let n(u) be the second derivative of -u**9/15120 + u**8/2240 - u**6/180 + 25*u**4/4 - 42*u. Let t(i) be the third derivative of n(i). Factor t(w).
-w*(w - 2)**2*(w + 1)
Let s(q) be the second derivative of 1/6*q**4 - 3*q**3 + 0 + 1/540*q**6 + 0*q**2 - 1/36*q**5 + 16*q. Let n(c) be the second derivative of s(c). Factor n(j).
2*(j - 3)*(j - 2)/3
Let 6241/3 + 1/3*k**2 - 158/3*k = 0. Calculate k.
79
Let i = 3239 - 3208. Let x(a) be the first derivative of -4/5*a - 1/3*a**3 - i - 4/5*a**2 - 1/20*a**4. What is j in x(j) = 0?
-2, -1
Suppose -5*z - 2 = -3*a - 3, -4*a = 3*z - 18. Factor -87*i + 5*i**a + 49*i - 4*i**4 + 4*i**2 - 13*i**3 + 46*i.
-4*i*(i - 1)*(i + 1)*(i + 2)
Suppose -10257*v - 283544 = -10391*v. Factor 1/3*s**5 + v*s**3 + 97336/3*s**2 + 46*s**4 + 0 + 0*s.
s**2*(s + 46)**3/3
Let x = -1182119 - -5910682/5. Solve -672/5*l - 3/5*l**3 + 588/5 + x*l**2 = 0 for l.
1, 14
Let k(c) be the first derivative of 22*c**3/7 - 29*c**2/7 - 8*c/7 + 2411. Factor k(s).
2*(s - 1)*(33*s + 4)/7
Let t(b) be the third derivative of b**8/672 + b**7/21 - 47*b**6/240 - 31*b**5/60 + 23*b**4/12 + 22*b**3/3 + b**2 + 1134*b. Determine a, given that t(a) = 0.
-22, -1, 2
Suppose 5*v - 3*v + 8 = 0. Let q be ((-2)/5)/((v/20)/1). Factor -23 + 19*f - f - 1 - 3*f**q.
-3*(f - 4)*(f - 2)
Let f be 16/40*(-6065)/(-1). Let r(g) = g**2 + 2*g - 5. Let p be r(-5). Factor f*m**2 - 2421*m**2 + 10*m - 5 - p.
5*(m - 1)*(m + 3)
Suppose -q + 17 = -2*d, -d - 11 = -q - 2*d. Suppose 4*l - q = 2*l - 3*c, 24 = 5*l - c. Factor -7*n - l*n + 71 - 71 - 4*n**2.
-4*n*(n + 3)
Let r be 6/(-135)*5 - (-4)/18. Let f(z) = -z**2 - 30*z + 31. Let w be f(1). Let r*d - 2/13*d**3 + w - 2/13*d**2 = 0. What is d?
-1, 0
Factor 1072881 - 10*c**2 - 1072881 + c**3 + 9*c.
c*(c - 9)*(c - 1)
Let y(a) = a**3 - 16*a**2 + 39*a - 101. Let p be y(15). Let f be (-936)/(-481) + 14/p. Factor 1/4 + 3/2*v**f + 2*v + 25/4*v**4 - 10*v**3.
(v - 1)**2*(5*v + 1)**2/4
Suppose 0 = 5*v + 13*v - 26838. Suppose -1485*g = -v*g + 24. Factor 8/5*j**g + 0 - 2/5*j**5 + 22/5*j**3 + 12/5*j**2 + 0*j.
-2*j**2*(j - 6)*(j + 1)**2/5
Let j(k) be the second derivative of -33*k + 121/4*k**5 - 75/2*k**4 + 0*k**2 + 125/6*k**3 + 0 - 12*k**6 + 40/21*k**7. Factor j(o).
5*o*(o - 1)**2*(4*o - 5)**2
Let t = -123 + 134. Let -a**3 + 3 - 7 - t*a + 5*a + 3*a**3 = 0. Calculate a.
-1, 2
Let g(i) = 2*i**2 + 360*i - 656. Let z(a) = -3*a**2 - 365*a + 652. Let b(c) = -5*g(c) - 4*z(c). Factor b(f).
2*(f - 168)*(f - 2)
Let c(m) be the first derivative of 2*m**3/3 + 3*m**2/2 - 6*m + 9. Let h be c(2). Solve 3*a**2 - 3*a**2 - 3*a**2 - 2 + h + 3*a = 0.
-1, 2
Let l(r) = r**3 - 2*r**2 + 113*r. Let k be l(0). Factor k - 2/3*n**2 - 28/3*n.
-2*n*(n + 14)/3
Let l be 1/(0 - 15/(-9)). Let q be ((-8*10/300)/(20/(-6)))/((-2)/(-30)). Factor 3/5*y + 6/5*y**2 - q - l*y**3.
-3*(y - 2)*(y - 1)*(y + 1)/5
Factor 2/7*w**2 + 96/7 + 38/7*w.
2*(w + 3)*(w + 16)/7
Suppose 11*z = 10*z + 7. Suppose 13 = 2*i + z. Factor 20 + 164*x**3 - 69*x**i - 95*x**2 - 75*x**3 + 55*x.
5*(x - 4)*(x - 1)*(4*x + 1)
Suppose 1423/3*v + 316/3 + 796/3*v**3 + 5/6*v**4 + 1267/2*v**2 = 0. Calculate v.
-316, -1, -2/5
Let f = 7294 + -7289. Let g(q) be the third derivative of -5/6*q**4 + 2/3*q**3 - 5*q**2 + 1/6*q**6 + 0 - 1/15*q**f + 0*q. Find b such that g(b) = 0.
-1, 1/5, 1
Factor -124*r - 107*r - 78 - r**2 + 16*r**2 + 373*r - 123*r.
(r + 3)*(15*r - 26)
Let b(d) = -5*d**3 - 2*d**2 + d - 6. Let y(n) = -2*n - 42*n**3 - 1 + 6 + 3*n**2 + 6 + 51*n**3. Let m(c) = 7*b(c) + 4*y(c). Solve m(p) = 0.
-1, 1, 2
Factor -1752/5 + 351*s - 3/5*s**2.
-3*(s - 584)*(s - 1)/5
Let p(l) be the first derivative of -45/4*l**3 - 25/2*l**2 - 39 + 15*l + 25/16*l**4. Find w, given that p(w) = 0.
-1, 2/5, 6
Factor -71128*m - 115*m**3 + 70928*m + 0 + 5*m**4 + 0 + 310*m**2.
5*m*(m - 20)*(m - 2)*(m - 1)
Let x(n) be the second derivative of 2*n**7/21 - 2*n**6/5 - n**5/5 + n**4 - 691*n - 2. Solve x(j) = 0.
-1, 0, 1, 3
Let q(a) be the first derivative of a**5/25 + 227*a**4/10 + 361*a**3/3 + 1126*a**2/5 + 180*a + 4301. Factor q(c).
(c + 1)**2*(c + 2)*(c + 450)/5
Let s(r) be the first derivative of -2*r**6/21 - 8*r**5/35 + 24*r**4/7 + 64*r**3/3 + 352*r**2/7 + 384*r/7 - 445. Factor s(q).
-4*(q - 6)*(q + 2)**4/7
Let c(k) be the third derivative of k**6/40 + 3*k**5/20 - 2*k**4 - 24*k**3 - 10117*k**2. Factor c(p).
3*(p - 4)*(p + 3)*(p + 4)
Let a(y) = y**3 + 3*y**2 - 6*y + 6. Let f be (-8 - (-174)/24)*-4. Let b(d) = d**3 + 2*d**2 - 4*d + 4. Let s(g) = f*b(g) - 2*a(g). Factor s(w).
w**3
Let i be (-38)/(-4) - 3/6. Let h(y) = -y**3 + 9*y**2 + 2*y - 13. Let o be h(i). Factor -16*m**4 - 2 - 16*m**2 + 4*m**o + 2 + 0*m + 4*m + 24*m**3.
4*m*(m - 1)**4
Factor 3/7*j**2 - 519/7*j + 0.
3*j*(j - 173)/7
Let x(f) = 8*f**3 - 220*f**2 - 199*f + 450. Let p(w) = -185*w**3 + 5060*w**2 + 4565*w - 10350. Let z(y) = 3*p(y) + 70*x(y). Determine m, given that z(m) = 0.
-2, 1, 45
Determine b, given that -4/3*b - 2/15*b**4 - 8/5*b**2 - 2/5 - 4/5*b**3 = 0.
-3, -1
Let b(t) be the third derivative of -1/105*t**7 + 92*t**2 + 0*t**3 + 0*t - 1/15*t**5 + 0 + 0*t**4 + 7/120*t**6 - 1/336*t**8. Suppose b(j) = 0. Calculate j.
-4, 0, 1
Let -50/11*g**2 + 2/11*g**4 + 0 + 12/11*g**3 + 36/11*g = 