. Factor 3 + u*i - 13*i - i**2 - 3*i**2.
-(i + 3)*(4*i - 1)
Suppose 99*w**3 + 80*w**2 - 77*w**4 - 95*w**2 - 3*w + 32*w**2 - 36*w**5 = 0. What is w?
-3, -1/4, 0, 1/9, 1
Let m be ((-139)/834)/((-3)/54). Factor 8/3*x**4 - 8*x**2 + 0 + 6*x - 4/3*x**m + 2/3*x**5.
2*x*(x - 1)**2*(x + 3)**2/3
Let w(x) be the third derivative of -x**7/2940 + x**6/120 + 5*x**4/24 + 7*x**3/3 - 2*x**2 + 64*x. Let h(r) be the second derivative of w(r). Factor h(i).
-6*i*(i - 7)/7
Factor 4*n**3 + 20*n**2 + 336*n + 23*n**2 + 49*n**2 - 293 - 139.
4*(n - 1)*(n + 6)*(n + 18)
Let a(u) be the third derivative of -3*u**7/14 + u**6/5 - 4*u**5/75 - u**2 - u + 32. Factor a(p).
-p**2*(15*p - 4)**2/5
Let l be 2/(5*120/825). Let l*u**2 - 35/4*u - 1/4*u**3 + 25/4 = 0. What is u?
1, 5
Let r be (5 + 16/((-2464)/825))*49/(-70). What is m in -1/4*m**2 + r*m**3 + 0 + 0*m + 1/4*m**4 - 1/4*m**5 = 0?
-1, 0, 1
Suppose 414/5*s - 83 + 1/5*s**2 = 0. Calculate s.
-415, 1
Let j(v) be the second derivative of -v**7/1120 + v**6/360 + v**5/96 - v**4/48 - 26*v**3/3 - 7*v. Let s(m) be the second derivative of j(m). Factor s(q).
-(q - 2)*(q + 1)*(3*q - 1)/4
Determine v so that 87 - 4*v**2 - 591 - 234*v + 0*v**2 + 54*v = 0.
-42, -3
Let i be (-4070)/156 - 53/(-318). Let c = 4409/143 + i. Suppose 0 + 8/11*r + 32/11*r**2 - c*r**4 - 30/11*r**3 = 0. Calculate r.
-1, -2/9, 0, 2/3
Let d(q) be the first derivative of 128*q - 1/5*q**5 - 8*q**3 + 5/2*q**4 - 16*q**2 - 96. Determine c, given that d(c) = 0.
-2, 4
Let h be (248/1 + -5)*1. Let w be (h/(-90))/(36/(-15)). What is f in -3/8*f**3 - w*f - 3/2*f**2 + 0 = 0?
-3, -1, 0
Suppose 318*a - 621*a + 1 - 1 = 0. Factor a*i + 0 + 2*i**3 + 0*i**2 - 2/9*i**4.
-2*i**3*(i - 9)/9
What is v in -539 - 63/2*v**3 + 1079/2*v**2 - 1/2*v**4 + 63/2*v = 0?
-77, -1, 1, 14
Let x = -69/323 + 9389/1615. Factor 2/5*d**3 + 0 + x*d**2 - 6*d.
2*d*(d - 1)*(d + 15)/5
Let -60 + 78*s**5 + 67*s**5 - 150*s**5 + 30*s**3 + 175*s - 160*s**2 + 20*s**4 = 0. Calculate s.
-3, 1, 4
Factor -1794*r + 264/5*r**2 - 2/5*r**3 + 3380.
-2*(r - 65)**2*(r - 2)/5
Let w(y) be the first derivative of -y**5/10 - 17*y**4/8 - 21*y**3/2 + 81*y**2/4 - 5301. Find p such that w(p) = 0.
-9, 0, 1
Let z = 285 - 276. Let -z*p**3 - 122*p**2 - p**3 + 5*p**3 + 0*p**3 + 3*p**3 = 0. What is p?
-61, 0
Let v = -982736 + 4913728/5. What is m in -v + 0*m**3 + 36/5*m**2 - 16/5*m - 4/5*m**4 = 0?
-3, -1, 2
Determine l, given that 284/7 - 148/7*l**2 - 422/7*l - 2/7*l**5 + 424/7*l**3 - 136/7*l**4 = 0.
-71, -1, 1, 2
Let a(r) = -5*r**4 - 11*r**3 + 77*r**2 + 55*r - 101. Let z(s) = -2*s**4 - 6*s**3 + 39*s**2 + 29*s - 51. Let l(o) = -3*a(o) + 5*z(o). Factor l(k).
(k - 1)*(k + 2)**2*(5*k - 12)
Let m be -2 - (-22)/10 - 288/(-60). Suppose -4 = -o - 4*r, m*r - 4 - 1 = -3*o. Find q such that -1/3*q**2 + 1/3*q + o = 0.
0, 1
Let u be (-1630)/(-60) + (-260)/156. Let -2*z**2 - 1/2*z**3 - 45 + u*z = 0. What is z?
-10, 3
Let s = -10442 + 10444. Let w(n) = -n**3 + 5*n**2 + 2. Let z be w(5). Determine t, given that 8*t**z - 3*t**2 - s*t**2 - 2*t**2 - 3 + 2*t = 0.
-3, 1
Solve -156*b**5 - 772*b**4 + 97917735 - 584*b**3 - 97917735 + 32*b**2 = 0.
-4, -1, 0, 2/39
Suppose 4*x - 610 = -6*x. Factor -34*r**2 + x*r**2 + 12 - 24*r**2 + 15*r.
3*(r + 1)*(r + 4)
Let 0 - 2046*r**3 - 46/5*r**5 - 1376/5*r**4 + 180*r**2 + 0*r = 0. What is r?
-15, 0, 2/23
Suppose 0 = -4*u - 0*u. Suppose 4*y - 13*y + 432 = u. Determine m so that 2*m**5 - 21*m**3 - 4*m**2 - 17*m**3 - 8*m**4 + y*m**3 = 0.
0, 1, 2
Let t(o) be the first derivative of 5*o**6/6 - 4*o**5 - 105*o**4/4 + 5346. Factor t(f).
5*f**3*(f - 7)*(f + 3)
Let h(a) = -a**2 - 277*a + 500. Let c(z) = -3*z**2 - 803*z + 1501. Let d(b) = 12*c(b) - 33*h(b). Factor d(s).
-3*(s - 3)*(s + 168)
Let h(l) = l**2 + l - 6. Let z(x) = -3*x**3 - 33*x**2 + 15*x + 30. Let o(d) = 20*h(d) + 4*z(d). Factor o(j).
-4*j*(j + 10)*(3*j - 2)
Let m(o) = o + 1. Let h(i) = 2*i**2 - 358*i + 15507. Let v(z) = -z**2 + 179*z - 7751. Let r(x) = -2*h(x) - 5*v(x). Let q(g) = -6*m(g) - 2*r(g). Factor q(k).
-2*(k - 88)**2
Let a = 36739 + -36713. Let g(d) be the second derivative of 0*d**3 - a*d - 2/15*d**6 + 0 + 4/3*d**4 + 0*d**2 + 0*d**5. What is l in g(l) = 0?
-2, 0, 2
Let t be (-84)/105*5/(-2). Let s be (-1*t - 8)*(-70)/175. Determine q, given that 9/4*q**s - 27/8*q - 21/4*q**3 + 3/4 - 3/8*q**5 + 6*q**2 = 0.
1, 2
Solve 0 - 25/2*u + 25/2*u**4 - 25/2*u**2 + 21/2*u**3 + 2*u**5 = 0 for u.
-5, -5/4, -1, 0, 1
Suppose -3*i = -29 + 2. Suppose -4*d**4 - 20*d**3 - 16 - d**5 + 16*d - 4*d**2 + i*d**2 + 15*d**2 + 5*d**5 = 0. Calculate d.
-2, -1, 1, 2
Suppose -43*d + 42 = -29*d. Factor -8*r - 173*r**2 + 4*r**4 - 3*r + 7*r + 10*r**d + 175*r**2.
2*r*(r + 1)*(r + 2)*(2*r - 1)
Let g(k) = -4*k - 6. Let z be g(-3). Suppose 4*f + 11 = -3*n, n + z*f = f - 22. Factor 6 - 32*c + 23*c**5 + 12*c**n + 42*c**2 + 7*c**5 - 9*c**5 - c - 48*c**4.
3*(c - 1)**3*(c + 1)*(7*c - 2)
Let z(h) be the first derivative of -2*h**6/39 - 22*h**5/65 + 15*h**4/26 + 82*h**3/39 - 73*h**2/13 + 60*h/13 + 2474. Let z(r) = 0. What is r?
-6, -5/2, 1
Let t(p) be the second derivative of 2/3*p**6 - 3/70*p**5 - 1 + 0*p**2 + 3*p - 10/21*p**4 + 4/21*p**3 + 1/3*p**7. What is n in t(n) = 0?
-1, 0, 2/7
Let k(y) be the third derivative of -y**5/100 - y**4/8 + 1078*y**3/5 + 4365*y**2. Factor k(z).
-3*(z - 44)*(z + 49)/5
Let g(q) be the first derivative of -q**5/30 - 11*q**4/24 + 3*q**3/2 + 81*q**2/4 - 99*q - 295. Find k such that g(k) = 0.
-11, -6, 3
Let f be (-4)/4 - ((-4)/8)/((-7)/(-56)). Let h(z) be the second derivative of 0 - 1/28*z**5 - 3/7*z**2 + 11/42*z**f + 10*z + 1/7*z**4. Factor h(g).
-(g - 3)*(g + 1)*(5*g - 2)/7
Let g(b) = 54*b + 49. Let h be g(21). Suppose 0 = -5*n - w + 1028 + h, -2*n + 898 = -3*w. Factor 2 + 445*f - n*f + f**2 - 2*f**2 - 3.
-(f - 1)**2
Find y, given that -4/3*y**3 - 699*y**2 - 68644/3 - 91700*y = 0.
-262, -1/4
Let v(w) be the second derivative of -w**6/30 - 3*w**5/4 + w**4/12 + 5*w**3/2 - 33*w + 22. Factor v(f).
-f*(f - 1)*(f + 1)*(f + 15)
Suppose -5 - 8 = -2*h + 9. Let p(g) be the first derivative of 3/7*g - 3/14*g**4 - 2/7*g**3 + 1/14*g**6 + 3/35*g**5 - h + 3/14*g**2. Factor p(f).
3*(f - 1)**2*(f + 1)**3/7
Let r = 66 - 50. Factor d**2 + 116 - r - 45*d - 48 - 8.
(d - 44)*(d - 1)
Let -3*i + 3/4*i**3 + 1/4*i**4 - 1/2*i**2 - 2 = 0. Calculate i.
-2, -1, 2
Let l(k) be the first derivative of -k**6/15 + 22*k**5/25 - 11*k**4/5 - 8*k**3 + 72*k**2/5 + 2639. Determine s so that l(s) = 0.
-2, 0, 1, 6
Let m be (300/(-1125))/(3/(-45)). Let y(s) be the third derivative of -1/35*s**6 + 4/105*s**5 + 1/84*s**m + 5*s**2 + 0 - 1/21*s**3 + 0*s. Factor y(q).
-2*(2*q - 1)**2*(3*q + 1)/7
Let y = 18 - 13. Suppose -2*h = -y*f + 16, 0*h + 4*h - 4 = f. Factor 4*i - i**h + 3 - 9*i + 2*i**2 + 9*i.
(i + 1)*(i + 3)
Let v(n) = -58*n**3 + 117*n**2 + 33*n - 68. Let s be v(2). What is b in -3/2 + 19/6*b - 11/6*b**s + 1/6*b**3 = 0?
1, 9
Let x = -4/5893 + 6013/176790. Let n(i) be the first derivative of -24 + 1/6*i**4 + 5/18*i**3 + x*i**5 + 1/6*i**2 + 0*i. Factor n(w).
w*(w + 1)**2*(w + 2)/6
Determine m, given that -13334*m**3 + 13346*m**3 - 74*m**2 + 81 - 402*m + 383*m**2 = 0.
-27, 1/4, 1
Suppose -4*x - 16 = 0, 0 = 4*m - 3*x + 5 - 81. Suppose 13*o**5 + 6*o**4 - 19*o**4 + m*o**2 - 3*o**4 - 17*o**5 + 4*o**3 = 0. What is o?
-4, -1, 0, 1
Let n(u) = -13*u**3 - 241*u**2 - 125*u + 21. Let d be n(-18). Factor 48*p + 100/3*p**d + 80*p**2 + 0.
4*p*(5*p + 6)**2/3
Let t(d) = 11*d**5 - 76*d**4 + 89*d**3 - 44*d**2 + 2. Let u(a) = -9*a**5 + 79*a**4 - 86*a**3 + 46*a**2 - 3. Let k(b) = 3*t(b) + 2*u(b). Factor k(s).
5*s**2*(s - 1)**2*(3*s - 8)
Let k(y) = -y**3 - 2*y**2 - 1. Let j(m) = -530*m**3 - 17720*m**2 - 142400*m - 2535. Let i(o) = -j(o) - 25*k(o). Factor i(h).
5*(h + 16)**2*(111*h + 2)
Let a(u) be the first derivative of u**4/10 - 1144*u**3/15 - 1147*u**2/5 - 1148*u/5 + 1606. What is y in a(y) = 0?
-1, 574
Let t(o) be the second derivative of 20*o - 1/2*o**4 + 0*o**3 + 0*o**2 - 1/20*o**5 - 2. Determine a so that t(a) = 0.
-6, 0
Let l(j) be the third derivative of j**8/504 - 11*j**7/315 - 53*j**6/180 + 43*j**5/10 + 60*j**4 + 300*j**3 - j**2 + 705. Suppose l(w) = 0. What is w?
-3, 10
Let z(y) be the third derivative of -y**8/756 + 1324*y**7/945 - 109561*y**6/270 - 373*y**2. Factor z(j).
-4*j**3*(j - 331)**2/9
Let g be 63*7/4410*((-30)/(-4))/3. L