225*j**2 - 900*j - 500. Let c(p) = 10*p**4 + 9*p**3 - 225*p**2 - 900*p - 500. Let y(i) = 8*c(i) - 7*s(i). Factor y(z).
(z - 10)*(z + 5)**2*(3*z + 2)
Let j(i) be the first derivative of -i**4/14 - 68*i**3/21 - 176*i**2/7 - 64*i - 3249. Suppose j(v) = 0. What is v?
-28, -4, -2
Factor -8/3*h**2 + 10/3*h + 0 - 2/3*h**3.
-2*h*(h - 1)*(h + 5)/3
Let l = 183/34 - 4193/918. Let v = 40/27 - l. Solve 8/3*t**2 - 2*t - v*t**3 + 0 = 0.
0, 1, 3
Let 89*m**2 + 23*m**3 + 1/4*m**4 + 0 + 88*m = 0. Calculate m.
-88, -2, 0
Let s be 3/((-14)/(22/(-4) - -3) - 5). Let b(u) be the first derivative of 11/16*u**4 + 3/20*u**s - 1/2*u**2 + 0*u + 4 + 2/3*u**3. Factor b(d).
d*(d + 2)**2*(3*d - 1)/4
Let h(l) be the second derivative of -l**6/6 + 49*l**5/4 - 980*l**4/3 + 3430*l**3 - 469*l + 2. Factor h(k).
-5*k*(k - 21)*(k - 14)**2
Factor 388/19*k - 2256/19 - 2/19*k**2.
-2*(k - 188)*(k - 6)/19
Suppose -11 = -4*t - 5*c + 14, -4*c = 3*t - 20. Find i such that -23*i**4 - 5*i**3 + 5*i**2 + t*i**3 + 11*i**4 + 15*i + i**2 - 7*i**3 - 3*i**5 + 6 = 0.
-2, -1, 1
Let m(g) be the third derivative of -4107*g**7/350 + 37*g**6/50 - g**5/75 + 127*g**2 + 4. Determine k so that m(k) = 0.
0, 2/111
Suppose -1378 = -622*d - 67*d. What is b in 0 + 1/5*b**3 - 1/5*b**d + 0*b = 0?
0, 1
Let k be 4 - ((-1 - -3) + -1). Suppose -k*f + 1626 + 729 = 0. Factor -f*o**2 + 6*o + 4 + 6*o - 12*o**3 + 781*o**2.
-4*(o - 1)*(o + 1)*(3*o + 1)
Let m = 0 + 3. Let b(p) = 1 - p**2 - p**4 + 2*p**2 + 0*p**m + p**3 - p + 2*p. Let d(n) = -3*n**4 - n**3 + 2*n + 2. Let z(v) = 4*b(v) - 2*d(v). Factor z(o).
2*o**2*(o + 1)*(o + 2)
Let m(n) = 2*n + 44. Let d be m(-14). Suppose -31 = -v - d. What is o in -v + 3*o**2 + 9*o + 0*o**2 + 3 = 0?
-4, 1
Factor 3/2*h**4 - 51/2*h**2 + 294 - 27/2*h**3 + 567/2*h.
3*(h - 7)**2*(h + 1)*(h + 4)/2
Let c be (9 - (-90)/(-9)) + 3. Let q be ((-2)/(-1))/2 - -75. Factor -34*d**c - 39*d**2 + q*d**2 + 6*d.
3*d*(d + 2)
Let p(a) be the second derivative of -a**7/483 - 11*a**6/345 - 19*a**5/230 - 3*a**4/46 - 64*a - 11. Let p(j) = 0. What is j?
-9, -1, 0
Let w(t) be the second derivative of -2*t**6/15 - 8*t**5 - 389*t**4/3 - 700*t**3/3 + 10693*t. Factor w(m).
-4*m*(m + 1)*(m + 14)*(m + 25)
Let h be ((-532)/114)/((-4)/(-2)) - (-3 + 0). Factor -h*a**2 + 7/3*a - 4/3 - 1/3*a**3.
-(a - 1)**2*(a + 4)/3
Suppose -16*h = -7*h - 3*h - 7*h. Let f(o) be the second derivative of h + 15/2*o**2 - 5/3*o**3 + 26*o - 5/12*o**4. Factor f(k).
-5*(k - 1)*(k + 3)
Suppose 0 = 18*d - 26 - 28. Suppose 4*o = n + d, 6 = 4*o + n - 7. Factor 0*h + 8/5*h**o + 0 - 4/5*h**3.
-4*h**2*(h - 2)/5
Suppose -2096*j - c - 10 = -2097*j, -2*j + c + 13 = 0. Factor 3*n**2 + 0 + 1/3*n**j + 14/3*n.
n*(n + 2)*(n + 7)/3
Let n(g) be the third derivative of -g**5/420 + 137*g**4/168 - 68*g**3/21 - 2344*g**2 + 2. Factor n(t).
-(t - 136)*(t - 1)/7
Let k(n) = 92*n**2 + 197*n + 125. Let r(i) = 31*i**2 + 66*i + 42. Let z(o) = o**2 - 3*o + 6. Let y be z(3). Let g(t) = y*k(t) - 17*r(t). Factor g(m).
(5*m + 6)**2
Let r(q) = -23*q**3 - 71*q**2 - 25*q + 43. Let c(k) = -81*k**3 - 249*k**2 - 87*k + 153. Let o(i) = -5*c(i) + 18*r(i). Suppose o(p) = 0. Calculate p.
-3, -1, 1/3
Let g(b) be the second derivative of -b**4 + 22*b**3/3 - 20*b**2 + 1210*b. Factor g(u).
-4*(u - 2)*(3*u - 5)
Let q(c) be the second derivative of c**6/900 + c**5/50 + 2*c**4/15 + c**3/6 + 25*c**2 - 6*c. Let g(b) be the second derivative of q(b). Factor g(i).
2*(i + 2)*(i + 4)/5
Let g(m) be the first derivative of m**4/12 + 7*m**3/9 - 28*m**2/3 + 16*m - 67. Factor g(u).
(u - 4)*(u - 1)*(u + 12)/3
Suppose -49*o = -78*o. Let h(q) be the second derivative of 1/5*q**4 + 13*q - 4/15*q**3 + o + 0*q**2 - 1/25*q**5. Factor h(c).
-4*c*(c - 2)*(c - 1)/5
Let v(w) be the first derivative of -5*w**4/8 + 6145*w**3/2 - 22656615*w**2/4 + 9281659945*w/2 - 3734. Factor v(z).
-5*(z - 1229)**3/2
Let 4428*d**2 + 5832 - 568*d**3 - 1/2*d**5 - 9720*d + 57/2*d**4 = 0. What is d?
1, 2, 18
Let d = -180 - -187. Factor 2 + 9 - 31*y - 67 + d*y + 2*y**2.
2*(y - 14)*(y + 2)
Let u(i) = -19*i - 74. Suppose 4*q = 3*n - 13, 4*n = -6*q + 5*q - 8. Let h be u(q). Factor -76/9*m**3 - 10/9*m**5 - 64/9*m**h - 44/9*m**4 - 4/9 - 26/9*m.
-2*(m + 1)**4*(5*m + 2)/9
Let z(j) be the second derivative of -32/9*j**4 + 41/9*j**3 + 1/63*j**7 + 55*j - 10/3*j**2 - 14/45*j**6 + 23/15*j**5 + 0. Suppose z(k) = 0. What is k?
1, 10
Let o(x) be the first derivative of -5*x**3/18 - 320*x**2/3 - 1006. Factor o(n).
-5*n*(n + 256)/6
Let q(n) = -n**3 + n**2 + n. Let x(c) = -9*c + 56. Let o be x(9). Let d(z) = 30*z**3 - 40*z**2 - 25*z. Let f(s) = o*q(s) - d(s). Factor f(p).
-5*p**2*(p - 3)
Let q(f) be the second derivative of 7*f**4/30 - 4*f**3/5 - 19*f**2/5 - 1434*f. Find z such that q(z) = 0.
-1, 19/7
Let y(t) = 30*t**2 + 2 - 3 - 28*t**2. Let l(h) = 10*h**2 + 18*h - 6. Let u(x) = -l(x) + 6*y(x). Let u(d) = 0. What is d?
0, 9
Let s(a) be the first derivative of -50 - 1/2*a**4 - 6/5*a**3 - 4/5*a - 7/5*a**2 - 2/25*a**5. Determine t so that s(t) = 0.
-2, -1
Let m = 2423206/9 - 269244. Factor 2/9*c**3 + m*c + 0 - 4/3*c**2.
2*c*(c - 5)*(c - 1)/9
Let q(x) = 3*x**2 - 341*x - 2532. Let w be q(-7). Factor 0*k**w + 3/2*k**3 + 0 + 5/2*k**4 + 0*k - k**5.
-k**3*(k - 3)*(2*k + 1)/2
Let a(s) be the third derivative of -s**5/80 + 1307*s**4/32 + 327*s**3/2 + 2684*s**2. Factor a(h).
-3*(h - 1308)*(h + 1)/4
Let g(f) be the first derivative of -4*f**3/3 + 1036*f**2 - 268324*f + 1512. Let g(m) = 0. Calculate m.
259
Suppose -37 = 31*r - 48*r - 3. Let t(p) be the first derivative of -3/7*p**r + 4/7*p + 18 + 2/21*p**3. What is w in t(w) = 0?
1, 2
Suppose 2*k = 5*h + 225, -2*k + 3*h - 63 = -286. Suppose 0 = 4*o + o - k. Find r such that o*r**3 - 15*r**3 - 12*r**3 = 0.
0
Let h be ((-176)/55)/((-60)/75). Let j(a) be the first derivative of 16 + 2/15*a**5 + 1/3*a**2 + 0*a - 2/9*a**3 - 1/6*a**h. Let j(g) = 0. Calculate g.
-1, 0, 1
Determine y, given that -923521/2*y + 887503681/6 - 1/6*y**3 + 961/2*y**2 = 0.
961
Let k(s) be the second derivative of 2*s**5/5 - 3*s**4/4 - 4*s**3/3 + 13*s**2/2 - 26*s + 2. Let f(j) = j**3 - j + 2. Let a(m) = -2*f(m) + k(m). Factor a(u).
3*(u - 1)*(u + 1)*(2*u - 3)
Let -108/5*j**2 + 7/5*j**4 - 1/5*j**5 + 0 + 18/5*j**3 - 216/5*j = 0. Calculate j.
-3, -2, 0, 6
Let p be (-15)/(-2) - (-1575)/(-350). Let s(m) be the third derivative of 37*m**2 + 0*m**p + 0*m - 1/40*m**6 + 0 + 0*m**4 + 1/20*m**5. Factor s(o).
-3*o**2*(o - 1)
Let n(i) = -5*i**3 + 29*i**2 + 855*i - 5091. Let c be n(6). Determine m, given that 0*m + 0 + 3/4*m**4 + 3*m**c - 3/4*m**5 - 3*m**2 = 0.
-2, 0, 1, 2
What is c in -16*c**2 - 121/4*c + 69/2 + 49/4*c**3 - 1/2*c**4 = 0?
-3/2, 1, 2, 23
Let g be (40/(-196))/(315/(-1323)). Determine x, given that g*x**2 + 94/7*x - 32/7 = 0.
-16, 1/3
Let f(t) be the second derivative of 91*t + 0*t**5 + 0 - 4/9*t**3 + 1/90*t**6 - 1/2*t**2 - 1/6*t**4. Factor f(m).
(m - 3)*(m + 1)**3/3
Suppose -2*l - 29*r = -27*r + 24, -76 = -3*l + 5*r. Factor 1/3*c**4 + 0 + 5/3*c**l + 4/3*c**3 + 2/3*c.
c*(c + 1)**2*(c + 2)/3
Factor -5/11*g**4 - 37/11*g**3 - 14/11*g**2 + 0 + 0*g.
-g**2*(g + 7)*(5*g + 2)/11
Let d be ((-4)/(-17))/((-2871)/(-106029) - 2/(-63)). Find c such that -3*c**d + 195/7*c**3 - 27/7*c**5 - 15/7*c**2 - 24*c + 36/7 = 0.
-3, -1, 2/9, 1, 2
Suppose -36192*g**2 - 989 - 615*g - 955 - 11529*g + 727*g - 5395*g + 676*g**3 = 0. Calculate g.
-3/13, 54
Let r(n) be the third derivative of n**7/840 - 11*n**6/240 + 2*n**5/5 + 3*n**4 - 3420*n**2. Factor r(p).
p*(p - 12)**2*(p + 2)/4
Let h(s) be the first derivative of s**6/18 - 386*s**5/15 + 36853*s**4/12 + 77992*s**3/9 - 132502*s**2/3 + 150544*s/3 - 73. What is t in h(t) = 0?
-4, 1, 194
Let y be 23/46*(20/2 + -2). Let k(u) be the second derivative of 0 - 3/20*u**5 + 0*u**3 + 1/2*u**y + 10*u + 0*u**2. Suppose k(l) = 0. What is l?
0, 2
Let h(q) be the third derivative of q**7/210 - 33*q**6/20 + 197*q**5/60 + 1099*q**2. Factor h(o).
o**2*(o - 197)*(o - 1)
Let d(k) be the first derivative of -3*k**4/20 + 2*k**3 - 33*k**2/10 - 42*k - 2038. Factor d(o).
-3*(o - 7)*(o - 5)*(o + 2)/5
Let g(a) be the third derivative of -a**8/70560 + a**7/588 + a**5/60 + 11*a**4/24 + 5*a**2 - a. Let k(c) be the third derivative of g(c). Factor k(u).
-2*u*(u - 30)/7
Let z(j) be the third derivative of -1/56*j**5 + 7*j**2 - 1/14*j**4 + 0 + 22/3*j**3 - j - 1/840*j*