440))*-1*-3. Factor -32/3*c**3 + 0 - 12*c**s - 4/3*c.
-4*c*(c + 1)*(8*c + 1)/3
Suppose 58*z - 162 - 147 = -41*z - 4*z. Factor 1/9*p**4 - 16000/9 + 120*p**2 + 5600/9*p + 58/9*p**z.
(p - 2)*(p + 20)**3/9
Let j(o) be the first derivative of 2/125*o**5 - 153 - 7/25*o**4 + 0*o + 26/75*o**3 + 0*o**2. Suppose j(d) = 0. Calculate d.
0, 1, 13
Let n(t) be the second derivative of -2*t**6/15 + 171*t**5/5 - 169*t**4 + 1010*t**3/3 - 336*t**2 - 252*t. Suppose n(a) = 0. What is a?
1, 168
Let w(y) be the second derivative of -y**6/10 + 27*y**4/4 + 27*y**3 - 12*y - 30. Factor w(d).
-3*d*(d - 6)*(d + 3)**2
Let p(r) be the first derivative of -r**5/90 + 13*r**4/18 + 3*r**3 + 29*r**2 - 273. Let h(k) be the second derivative of p(k). Factor h(q).
-2*(q - 27)*(q + 1)/3
Let g(m) = -m**3 - 6*m**2 + 30*m - 2. Let r be g(-9). Let s = r - -31. Factor 5*h**2 + 5*h**2 - 56*h**3 - 3*h**4 - s*h**4 + 51*h**3.
-5*h**2*(h - 1)*(h + 2)
Let a(r) be the second derivative of r**4/12 + 13*r**3/6 - 330*r**2 + 75*r + 9. Let a(f) = 0. What is f?
-33, 20
Factor 4/7*z**2 - 1/7*z**4 + 8/7*z - 6/7*z**3 + 1/7*z**5 + 0.
z*(z - 2)**2*(z + 1)*(z + 2)/7
Let r(l) be the first derivative of 4*l**3/3 + 790*l**2 + 1576*l - 2970. Suppose r(z) = 0. Calculate z.
-394, -1
Let v(s) = -s**3 - s**2 + 11*s + 22. Let r be v(-2). Factor 68 + 16*h**4 + 100*h**2 - 37*h**3 - 92*h**3 + 216*h - r - 15*h**3.
4*(h - 8)*(h - 2)*(2*h + 1)**2
Let n(c) be the second derivative of c**7/1260 - c**6/120 + c**4/12 + 5*c**3/3 - 5*c. Let q(p) be the third derivative of n(p). Solve q(v) = 0 for v.
0, 3
Suppose -83*q - 135672 + 1307*q - 162991 + 81*q**2 - 83*q**2 + 111391 = 0. What is q?
306
Let a(x) be the second derivative of x**4/3 + 778*x**3/3 + 776*x**2 + 4*x + 194. Factor a(b).
4*(b + 1)*(b + 388)
Let z be (-2)/20 + 485/600. Let n = 191/168 - z. Factor n*b**4 + 0*b + 0 + 0*b**2 - 3/7*b**3.
3*b**3*(b - 1)/7
Suppose 13*n = 140*n. Let x(b) be the third derivative of n*b + b**3 - 8*b**2 + 1/210*b**7 + 0 + 7/24*b**4 - 1/40*b**6 - 1/20*b**5. Suppose x(c) = 0. What is c?
-1, 2, 3
Suppose 13*y - 102 = -76. Suppose -4 = -y*w, w = 5*k - 4 + 6. Factor 0 - 1/6*m**3 - 1/6*m**2 + k*m.
-m**2*(m + 1)/6
Suppose h = 3*k + 24, 12*k = 16*k + 8. Let p be 117/(-195)*(-20)/h. Suppose p*d**2 + 0*d - 2/3 = 0. What is d?
-1, 1
Suppose -3*a = 3*r - 2*r - 7, 4*a - 22 = 5*r. Suppose -9 = -a*z - 4*q, 5*q + 1 = z - 2. Factor 5*b**2 - 5*b**4 - 7*b**3 + 15*b**3 - 6*b**z + 3*b**3 - 5*b.
-5*b*(b - 1)**2*(b + 1)
Let c(u) = u**3 - 37*u**2 + 335*u + 87. Let f be c(17). Suppose 8/9 + 4/9*l - 4/9*l**f = 0. Calculate l.
-1, 2
Let i(b) be the third derivative of b**5/20 + 217*b**4/2 + 94178*b**3 + 1093*b**2. Factor i(z).
3*(z + 434)**2
Suppose 0 = -29*i + 16*i. Find k such that i - 28*k - 26 + 0*k**2 + 5*k**2 - 7*k**2 = 0.
-13, -1
Let q be 3/(-28)*(30 - 55556/102). Let -624/7*n + 288/7 - 52/7*n**3 + 2/7*n**4 + q*n**2 = 0. Calculate n.
1, 12
Solve 2/13*f**4 + 10/13 - 16/13*f**3 + 36/13*f**2 - 32/13*f = 0.
1, 5
Let g be ((-84)/63)/(16/(-60)). Factor -30*c**2 + 25*c**3 - 45*c + 371600*c**5 + 30*c**4 + 15*c**3 - 371595*c**g.
5*c*(c - 1)*(c + 1)*(c + 3)**2
Suppose 0 + 1/2*v**5 - 305*v**4 + 46512*v**3 + 305*v**2 - 93025/2*v = 0. What is v?
-1, 0, 1, 305
Let m(o) be the first derivative of 12*o - 21 - 5/2*o**4 + 8/3*o**3 + 31*o**2. Factor m(u).
-2*(u - 3)*(u + 2)*(5*u + 1)
Determine i, given that -6*i**2 + 883 - 15*i**2 - 383 + 575*i - 10*i**2 + i**2 = 0.
-5/6, 20
Let u = -75 + 73. Let d(k) = -k**2 - k + 1. Let r(p) = -9*p**2 + p - 1. Suppose -3*n - 5 = -2*a + 14, -3*a + 4*n = -30. Let t(y) = a*d(y) + u*r(y). Factor t(c).
4*(c - 2)**2
Let c(u) = -84*u - 586. Let b be c(-7). Let l(f) be the second derivative of -1/2*f**4 - b*f**2 + 0 + 3*f - 7/3*f**3. Factor l(x).
-2*(x + 2)*(3*x + 1)
Let c = -1036 + 3113/3. Let r be ((660/(-77))/15)/(2/(-14)). Factor -20/3*y**2 + 0 + 5/3*y**r - c*y**3 + 20/3*y.
5*y*(y - 2)*(y - 1)*(y + 2)/3
Let k(b) be the second derivative of -14/15*b**5 - 265/18*b**3 - 7*b**2 + 187*b + 0 - 143/12*b**4. Suppose k(q) = 0. What is q?
-7, -3/8, -2/7
Let k(q) = -11*q**2 + 9*q - 7. Let b(g) be the first derivative of -g**3/3 - g**2/2 + g + 52. Let m(o) = 18*b(o) - 2*k(o). Find j, given that m(j) = 0.
1, 8
Let z be (-3 + (-9)/(-6))/(3/(-16)). Let p(h) = 12 + z*h - 12*h**3 + 4 + 8*h**2 - 2. Let r(j) = j**3 - 1. Let o(d) = -2*p(d) - 28*r(d). Solve o(n) = 0 for n.
-2, 0
Let g(u) = -5*u**4 - 8*u**3 + 16*u**2 - 6. Let i = -449 - -450. Let l(q) = -q**4 - 1. Let f(p) = i*g(p) - 6*l(p). Find s such that f(s) = 0.
0, 4
Let s = -228 + 230. Find x such that -2*x**3 - 2*x**4 + 2*x + 29*x**s - 27*x**2 + 0*x**4 = 0.
-1, 0, 1
What is u in 33/4 + 15/4*u**2 - 1/2*u**3 + 37/2*u = 0?
-3, -1/2, 11
Let n be -29 - -7 - (-69)/(4140/1752). Factor -8/5*z - 11/5*z**4 + n*z**2 - 2/5*z**3 - 32/5 + 3/5*z**5.
(z - 2)**3*(z + 1)*(3*z + 4)/5
Solve 1/9*b**5 + 137/9*b**3 + 7/3*b**4 + 31*b**2 + 18*b + 0 = 0 for b.
-9, -2, -1, 0
Suppose 117 + 18 = 198*x - 261. Let o(z) be the first derivative of -3/5*z**5 - 33/2*z**x + 2 - 3/4*z**4 + 12*z + 9*z**3. Find y such that o(y) = 0.
-4, 1
Let w be (-3 - -7) + 15/(135/(-18)). Suppose -4*x - 12 = -4*m, -5*m = -w*m + x - 5. Suppose 10/7*r + 3/7 - 9/7*r**m - 4/7*r**3 = 0. Calculate r.
-3, -1/4, 1
Let j = -34 - -37. Suppose -j*s + 36 = s. Factor -3*d + 6*d - 3*d**3 + 0*d - s*d**2 + 9.
-3*(d - 1)*(d + 1)*(d + 3)
Let r = 3220340979555/7163 - 449579921. Let h = r + 6/551. Factor 6/13*c**2 + 2/13*c**3 + h - 18/13*c.
2*(c - 1)**2*(c + 5)/13
Determine p, given that -105/2*p + 603/4 + 3/4*p**2 = 0.
3, 67
Let h be (-2)/(-13) - 335/((-3932565)/1548). Suppose h*t**2 - 40/7*t + 0 + 2/7*t**3 = 0. What is t?
-5, 0, 4
Let a(y) be the second derivative of 5*y**4/24 + y**3/18 - 622*y. Factor a(d).
d*(15*d + 2)/6
Let s(j) = j + 16. Let t be s(-7). Let p be 30*1/4*30/t. Find v, given that 5*v**2 + 5 + p + 125*v - 90*v = 0.
-6, -1
Let a(q) = -16*q**3 - 6372*q**2 - 3383528*q - 598885164. Let m(y) = -35*y**3 - 12744*y**2 - 6767055*y - 1197770328. Let n(g) = -9*a(g) + 4*m(g). Factor n(k).
4*(k + 531)**3
Let s be 60/14 - 2/7. Suppose -11*y + 14 = -s*y. Suppose -6*u**5 - 3*u**4 - 11*u**3 + 17*u**3 - 3*u**y + 6*u**4 = 0. Calculate u.
-1, 0, 1/2, 1
Let u(k) = k**2 + k - 73. Let q be u(0). Let s = 76 + q. Let -l**3 - 4*l**2 + 2*l**5 + 4*l**4 - 3*l**s + 2*l**3 = 0. What is l?
-2, -1, 0, 1
Let h(p) be the first derivative of -3*p**5/25 + 159*p**4/5 - 11021*p**3/5 - 34347*p**2/5 - 5748. Factor h(w).
-3*w*(w - 107)**2*(w + 2)/5
Let s be 16 - (8 - (-572)/77). Find t, given that 20*t - s - 175*t**2 = 0.
2/35
Factor 3*v + 84 - 10*v**2 - 2*v + 10*v**4 - 10*v + v**5 + 8*v**3 - 84.
v*(v - 1)*(v + 1)**2*(v + 9)
Let y = 118876 - 118856. Factor 0*l + 0*l**2 + 0 + 24/5*l**3 - 36/5*l**5 + y*l**4.
-4*l**3*(l - 3)*(9*l + 2)/5
Let k(w) be the second derivative of 4*w**5/5 - 17*w**4/2 + 6*w**3 + 2877*w. Suppose k(o) = 0. What is o?
0, 3/8, 6
Let c be (((-135)/25)/9)/((-36)/120). Solve 0 + 2/3*w**3 + 0*w + w**c - 1/3*w**4 = 0 for w.
-1, 0, 3
Let n(x) be the second derivative of -x**7/105 - 19*x**6/75 + 21*x**5/25 - 5777*x. Factor n(q).
-2*q**3*(q - 2)*(q + 21)/5
Factor 2*t - 172942*t**2 + 172648*t**2 - 2*t**3 + 132 + 162.
-2*(t - 1)*(t + 1)*(t + 147)
Find y such that 4/5*y**3 + 1/5 + 2/5*y**2 - 3/5*y**4 - 4/5*y = 0.
-1, 1/3, 1
Let k(o) be the third derivative of o**5/20 - 7*o**4/2 - 29*o**3/2 + 4*o**2 + 39*o - 1. Factor k(z).
3*(z - 29)*(z + 1)
Suppose 393 = -10*a + 423. Factor 208*w**3 + 120 + 1339*w**2 - 909*w**2 + 10*w**4 - 28*w**a - 5*w**5 + 385*w.
-5*(w - 8)*(w + 1)**3*(w + 3)
Let t(b) be the second derivative of 17/2*b**3 - 16 - 37/5*b**6 - 7*b**4 - 15/14*b**7 + 9*b**2 - 147/10*b**5 + b. What is i in t(i) = 0?
-3, -1, -1/3, 2/5
What is z in -2883/2 - 868*z + 1/2*z**4 + 541*z**2 - 32*z**3 = 0?
-1, 3, 31
Let i = 947 - 438. Find q, given that 16 + 158*q - q**2 - i*q + 170*q + 166*q = 0.
-16, 1
Let r(y) be the second derivative of -1/3*y**3 - 11*y**2 + 11/6*y**4 - 7*y - 4 + 1/10*y**5. Factor r(h).
2*(h - 1)*(h + 1)*(h + 11)
Let t(x) = 550*x**2 + 231*x - 176. Let g(s) = -2748*s**2 - 1155*s + 918. Let q(b) = -4*g(b) - 21*t(b). What is c in q(c) = 0?
-1/2, 8/93
Let y(b) be the second derivative of -1/8*b**4 - 130*b - 5/4*b**3 + 0 + 27*b**2. Solve y(h) = 0.
-9, 4
Let x be (6/(-16))/(5*13/(-520)). 