3*a + 4*a - 2. Let o(i) be the first derivative of i**3/3 + i**2/2 + 3*i + 930. Let w(t) = 3*h(t) - o(t). Factor w(n).
-n*(n - 2)
Let l(r) be the third derivative of -r**7/630 - 11*r**6/60 + 3*r**5/4 - 17*r**4/18 + 32*r**2 + 6*r - 4. Determine y so that l(y) = 0.
-68, 0, 1
Solve 438020 + 4064864 + 9332*m - 844*m + 4*m**2 = 0.
-1061
Suppose 0 = 3*y - 3*q + 21, 3*y + 3*q + 6 = q. Let r(t) = -t**3 + 3*t**2 + 6*t - 1. Let p(v) = -1. Let i(m) = y*r(m) - 28*p(m). What is b in i(b) = 0?
-2, 1, 4
Find t, given that 0 + 16016/3*t**2 - 206/3*t**3 + 2/9*t**4 - 47432/9*t = 0.
0, 1, 154
Let j(b) be the first derivative of b**3 - 12246*b**2 + 49988172*b - 116. Factor j(q).
3*(q - 4082)**2
Let x(d) = -d**2 + 16*d - 53. Let j = -111 + 122. Let l be x(j). Factor 25/2 + 15*a + 5/2*a**l.
5*(a + 1)*(a + 5)/2
Let r(u) be the third derivative of u**6/1020 - 197*u**5/255 - 686*u**2 + 5*u. Suppose r(w) = 0. Calculate w.
0, 394
Let o(z) = -10*z - 38. Let j be o(-4). Factor 12*u**2 - 17*u**2 + 12*u + j*u**2.
-3*u*(u - 4)
Let b(a) be the second derivative of -a**4/12 + 53*a**3/6 + 84*a**2 + 1203*a. Factor b(d).
-(d - 56)*(d + 3)
Let z(s) be the third derivative of s**6/300 + 18*s**5/25 + 419*s**4/60 + 104*s**3/5 + 3*s**2 + 297*s + 2. Determine i, given that z(i) = 0.
-104, -3, -1
Let f be -27 + (-5080)/(-188) - 1530/(-3196). Factor -33/2*c**2 + 0 - f*c**3 - 16*c.
-c*(c + 1)*(c + 32)/2
Let u(o) be the first derivative of 2*o**3/45 - 654*o**2/5 + 641574*o/5 - 6157. Factor u(w).
2*(w - 981)**2/15
Let o(k) = -22*k**3 + 52*k**2 - 70*k + 16. Let z(b) = -17*b**2 + 28*b - 50*b - 8 + 7*b**3 + 45*b + 3. Let l(s) = -5*o(s) - 16*z(s). What is d in l(d) = 0?
0, 3
Determine k so that -183*k**3 + 37*k**4 - 32400 - 236*k + 2844*k**2 - 392*k - 8*k**4 - 26*k**4 + 88*k = 0.
-3, 4, 30
Let 26*w**3 + 63*w**3 - 274*w**3 - 306*w**2 - 28*w + 46*w**2 - 32*w - 35*w**4 = 0. What is w?
-3, -2, -2/7, 0
Let n(h) be the first derivative of -h**3/18 - h**2 - 9*h/2 + 10224. Factor n(m).
-(m + 3)*(m + 9)/6
Suppose -3*y**2 - 146*y + 927156 + 13*y - 437*y - 929388 = 0. Calculate y.
-186, -4
Let h(p) be the first derivative of -3/10*p**5 - 9/8*p**4 + 0*p**2 + 51 - p**3 + 0*p. Factor h(b).
-3*b**2*(b + 1)*(b + 2)/2
Suppose 4*d + 4*v - 24 = 0, 2*v = -3*v + 20. Let y be ((-6)/(-4))/((-10)/(10/(-3))). Solve -y*t + 1/2*t**3 + t**d - 1 = 0.
-2, -1, 1
Let i = 2/19 + -1747/16055. Let s = 4053/845 - i. Factor -4/5*l**2 + 4*l - s.
-4*(l - 3)*(l - 2)/5
Factor 62*i**3 + 55*i**4 - 15*i**4 - i**2 + 12*i**2 + i**2 + 16*i**4.
2*i**2*(4*i + 1)*(7*i + 6)
Let m(o) be the second derivative of 7/40*o**5 + 3/4*o**4 + 2*o**2 + 1/60*o**6 + 0 + 52*o + 5/3*o**3. Determine f, given that m(f) = 0.
-2, -1
Suppose -79 = -263*o + 261*o + 5*k, 2*o = 3*k + 49. Suppose 23/4*l + 1/2 + 31/4*l**o + 5/2*l**3 = 0. What is l?
-2, -1, -1/10
Let r(g) be the second derivative of 2 + 1/18*g**4 - 19/3*g**2 + 2*g**3 - 49*g. Factor r(t).
2*(t - 1)*(t + 19)/3
Let y(j) = 4*j**2 + 118*j - 1682. Let b(w) = -3*w**2 - w. Let m(v) = 23*v - 117. Let g be m(5). Let p(r) = g*y(r) - 4*b(r). What is a in p(a) = 0?
29
Let x be 55 + -46 + -1*7. Determine q so that -737*q**x - q**3 + 735*q**2 + 3*q**3 = 0.
0, 1
Let a = 3264867/5 - 652968. Determine m so that a*m + 1/5*m**5 - 54/5*m**2 + 162/5 + 4/5*m**4 - 12/5*m**3 = 0.
-3, 2, 3
Let u(c) be the first derivative of -279 + 34/3*c**3 + 5*c + 11/8*c**4 + 67/4*c**2. Solve u(h) = 0.
-5, -1, -2/11
Let c be ((-123)/(-7) - (150 - 132))/((-2)/14). Determine x, given that -5/3 + 1/3*x**4 - 14/3*x - 2/3*x**c - 4*x**2 = 0.
-1, 5
Suppose 0 = -4*f + 2*h - 1006, -2*h = -f + 5*f + 1018. Let s = -1011/4 - f. Find l, given that 0 - 1/8*l**3 + 3/8*l**2 - s*l = 0.
0, 1, 2
Let s(w) be the third derivative of -1/1575*w**7 + 1/450*w**5 + 0 + 82*w**2 + 0*w + 1/900*w**6 - 1/180*w**4 + 0*w**3. What is l in s(l) = 0?
-1, 0, 1
Let m(n) = -25*n**3 - 5*n**2 - 15*n + 5. Let r(w) = 24*w - 3 - 8*w - 11*w - w**2 + 2*w**3 + 4 - 3*w. Let t(x) = -m(x) - 10*r(x). Factor t(y).
5*(y - 1)*(y + 1)*(y + 3)
Let -9*m**5 - 74*m + 0*m**2 - 14*m**4 + 14*m**2 + 90*m**3 - 4*m**5 + 11*m**5 - 14*m = 0. Calculate m.
-11, -1, 0, 1, 4
Let m be (16/(-5) - -3)/(168/(-3360)). Let t(d) be the first derivative of 1/4*d**2 + 1/3*d**3 - 3 - 1/8*d**m - d. Factor t(l).
-(l - 2)*(l - 1)*(l + 1)/2
Factor -69/7*d + 3/7*d**3 - 60/7*d**2 + 18.
3*(d - 21)*(d - 1)*(d + 2)/7
Let s(v) be the first derivative of -15*v + 0*v**2 - 2/27*v**3 + 12 + 7/90*v**5 - 5/54*v**4. Let x(k) be the first derivative of s(k). Factor x(z).
2*z*(z - 1)*(7*z + 2)/9
Suppose -4333*k = -4431*k. Factor k + 2/5*h**2 - 2*h.
2*h*(h - 5)/5
Let u(s) be the second derivative of s**4/42 - 12*s**3/7 + 320*s**2/7 + 8080*s. Factor u(h).
2*(h - 20)*(h - 16)/7
Let q(w) = 9*w**2 + 11*w + 2. Let v(m) = -11*m**2 - 13*m. Let c(u) = 6*q(u) + 5*v(u). Find k such that c(k) = 0.
-3, 4
Factor -1/6*o**3 - 7701/2*o - 101/2*o**2 - 22801/6.
-(o + 1)*(o + 151)**2/6
Let q(o) = -o**2 - 8*o - 13. Let x be q(-4). Factor 10*r - 3*r**2 - 3*r**2 - 12*r**2 + 5*r**3 + x*r**2.
5*r*(r - 2)*(r - 1)
Find p such that 8 - 919*p + 239*p + 10165*p**2 + 4285*p**2 = 0.
2/85
Let j(u) = u**3 + 7*u**2 - 8*u + 12. Suppose 3*c = 5*c + 16. Let y be j(c). Factor -7*f**3 + 598*f**4 - 3 - y*f - 6*f**2 + 19*f**3 - 589*f**4.
3*(f - 1)*(f + 1)**2*(3*f + 1)
Let t be 4/3606*(-22)/44. Let w = 3004/1803 - t. Find h, given that -w*h**2 - 22/3 + 19*h = 0.
2/5, 11
Let s = 186 + -606. Let g = s - -420. Find h, given that 0*h + 6/7*h**2 + 3/7*h**3 + g = 0.
-2, 0
Let t(g) be the third derivative of 2/5*g**5 - 20/3*g**3 + 47*g**2 + 1/2*g**4 + 1/30*g**6 + 0 + 0*g. Factor t(r).
4*(r - 1)*(r + 2)*(r + 5)
Let d(c) = c**3 - c. Let f(o) = 4*o**4 + 28*o**3 - 8*o**2 - 60*o + 36. Let v(z) = 12*d(z) - f(z). Factor v(u).
-4*(u - 1)**2*(u + 3)**2
Let f(a) be the third derivative of -8*a**7/21 + a**6/3 + 37*a**5/4 - 255*a**4/8 + 45*a**3 - 3819*a**2. Let f(d) = 0. What is d?
-3, 3/4, 2
Let f(t) = 73*t + 503. Let o be f(-7). Let l(x) = -x**2 - 5*x + 24. Let v be l(o). Find u, given that 0*u + 2/7*u**5 + 2/7*u**2 + v + 6/7*u**3 + 6/7*u**4 = 0.
-1, 0
Let x(y) = 5*y + 45. Let h be x(-8). Solve -5*a**2 - 10*a + 421*a**5 - 2 + 7*a**4 - 841*a**h + 3*a + 422*a**5 + 5*a**3 = 0.
-2, -1, -1/2, 1
Let n(u) be the second derivative of -u**5/30 + 2*u**4/3 - 7*u**3/3 + 10*u**2/3 + 1373*u. Factor n(h).
-2*(h - 10)*(h - 1)**2/3
Suppose -2*s - 311 + 347 = 0. Let j(r) = 21*r**2 + 81*r - 378. Let q(x) = -6*x**2 - 23*x + 108. Let k(a) = s*q(a) + 5*j(a). Factor k(y).
-3*(y - 3)*(y + 6)
Let k = -161521/87 - -53850/29. Let 0 + 0*i + 4/3*i**2 + 8/3*i**3 + 5/3*i**4 + k*i**5 = 0. What is i?
-2, -1, 0
Let p be (-17040)/(-630) - 26 - ((-2)/(-11) + (-1763)/(-3311)). Suppose -24 - 34/3*a + p*a**2 = 0. What is a?
-2, 36
Let f(w) be the first derivative of 56 - 4/5*w + 4/15*w**3 - 1/30*w**4 + 1/15*w**2. Factor f(r).
-2*(r - 6)*(r - 1)*(r + 1)/15
Factor -2/9*g**5 + 14/9*g**2 - 4/9*g + 0 - 2*g**3 + 10/9*g**4.
-2*g*(g - 2)*(g - 1)**3/9
Let s(o) = -9*o**2 - 8*o - 14. Suppose 3*p + 84 = -9*p. Let r(q) = 5*q**2 + 4*q + 8. Let z(a) = p*r(a) - 4*s(a). Factor z(m).
m*(m + 4)
Let w(b) be the second derivative of b**4/14 + 536*b**3/3 + 2500*b**2/7 - 1608*b. Suppose w(a) = 0. Calculate a.
-1250, -2/3
Let -522*w**2 + 429/7*w + 1452/7 + 2400/7*w**3 - 384/7*w**4 = 0. Calculate w.
-1/2, 11/8, 4
Let w(k) be the third derivative of k**7/3780 - k**6/810 - 8*k**3 - 32*k**2 - 2. Let c(g) be the first derivative of w(g). What is p in c(p) = 0?
0, 2
Let s be (-7616)/(-3264) + (-5)/3. Factor -4/3 + s*h**2 + 2/3*h.
2*(h - 1)*(h + 2)/3
Let s(b) = 9*b - 192. Let h be s(22). Let z(r) be the first derivative of 1/3*r**3 + 0*r - h - r**5 + 0*r**2 - 1/4*r**4 - 1/2*r**6. Let z(p) = 0. What is p?
-1, 0, 1/3
Let l(x) be the second derivative of -47*x**4/3 - 34*x**3 - 8*x**2 + 2*x - 757. Factor l(z).
-4*(z + 1)*(47*z + 4)
Factor 1161 - 147 - 1052*b + 551 + 1179 + 2*b**2 - 648.
2*(b - 524)*(b - 2)
Suppose 3/7*a**2 + 1296/7 + 186/7*a = 0. What is a?
-54, -8
Let t(q) be the third derivative of q**7/1575 + 2*q**6/225 + 2*q**5/45 + 4*q**4/45 - 8695*q**2. Solve t(l) = 0 for l.
-4, -2, 0
Let n(o) be the third derivative of -o**5/240 - 12*o**4 - 13824*o**3 + 2*o**2 + 332*o - 1. Factor n(i).
-(i + 576)**2/4
Suppose 328*r + 5*r**3 + 721*r + 152*r + 72*r + 170*r**2 + 1