 be j(-9). Let k(w) be the first derivative of 9 + i*w - 3/4*w**4 + 3/2*w**2 - w**3. Factor k(a).
-3*(a - 1)*(a + 1)**2
Let w(r) be the first derivative of 64/9*r - 100 + 4/27*r**3 - 34/9*r**2. Suppose w(v) = 0. What is v?
1, 16
Let o(v) be the second derivative of v**4/66 - 2*v**3/33 + v - 1273. Factor o(r).
2*r*(r - 2)/11
Find t such that 349*t - 204*t**2 - 2*t**3 + 5*t**3 + 1586*t - 300*t**2 + 33*t = 0.
0, 4, 164
Solve 150 + 2/9*u**2 + 104/9*u = 0.
-27, -25
Let z(p) be the third derivative of p**7/1260 + 43*p**6/60 - 259*p**5/60 + 389*p**4/36 - 173*p**3/12 + p**2 - 23*p. Factor z(n).
(n - 1)**3*(n + 519)/6
Let d(i) = 2*i**2 + 4*i - 6. Let o = 3 - -1. Let s(u) = -u**2 + 1. Let y be (-58)/261*(-18)/4. Let v(t) = o*s(t) + y*d(t). Factor v(a).
-2*(a - 1)**2
Let i(q) be the third derivative of q**6/600 - 53*q**5/100 - 27*q**4/20 + 32*q**3/3 - 8648*q**2. Suppose i(g) = 0. What is g?
-2, 1, 160
Let o(f) be the third derivative of 18481401*f**7/70 + 18489999*f**6/20 + 18515797*f**5/20 + 4301*f**4/2 + 2*f**3 + 2*f**2 - 13*f. Factor o(t).
3*(t + 1)**2*(4299*t + 2)**2
Let q(n) be the second derivative of -n**4/108 - 4*n**3/9 - 6*n**2 - 75*n - 3. Find x, given that q(x) = 0.
-18, -6
Suppose -124 + 268 = 17*h - 94. Let i(u) be the second derivative of -h*u + 1/48*u**3 - 1/80*u**5 + 0*u**2 + 0 + 0*u**4 + 1/336*u**7 + 0*u**6. Factor i(o).
o*(o - 1)**2*(o + 1)**2/8
Let w(x) be the second derivative of -x**4/66 - 4376*x**3/33 - 4787344*x**2/11 + 5234*x. Solve w(p) = 0 for p.
-2188
Factor 2/3*t - 2/3*t**3 + 8/3*t**2 - 8/3.
-2*(t - 4)*(t - 1)*(t + 1)/3
Suppose -15*b = -11*b - 3*u - 1270, 2*b - 638 = 3*u. Let d = b + -314. Factor 0 + 12/5*o**4 + 16/5*o**d + 0*o - 24/5*o**3 - 2/5*o**5.
-2*o**2*(o - 2)**3/5
Let u(a) be the second derivative of -1849*a**4/20 + 258*a**3/5 - 54*a**2/5 + 76*a + 2. Let u(b) = 0. Calculate b.
6/43
Suppose -451*a + 454*a - 1608 = 0. Let s = a + -534. Factor 8/3*w + 0 - 16/3*w**s - 10/3*w**3.
-2*w*(w + 2)*(5*w - 2)/3
Suppose z + 3*c = -7 - 4, 2*c = 5*z + 4. Let h(a) = -14*a**3 - 23*a**2 - a + 28. Let l(o) = 6*o**3 + 12*o**2 - 14. Let p(v) = z*h(v) - 5*l(v). Factor p(d).
-2*(d - 1)*(d + 1)*(d + 7)
Let a be 53/156 - (-6)/78. Let o(z) be the second derivative of -5*z + 5/8*z**5 - 25/12*z**3 + 5/2*z**2 + 0 - a*z**4. Factor o(r).
5*(r - 1)*(r + 1)*(5*r - 2)/2
Let w = -205268 - -205276. What is g in 44/3*g - 8 - w*g**2 + 4/3*g**3 = 0?
1, 2, 3
Let w(v) be the first derivative of -v**6 - 74*v**5/5 - 295*v**4/6 - 50*v**3 + 4*v**2/3 + 24*v - 1526. What is y in w(y) = 0?
-9, -2, -1, -2/3, 1/3
Suppose h + 21 = 7*h + h. Factor 16*a + 1/4*a**5 - 7/2*a**4 + 0 + 28*a**2 + 33/4*a**h.
a*(a - 8)**2*(a + 1)**2/4
Let r = 868 + -864. Let k + 24 + r*k - 4*k - 14*k**2 + 9*k + 15*k**2 = 0. Calculate k.
-6, -4
Let s(n) = -2*n**3 + 203*n**2 - 84*n - 1717. Let g be s(101). Determine t, given that g*t + 9/4*t**2 + 1/4*t**3 + 0 = 0.
-9, 0
Let o(n) be the third derivative of n**6/30 + 5*n**5/2 + 1539*n**4/32 + 2527*n**3/6 + 10*n**2 + 2*n + 75. Factor o(f).
(f + 28)*(4*f + 19)**2/4
Suppose -2*d - 3*d = 2*d. Let n = 4 + d. What is o in -21*o**4 - 26*o**n + 51*o**4 - 4*o**5 - 4*o**2 + 0*o**2 + 4*o**3 = 0?
-1, 0, 1
Let q be (-2)/(14/(-97)) + (-74)/(-518). Let m be (119/102)/(q/8). Suppose -2/3*u**5 + 4/3*u**2 - 4/3*u**4 + 0*u**3 + m*u + 0 = 0. What is u?
-1, 0, 1
Suppose -16 = 2*v - n - 3*n, -3*v + 2*n = 12. Let f(t) = -t**3 - t**2 - t - 2. Let r be f(v). Factor -r - 3*s**3 - 45*s + 0*s**3 - 23 - 21*s**2.
-3*(s + 1)*(s + 3)**2
Let a be (-45)/(-6) - (3/(-16))/((-420)/10080). Solve 1/2 + 3*s**4 - 7/2*s**2 - 1/2*s + 1/2*s**a = 0.
-1, -1/2, 1/3, 1
Let i(o) be the third derivative of -o**5/240 - 3*o**4/16 + 26*o**3/3 - 1157*o**2. Solve i(c) = 0 for c.
-26, 8
Factor 9*b**2 + 2239*b + 2864 - 708*b - 13*b**2 + 2169*b - 840*b.
-4*(b - 716)*(b + 1)
Let x(m) be the first derivative of m**5/5 - 79*m**4/16 + 112*m**3/3 - 531*m**2/8 - 81*m/2 + 1878. Factor x(k).
(k - 9)**2*(k - 2)*(4*k + 1)/4
Let m(s) be the second derivative of -s**5/100 - s**4/12 + 3*s**3/10 + 9*s**2/2 - 75*s. Find q such that m(q) = 0.
-5, -3, 3
Let k(s) be the second derivative of 3*s**2 + 1 + 15*s + 43/10*s**3 - 9/20*s**4. Solve k(r) = 0.
-2/9, 5
Let v(w) be the first derivative of w**4/18 + 4*w**3/27 - 31*w**2/9 + 56*w/9 - 11261. Find c, given that v(c) = 0.
-7, 1, 4
Let r(g) = 7*g**3 - 146*g**2 + 139*g + 290. Let a(f) = 29*f**3 - 582*f**2 + 558*f + 1160. Let l(v) = 2*a(v) - 9*r(v). Solve l(b) = 0.
-1, 2, 29
Let k = 787 + -784. Let q be k - 7 - (-448)/98. Factor -q*p**2 - 4/7*p**3 - 2/7 + 6/7*p**4 + 6/7*p - 2/7*p**5.
-2*(p - 1)**4*(p + 1)/7
Let m(h) be the second derivative of h**7/21 - 21*h**5/10 + 10*h**4/3 - 302*h. Let m(o) = 0. Calculate o.
-5, 0, 1, 4
Let b(c) be the second derivative of 0 + 88*c - 20*c**3 - 3/2*c**2 + 41/4*c**4. Factor b(d).
3*(d - 1)*(41*d + 1)
Let k(c) be the first derivative of -26 - 2/9*c**3 - 16/3*c**2 - 10*c. Suppose k(f) = 0. Calculate f.
-15, -1
Let f(c) be the second derivative of -c**4/27 + 22*c**3/27 + 52*c**2/9 - 3455*c. What is w in f(w) = 0?
-2, 13
Factor -39/8*k**2 + 3/4*k + 33/8*k**3 + 0.
3*k*(k - 1)*(11*k - 2)/8
Let n = -28837/4 + 7210. Factor -15/2*c + 0 + n*c**2.
3*c*(c - 10)/4
Let o(k) = -8*k**2 + 73*k - 248. Let d(n) = -n**2 + n - 1. Suppose 1 = v + 2. Suppose 78 = 23*a + 9. Let t(r) = a*d(r) + v*o(r). Find x, given that t(x) = 0.
7
Let w be 12/(-64)*-66 + (-3)/8. Factor 21*p - 27 - w + 32*p**2 - 35*p**2 + 3.
-3*(p - 4)*(p - 3)
Let g(o) be the third derivative of o**7/168 - o**6/18 - o**5/6 + 10*o**4/3 + 9*o**3 + 4*o**2 - 1. Let t(a) be the first derivative of g(a). Factor t(s).
5*(s - 4)*(s - 2)*(s + 2)
Suppose -2*s = 4*b + 44, -2*s + 5*s = 6. Let m be b/(-5) - (-6)/(-15). Factor -25*t**2 + 57*t**2 - 31*t**m.
t**2
Let o be (-153)/68 + (-903)/(-396). Let z(y) be the second derivative of o*y**4 - 1/231*y**7 + 0*y**3 + 3/110*y**5 + 0 + 0*y**6 + 0*y**2 + 5*y. Factor z(g).
-2*g**2*(g - 2)*(g + 1)**2/11
Let u be (3/(-2))/((-3)/16). Let y(v) = -12*v - v**3 - 2 - 2 - 5*v**2 + 9*v**2 - 3*v**3. Let a(r) = r**3 + r. Let z(w) = u*a(w) + y(w). Factor z(j).
4*(j - 1)*(j + 1)**2
Let b = -1/4894 - -2457/48940. Let r(i) be the second derivative of -b*i**5 + 0*i**3 + 0 - 30*i - 1/60*i**6 + 0*i**2 - 1/24*i**4. Factor r(f).
-f**2*(f + 1)**2/2
Let u(c) be the third derivative of 5*c**8/336 - c**7/42 - c**6/8 + c**5/12 + 5*c**4/12 - c**2 + 135*c. Determine d so that u(d) = 0.
-1, 0, 1, 2
Let l(n) be the second derivative of -14/27*n**3 + 40*n - 49/9*n**2 + 3 - 1/54*n**4. Factor l(u).
-2*(u + 7)**2/9
Suppose 10*h - 636 = -626. Suppose 2 + h = m. Factor 1/5*a + 4/5*a**2 - 1/5*a**m - 4/5.
-(a - 4)*(a - 1)*(a + 1)/5
Let m(v) = -2*v**4 + 172*v**3 - 240*v**2 + 14*v - 14. Let q(i) = -i**4 + 116*i**3 - 160*i**2 + 9*i - 9. Let o(x) = -9*m(x) + 14*q(x). Factor o(p).
4*p**2*(p - 1)*(p + 20)
Factor -110 - q**3 + 148*q + 58 - 124 - 64 - 12*q**2.
-(q - 6)*(q - 2)*(q + 20)
Let f(m) = -80*m + 485. Let g be f(-9). Let s = -10823/9 + g. Let -2/9*v**2 + 8/3 - s*v = 0. Calculate v.
-12, 1
Let x(k) be the third derivative of -2*k**5/75 - 7*k**4/5 - 147*k**3/5 + 2330*k**2. Factor x(o).
-2*(2*o + 21)**2/5
Let s = -36993/14 + 18675/7. Factor 15/2*h**3 + 1/2*h**4 - s*h**2 - 9 + 53/2*h.
(h - 1)**3*(h + 18)/2
Let s(n) be the second derivative of n**5/12 - 25*n**4/12 + 15*n**3/2 + 14*n**2 + 40*n. Let y(o) be the first derivative of s(o). Factor y(w).
5*(w - 9)*(w - 1)
Let o(a) = a**3 - 231*a**2 - 1640*a - 6184. Let i be o(238). Solve 0 - 3/2*y**i + 0*y + 6*y**2 - 9/2*y**3 = 0.
-4, 0, 1
Let s(v) be the first derivative of 11/15*v**3 - 1/50*v**5 - 22*v - 2/15*v**4 - 6/5*v**2 + 24. Let x(i) be the first derivative of s(i). Factor x(h).
-2*(h - 1)**2*(h + 6)/5
Let u = -473 - -393. Let w be ((-32)/u)/(2/15). Suppose 3/4*p**4 - 3/4*p**2 + 0 + 3/2*p - 3/2*p**w = 0. Calculate p.
-1, 0, 1, 2
Suppose -4*f = -414*p + 416*p + 6, -5*f - 6 = 3*p. Solve -6 - 4*d + 7/2*d**p - 33/2*d**4 + 9/2*d**5 + 37/2*d**2 = 0 for d.
-2/3, 1, 3
Let j(c) = -2*c**2 + c + 4. Let w(h) = 21*h**2 - 36*h - 144. Let z(s) = -9*j(s) - w(s). Factor z(q).
-3*(q - 12)*(q + 3)
Factor -637*x**2 - 1004*x**3 - 256*x - 35*x**2 + 508*x - 252*x + 6*x**4.
2*x**2*(x - 168)*(3*x + 2)
Let z(y) = -12*y**5 + y**4 + 17*y**3 - 5*y**2 - 2*y - 8. Let t(f) = 12*f**5 - 17*f