vative of -g**5/60 + g**4/4 - 3*g**3/2 - 9*g**2/2 + 10. Let m(q) be the second derivative of z(q). Factor m(w).
-(w - 3)**2
Let f(l) be the second derivative of l**6/420 - l**5/210 + 21*l**2/2 + 9*l. Let m(h) be the first derivative of f(h). Factor m(v).
2*v**2*(v - 1)/7
Let f = 177/13 - 872/65. Suppose 1/5*c**2 - 2/5*c - f*c**4 + 0 + 2/5*c**3 = 0. What is c?
-1, 0, 1, 2
Let u(g) be the second derivative of -2/21*g**3 - 25*g - 1/42*g**4 + 3/7*g**2 + 0. Factor u(y).
-2*(y - 1)*(y + 3)/7
Let o(n) be the second derivative of -8*n**6/105 - 16*n**5/7 + n**4/7 + 118*n**3/21 - 40*n**2/7 + 3*n + 26. Let o(v) = 0. Calculate v.
-20, -1, 1/2
Let b(v) be the first derivative of 9*v**5/5 - 57*v**4/4 + 4*v**3 + 18*v**2 + 91. Factor b(z).
3*z*(z - 6)*(z - 1)*(3*z + 2)
Let d(z) be the second derivative of 2/9*z**3 + 0*z**2 - 1/3*z**4 + 1/20*z**5 + 0 + 1/18*z**6 + 13*z. Factor d(w).
w*(w - 1)*(w + 2)*(5*w - 2)/3
Let r be 492/(-60) - -12 - (-8)/(-10). Suppose 1/4*j**r - 1/4*j + 0*j**2 + 0 = 0. Calculate j.
-1, 0, 1
Suppose 60*q - 64*q + 18 = o, 10 = 4*q - 3*o. Find t such that 24/7*t**2 + 0 + 6/7*t**q + 0*t + 30/7*t**3 = 0.
-4, -1, 0
Let c = -6254 - -6254. Factor c + 1/4*j**2 + 1/4*j.
j*(j + 1)/4
Let n(f) be the first derivative of -1/6*f**2 + 37 + 1/12*f**4 + 0*f - 1/18*f**3 + 1/30*f**5. Find a such that n(a) = 0.
-2, -1, 0, 1
Factor 5/4*z**4 + 0*z**2 - 5/2*z**3 + 0 + 0*z.
5*z**3*(z - 2)/4
Let a(i) = 28*i - 560. Let q be a(20). Solve 6/5*r**3 + 2*r**2 - 18/5*r**4 + 2/5*r + q = 0 for r.
-1/3, 0, 1
Let m be (-3 - 24/(-9))*-9. Let g(b) = -8*b**2 - 2*b + 10. Let n(j) = -9*j**2 - j + 10. Let c(p) = m*n(p) - 4*g(p). What is u in c(u) = 0?
-2, 1
Suppose 479 = 5*p + 44*p + 430. Determine b so that 13/4*b**2 - 3*b + 1/4*b**4 + p - 3/2*b**3 = 0.
1, 2
Suppose -6*p + 0 = -12. Suppose v**4 - 2*v**4 - 24*v**3 + v**p + 22*v**3 + 3*v - v = 0. What is v?
-2, -1, 0, 1
Factor 0 + 0*d + 0*d**2 - 2/9*d**3 + 1/9*d**4.
d**3*(d - 2)/9
Let u = 207/7 + -29. Let g = 6/11 + -20/77. Determine v, given that g - u*v + 2/7*v**2 = 0.
1
Let p(g) = -9*g + 30. Let k be p(3). Let t(u) be the second derivative of -1/18*u**4 + 0 + 4*u + 4/9*u**k - 4/3*u**2. Determine m, given that t(m) = 0.
2
Let x = 169561/120 - 1413. Let p(y) be the third derivative of -1/12*y**3 + 7*y**2 + 0 + 0*y + x*y**5 - 1/48*y**4 + 1/240*y**6. Factor p(o).
(o - 1)*(o + 1)**2/2
Let c = -31262 + 156311/5. Let q be ((-2)/20)/((-2)/4). What is b in -2/5*b**2 + c*b**3 - q*b + 2/5 = 0?
-1, 1, 2
Suppose 23 = 10*u - 17. Let b(c) be the second derivative of 0*c**2 + 9/10*c**6 + 0 + 9/10*c**5 + 1/4*c**u - c + 2/7*c**7 + 0*c**3. Factor b(j).
3*j**2*(j + 1)**2*(4*j + 1)
Let v(w) be the third derivative of -w**6/90 + 2*w**5/15 - w**4/2 + 16*w**3/3 + 43*w**2. Let y(q) be the first derivative of v(q). Find f, given that y(f) = 0.
1, 3
Let h = 11671/7 + -1667. Factor -8/7 - h*p**2 - 8/7*p.
-2*(p + 2)**2/7
Let -1352*z**2 - 122*z**3 + 1624*z**2 + 36*z**4 + 48*z + 382*z**3 = 0. Calculate z.
-6, -1, -2/9, 0
Let r be 2/(-8)*(2 - 6). Let u be (-3)/(-5)*r*5. Factor -3*p**5 + 0*p**3 + 0*p**5 + 6*p**3 - u*p + 0*p**3.
-3*p*(p - 1)**2*(p + 1)**2
Factor 6 - 3/5*f**3 + 7/5*f - 2*f**2.
-(f + 2)*(f + 3)*(3*f - 5)/5
Let s be (-3)/(-12 - (-24)/(-8)). Find d, given that -s*d**2 + 1/5 + 0*d = 0.
-1, 1
Let h(n) = 8*n**2 - 2*n - 2. Let x be h(-1). Factor 21 + 20*r - x + 5*r**2 + 2 + 0*r**2.
5*(r + 1)*(r + 3)
Factor 9/7 + 3/7*j - 9/7*j**2 - 3/7*j**3.
-3*(j - 1)*(j + 1)*(j + 3)/7
Let w(k) be the third derivative of -k**7/135 + k**6/60 - k**5/135 + 13*k**2. Factor w(f).
-2*f**2*(f - 1)*(7*f - 2)/9
Determine d, given that 0 - 9/4*d**3 - 1/4*d**5 - 9/2*d**2 + 2*d**4 + 0*d = 0.
-1, 0, 3, 6
Let b = -6 - -10. Factor -37*q + 14*q + b*q**2 + 15*q.
4*q*(q - 2)
Suppose 5*n - 5 = 0, 5*n + 12 - 27 = -5*s. Factor -2/5*d**4 + 0 + 2/5*d**3 - 2/5*d + 2/5*d**s.
-2*d*(d - 1)**2*(d + 1)/5
Let x = -176 + 105. Let f = 356/5 + x. Find k such that -f*k + 1/5*k**2 - 2/5 = 0.
-1, 2
Solve 6*a**3 + 9/2*a**4 - 21/4*a - 9/2*a**2 + 0 - 3/4*a**5 = 0.
-1, 0, 1, 7
Let a(r) = 44*r**5 - 64*r**4 + 252*r**3 + 84*r**2 - 256*r + 20. Let d(m) = 2*m**5 + m**2 + 1. Let l(q) = a(q) - 20*d(q). Find w such that l(w) = 0.
-1, 0, 1, 8
Let b(h) be the second derivative of -h**4/6 + 14*h**3/3 + 15*h**2 + h - 21. What is w in b(w) = 0?
-1, 15
Suppose 11*h - 7 = 2*i + 8*h, 9 = i + h. Let w(p) be the third derivative of 0*p**3 - 1/120*p**5 - 11*p**2 + 0*p + 0 - 1/240*p**6 + 1/24*p**i. Factor w(y).
-y*(y - 1)*(y + 2)/2
Factor 0 + 1/8*m**3 + 11/4*m + 23/8*m**2.
m*(m + 1)*(m + 22)/8
Let r = -984 - -984. Let x(j) be the third derivative of 0*j**3 - 1/4*j**6 + 0 - 2/15*j**5 + r*j**4 - 1/30*j**7 - 5*j**2 + 0*j. Factor x(t).
-t**2*(t + 4)*(7*t + 2)
Let t be 6/15*(-1)/(-126). Let x(z) be the second derivative of 1/225*z**6 + 0*z**3 - 1/90*z**4 - 1/150*z**5 + 0 + 3*z + t*z**7 + 0*z**2. Factor x(b).
2*b**2*(b - 1)*(b + 1)**2/15
Suppose 5 = 4*n - 3. Suppose 0 = 5*g + 15, 0 = 5*v - 4*g - 19 - 3. Factor -8*x + 1 + 2*x**n + v*x + 3.
2*(x - 2)*(x - 1)
Factor -3/5*b**5 - 729/5*b**2 - 297/5*b**3 - 51/5*b**4 - 648/5*b + 0.
-3*b*(b + 3)**3*(b + 8)/5
Let b(a) = a**2 - 5*a + 7. Let y(n) = 14*n - 20 + 16*n**2 - 28*n**2 + 10*n**2. Let d(f) = 8*b(f) + 3*y(f). Find k, given that d(k) = 0.
-2, 1
Suppose 5 = -m + 7. Solve 8*l - 5*l**2 - l**m - 5*l**2 + 7*l**2 = 0 for l.
0, 2
Let i(y) be the third derivative of y**8/630 + y**7/180 + y**6/270 - y**5/180 - y**3 - 6*y**2. Let x(v) be the first derivative of i(v). Factor x(a).
2*a*(a + 1)**2*(4*a - 1)/3
Suppose -2 - 8 = -5*l. Let t = -166/3 + 167/3. Let -1/3*s**3 - s**l - s - t = 0. Calculate s.
-1
Let n = -11455/2234106 - -3/5066. Let s = 128/441 + n. What is g in -2/7*g**2 + 0*g + s = 0?
-1, 1
Let r(o) = -o**3 - 11*o**2 - 11*o - 8. Let u be r(-10). Suppose -u = 27*p - 28*p. Solve 0 + a**p + 1/2*a**3 + 0*a = 0 for a.
-2, 0
Let m(d) be the second derivative of -3*d**5/140 - 11*d**4/28 - d**3/2 + 17*d**2/2 - 6*d. Let c(y) be the first derivative of m(y). Factor c(u).
-3*(u + 7)*(3*u + 1)/7
Let b = 12813/4 + -3203. Determine r, given that -1/2*r + 0 - r**3 - b*r**4 - 5/4*r**2 = 0.
-2, -1, 0
Let u(p) be the third derivative of -p**5/300 - p**4/40 + 3*p**3/5 + 5*p**2 - 9. Let u(s) = 0. What is s?
-6, 3
Let d(c) be the third derivative of -c**10/151200 + c**9/30240 - c**7/2520 + c**6/720 + c**5/30 + 3*c**2. Let g(o) be the third derivative of d(o). Factor g(i).
-(i - 1)**3*(i + 1)
Let n(m) be the first derivative of 2*m**5/35 + 2*m**4 + 180*m**3/7 + 1100*m**2/7 + 3250*m/7 + 144. Factor n(s).
2*(s + 5)**3*(s + 13)/7
Let 0 + 1/4*j**3 + 0*j**2 + 0*j - 1/4*j**5 + 0*j**4 = 0. What is j?
-1, 0, 1
Let u(y) = -y**3 + 2*y**2 + 2*y + 5. Let h be u(3). Let f(b) = 7*b**2 + 2*b - 7. Let w(c) = 15*c**2 + 5*c - 15. Let i(q) = h*w(q) - 5*f(q). Factor i(o).
-5*(o - 1)*(o + 1)
Let u(m) = -m**2 - 10*m + 5. Let h be u(-10). Find t such that -45*t + h*t**2 + 32*t + 320 - 45*t - 22*t = 0.
8
Let t = -6 + 8. Let f(c) = 6*c**2 + 40*c + 19. Let u(b) = 3*b**2 + 20*b + 10. Let o(d) = t*f(d) - 5*u(d). Factor o(a).
-(a + 6)*(3*a + 2)
Suppose -2*k + 2*s + 2 = 0, 1 = -5*k - 3*s + 14. Suppose -1/4*y - 1/2*y**k + 1/4*y**5 + 0 + 1/2*y**4 + 0*y**3 = 0. What is y?
-1, 0, 1
Let i(r) = 5*r**2 - r. Let b be i(1). Suppose 0 = 3*h - 2*d - 2, 5*d - 2*d - 16 = -5*h. Factor 3*j**3 + 10*j**2 - b*j**h - j + j.
3*j**2*(j + 2)
Suppose 0 = 23*a - 25*a + 5*w + 41, 4*a - 43 = -3*w. Let o(h) = h**2. Let l be o(5). Factor -10*g**3 - l*g**2 + a*g - 15*g - 8*g.
-5*g*(g + 2)*(2*g + 1)
Solve -9/7 - 5*j - 5/7*j**4 - 50/7*j**2 + 1/7*j**5 - 30/7*j**3 = 0 for j.
-1, 9
Let q(a) = -a**3 - 5*a**2 + a + 7. Let x be q(-5). Suppose -14 = -x*c - 8. Factor -2*u - u**2 + 2*u**2 + 3*u**2 - 2*u**c + 0*u**3.
-2*u*(u - 1)**2
Let g = 22 - 13. Suppose g*a + 8 = 13*a. Factor 3*u**3 - a*u**4 - u**4 - u**3 + 2*u**5 - u**4.
2*u**3*(u - 1)**2
Let k = -3367 + 3377. Solve 2 + 25/2*m**2 - k*m = 0.
2/5
Let q(u) be the third derivative of 5*u**8/1008 + 5*u**7/63 + u**6/2 + 14*u**5/9 + 20*u**4/9 + u**2 + 14*u. Find j, given that q(j) = 0.
-4, -2, 0
Let a(k) = 3*k + 12. Let m be a(-16). Let c = 39 + m. Factor -p - 2/3 - p**c + 8/3*p**2.
-(p - 2)*(p - 1)*(3*p + 1)/3
Let k be (((-78)/12)/13)/(5/(-2)). Let b(p) be the first derivative of k*p**3 - 1 + 0*p**2 - 3/5*p. What is i in b(i) 