t o be (-1 + 4 - t)*-1. Factor -2 + 1 + o - 2*s**2 - 2*s.
-2*s*(s + 1)
Let x(d) be the third derivative of 0*d**3 - 4/39*d**4 + 0 - 4/195*d**6 + 8/65*d**5 + 24*d**2 + 5/2184*d**8 - 2*d - 4/455*d**7. Solve x(y) = 0.
-2, 0, 2/5, 2
Let v = 35 - 33. Factor 2 - 4*f + 5/2*f**v - 1/2*f**3.
-(f - 2)**2*(f - 1)/2
Let m be 42*(10 - 715/78). Suppose 49/3*w**3 + 16/3 + m*w**2 + 24*w = 0. Calculate w.
-1, -4/7
Let z(d) = -d**2 - 10*d + 1. Let s be z(-9). Find h such that s*h**2 - 8 + 11 + 4*h - 3 = 0.
-2/5, 0
Let w(m) be the second derivative of -m**8/1176 + m**6/210 - m**4/84 - 2*m**2 + 3*m. Let q(h) be the first derivative of w(h). Factor q(f).
-2*f*(f - 1)**2*(f + 1)**2/7
Suppose 4*q - 2*q + 607 = x, -q - 3*x - 293 = 0. Let h = q + 2118/7. Factor -4/7*k**2 - 2/7*k**5 - 2/7 + 6/7*k**4 + 6/7*k - h*k**3.
-2*(k - 1)**4*(k + 1)/7
Suppose -h + 3*h + 4 = 0. Let q be (-24)/(-9) + h/3. Factor r - 3*r**q - 3*r - 2*r + r.
-3*r*(r + 1)
What is r in 4*r**2 - 17*r + 41 + 6*r**2 + 2*r**2 - 59 - 11*r**2 = 0?
-1, 18
Let s(c) be the third derivative of -c**6/120 + c**5/60 + c**4/4 + 361*c**2. Factor s(b).
-b*(b - 3)*(b + 2)
Let k(y) = y**2 + 24*y + 147. Let b be k(-12). Let g be 8/12 - (-1)/(-6). Factor 2*h + 2*h**3 - b*h**2 - g*h**4 - 1/2.
-(h - 1)**4/2
Let s = 2942/7 - 420. Factor s*l**2 - 18/7*l + 0.
2*l*(l - 9)/7
Let w(n) be the third derivative of n**5/150 + n**4/12 - 14*n**3/15 + 32*n**2 + 1. Factor w(l).
2*(l - 2)*(l + 7)/5
Let r(s) be the first derivative of 0*s - 8 + 3/2*s**2 + 5/4*s**3. Determine l, given that r(l) = 0.
-4/5, 0
Factor 1/7*d**2 - 3/7*d + 0.
d*(d - 3)/7
Suppose 31 = 4*b + 3*a, 3*b + 3*a = 8*a - 13. Let f = -1 + b. Factor 0*j**4 + 4*j**5 - j - j**4 + 3*j**4 - 2*j**2 - f*j**5.
j*(j - 1)*(j + 1)**3
Find j, given that -9*j**2 + 12*j**3 - 4*j**4 - j - 6*j + 0*j + 9*j = 0.
0, 1/2, 2
Let t(z) be the second derivative of -5*z**4/12 + 5*z**3/6 + 50*z**2 + 644*z. Solve t(d) = 0 for d.
-4, 5
Factor -5/3*r**2 + 0 + 5/3*r**3 - 10/3*r.
5*r*(r - 2)*(r + 1)/3
Let n(l) = -l**2 - 13*l + 3. Let d be n(-13). Let 2/9*j**d + 4/9 + 10/9*j + 8/9*j**2 = 0. Calculate j.
-2, -1
Let b(h) be the second derivative of -h**6/80 + h**4/16 - 3*h**2/16 + 201*h. Solve b(r) = 0.
-1, 1
Let b = 13 + -6. Let a(f) = f**3 - 7*f**2 + 4. Let m be a(b). Find q, given that 2*q**4 + 3 - 4*q - 1 - 4 + m*q**3 = 0.
-1, 1
Let o(f) be the second derivative of -f**4/96 - 13*f**3/8 - 1521*f**2/16 - 112*f. Solve o(z) = 0.
-39
Let d(v) be the second derivative of -3*v**6/85 + 3*v**5/85 + 10*v**4/51 + 8*v**3/51 - 2*v - 10. Factor d(o).
-2*o*(o - 2)*(3*o + 2)**2/17
Let -5*w**3 - 200 + 97*w + 1733*w**4 - 1728*w**4 + 163*w - 90*w**2 = 0. What is w?
-5, 2
Let p be 3/1 + 1 + -3. Let s be (p - (3 - 5)) + 0. Factor 7*n - s*n + 4*n + 4*n**4 - 4*n**2 - 8*n**3.
4*n*(n - 2)*(n - 1)*(n + 1)
Let m(d) = 6480*d**2 - 350*d + 7. Let f(x) = -25920*x**2 + 1395*x - 29. Let a(n) = -2*f(n) - 9*m(n). Find l such that a(l) = 0.
1/36
Let d be ((-3)/255)/(-6 - 2006/(-335)). Let u = d + -4/17. Factor u*i**2 + 0 + 0*i - 3/8*i**4 - 3/8*i**3.
-3*i**2*(i - 1)*(i + 2)/8
Let b(w) be the first derivative of w**4/6 - 4*w**3/9 - 7*w**2/3 - 8*w/3 - 74. Solve b(p) = 0 for p.
-1, 4
Let y = -3/56 + 281/4200. Let d(w) be the second derivative of y*w**6 + 9*w - 2/15*w**4 + 0 + 1/25*w**5 - 2/15*w**3 + 3/5*w**2. Factor d(z).
2*(z - 1)**2*(z + 1)*(z + 3)/5
Suppose -4*a - g + 0*g = -11, 0 = a - 3*g - 19. Factor 10*n**2 - 6*n**2 + 2*n**a + 0*n**4 - 6*n**3.
2*n**2*(n - 2)*(n - 1)
Suppose 5*a = l - 15, -2*l = 3*a - 9 + 18. Let 0*c**2 + l*c + 0 - 2/5*c**3 = 0. Calculate c.
0
Let p(c) be the third derivative of 0*c**4 + 3*c**2 + 0*c**3 + 7/540*c**6 + 0 + 0*c + 2/945*c**7 - 1/504*c**8 + 1/135*c**5. Solve p(d) = 0.
-1, -1/3, 0, 2
Let a = 965 - 960. Find s, given that 0*s**4 - 1/2*s**a + s**3 + 0 - 1/2*s + 0*s**2 = 0.
-1, 0, 1
Let j(o) be the third derivative of -o**7/945 + o**6/180 + o**5/30 + 5*o**4/108 - 195*o**2. Factor j(v).
-2*v*(v - 5)*(v + 1)**2/9
Suppose 31*i = 148 + 38. Let d be (1 - 2)/(-1) - -2. Factor c + 2*c - 2*c**4 - d*c**5 - 4*c**4 + i*c**2.
-3*c*(c - 1)*(c + 1)**3
Let j be 1/27*3*3. Let h be (8/(-96)*8)/(1/(-1)). Factor 2/3*b**3 - j - h*b**2 - b + 1/3*b**5 + b**4.
(b - 1)*(b + 1)**4/3
Let i = -2331 - -2335. Factor -8/7*h**3 + 6/7*h + 4/7*h**2 + 2/7*h**5 + 0*h**i - 4/7.
2*(h - 1)**3*(h + 1)*(h + 2)/7
Suppose -19*u + 444 - 406 = 0. Suppose -1/3*o + 1/3*o**4 + o**u - o**3 + 0 = 0. What is o?
0, 1
Factor -80*h**3 + 127*h**3 + 105*h**4 + 5*h**5 + 179*h**2 + 553*h**3 + 359*h**2 - 38*h**2.
5*h**2*(h + 1)*(h + 10)**2
Suppose z + o - 4 = 0, 2 = 4*o - 2. Suppose 2 = -a - 4*v, -z*v - 7 = -a - a. Factor -6 + 5*u + 3 + u + u**a - 4*u**2.
-3*(u - 1)**2
Let s = 62 + -184/3. Suppose 5*d - 7*d = -4. What is j in -10/3*j**d - s - 4*j = 0?
-1, -1/5
Let q(x) be the first derivative of 5*x**6/6 + 3*x**5 + 5*x**4/2 - 10*x**3/3 - 15*x**2/2 - 5*x + 62. Determine a, given that q(a) = 0.
-1, 1
Let b(t) be the first derivative of -20*t**2 + 0*t - 5/3*t**3 - 27. Factor b(d).
-5*d*(d + 8)
Solve 16/3*h + 50/9 - 2/9*h**2 = 0 for h.
-1, 25
Let i = -2486 + 2488. Factor 32/7 + 16/7*g**i - 40/7*g - 2/7*g**3.
-2*(g - 4)*(g - 2)**2/7
Solve 2/3*k**4 - 10/3*k**2 + 2*k + 2/3*k**3 + 0 = 0 for k.
-3, 0, 1
Factor 510*k**3 - 1935*k**2 - 340*k**4 + 11*k**5 + 1620*k - 62*k**3 + 29*k**5 - 540 + 702*k**3.
5*(k - 2)**2*(2*k - 3)**3
Factor 4545 - 2*f**2 - 4537 + 0*f**2.
-2*(f - 2)*(f + 2)
Factor 1/9*t**3 + 0 + 19/9*t**2 + 0*t.
t**2*(t + 19)/9
Let p = -22963/1320 - -192/11. Let l(a) be the third derivative of 0*a + p*a**6 + 1/3*a**4 + 0 + 8*a**2 - 2/9*a**3 - 41/180*a**5. Factor l(h).
(h - 1)*(3*h - 2)*(7*h - 2)/3
Let c(s) = -2*s**2 - 42*s - 34. Let l be c(-20). Let n be (l/9)/(6/18). Let -250/7*x**4 - 60*x**n + 550/7*x**3 - 16/7 + 136/7*x = 0. What is x?
2/5, 1
Determine b so that -54/7 + 15/7*b - 1/7*b**2 = 0.
6, 9
Solve -21*s**2 + 40*s**2 - 3 - 6*s - 22*s**2 = 0.
-1
Let s(h) be the second derivative of -h**6/15 - h**5/20 + h**4/6 + h**3/6 + 143*h. Let s(c) = 0. What is c?
-1, -1/2, 0, 1
Let v(y) = 5*y**5 + 9*y**4 + 16*y**3 - 4*y**2 - 3*y - 5. Let x(q) = 9*q**5 + 17*q**4 + 31*q**3 - 7*q**2 - 7*q - 10. Let l(i) = 11*v(i) - 6*x(i). Factor l(c).
(c - 5)*(c - 1)*(c + 1)**3
Let n(k) be the second derivative of -k**4/90 - 4*k**3/45 + 34*k + 1. Factor n(g).
-2*g*(g + 4)/15
Let h(o) be the second derivative of 6*o + 0 + 1/27*o**3 + 1/108*o**4 + 0*o**2. Solve h(d) = 0.
-2, 0
Let x(l) be the first derivative of -l**6/4 + 21*l**4/8 + l**3 - 9*l**2 - 12*l + 276. Suppose x(t) = 0. What is t?
-2, -1, 2
Factor -x**5 - 36*x**4 - 2*x**5 + 570*x**3 - 678*x**3.
-3*x**3*(x + 6)**2
Let y be (-12)/4 + (-1*4)/(-2). Let g(z) = 12*z**2 + 3*z + 3. Let j(r) = -1 - 1 + 1 - r**2 - r. Let s(v) = y*g(v) - 6*j(v). Factor s(l).
-3*(l - 1)*(2*l + 1)
Let w = 27 + -25. Let c(p) be the first derivative of -8/13*p + 44/13*p**w - 242/39*p**3 - 5. Factor c(z).
-2*(11*z - 2)**2/13
Suppose 18*n = 12*n + 36. Let i(h) be the second derivative of 1/5*h**5 - 1/3*h**3 - h - 1/21*h**7 + 0 + 0*h**2 + 0*h**n + 0*h**4. Factor i(m).
-2*m*(m - 1)**2*(m + 1)**2
Let f = 51 + -31. Suppose -60*x + 65*x = f. Factor 0*a**3 + 1/3*a + 0 - 1/3*a**5 - 2/3*a**2 + 2/3*a**x.
-a*(a - 1)**3*(a + 1)/3
Let m = 118/1335 - -4/89. Let a(y) be the first derivative of 4/5*y + 5 + m*y**3 + 3/5*y**2. Solve a(j) = 0.
-2, -1
Let c = 19010 - 95032/5. Solve 1656/5*m + 264/5*m**4 + 432/5 + 1266/5*m**3 + 2244/5*m**2 + c*m**5 = 0 for m.
-6, -1, -2/3
Let i(r) be the third derivative of -r**8/168 - 6*r**7/245 + r**6/210 + 4*r**5/35 + 5*r**4/84 - 2*r**3/7 - 87*r**2 - 2. Find l, given that i(l) = 0.
-2, -1, 3/7, 1
Suppose -5*f + 10 = -0*f. Factor -17*i + 16*i**2 + 5*i**2 + 4*i**2 + f*i - 10.
5*(i - 1)*(5*i + 2)
Let m(c) = 2*c**5 + 47*c**4 + 84*c**3 + 28*c**2 - 21*c + 5. Let v(k) = k**5 + k - 1. Let s(a) = -m(a) - 5*v(a). Solve s(d) = 0 for d.
-4, -2, -1, 0, 2/7
Let p be 12*(26/(-130))/(12/(-15)). Determine y, given that -4/9*y**5 + 4/9*y**2 + 14/9*y**4 + 4/9*y - 16/9*y**p - 2/9 = 0.
-1/2, 1
Let x = 162 + -156. Let a(p) be the first derivative of 0*p**3 + 1/4*p**4 + 1/6*p**x + 0*p**2 + 4 + 0*p + 2/5*p**5. Solve a(z) = 0 for z.
-1, 0
Let z(x) = 6*x**2 + 17*x - 18. Let d(c) = -c**2 - c - 1. Let m = -35 + 49. Let s(y) = m*d(y) + 2*z(y). Find t such that s(t) = 0.
5
Let m 