Let i(y) = y**3 - 14*y**2 - 16*y + 17. Let k be i(15). Let j(o) be the second derivative of 0*o**k + 1/120*o**5 - 4*o + 1/18*o**3 - 1/24*o**4 + 0. Factor j(m).
m*(m - 2)*(m - 1)/6
Let h(l) be the first derivative of -l**4/44 + 8*l**3/33 - 21*l**2/22 + 18*l/11 - 176. Factor h(y).
-(y - 3)**2*(y - 2)/11
Let t(g) be the second derivative of -g**6/165 + 7*g**5/55 - 4*g**4/33 - 62*g**3/33 - 39*g**2/11 + 211*g - 1. Find r such that t(r) = 0.
-1, 3, 13
Solve -168167*t + t**2 + 168092*t - 3*t**2 + t**2 - 146 = 0.
-73, -2
Factor 3/7*d**2 + 27/7*d - 30/7.
3*(d - 1)*(d + 10)/7
Let d(m) be the first derivative of 0*m + 2/15*m**3 - 2/5*m**2 + 3. Factor d(w).
2*w*(w - 2)/5
Let p(o) = -4*o + 13. Let m(x) = x + 1. Let j(r) = -m(r) - p(r). Let k be j(6). Determine w so that -w**2 + 2 - 9*w + 4*w + k*w = 0.
-2, 1
Factor -72/7*f + 4/7*f**3 + 2/7*f**4 - 30/7*f**2 + 0.
2*f*(f - 4)*(f + 3)**2/7
Let w(c) = -c**2 + 9*c - 6. Let p be w(8). Let l = -9 + 11. Factor n**3 - 62*n**p - 3*n + 62*n**l + 2.
(n - 1)**2*(n + 2)
Suppose 0 = -p - 15 + 17. Let d(m) be the first derivative of 0*m**4 + 0*m**p + 0*m + 0*m**3 - 5 - 1/2*m**6 - 3/5*m**5. Factor d(f).
-3*f**4*(f + 1)
Suppose -64*p = -67*p + 114. Let y be (p/171)/(-1*(-2)/18). Solve -1/4*b**y + 0 + 1/8*b**3 + 0*b = 0 for b.
0, 2
Suppose -q + 55 = 10*q. What is c in 7*c**4 + q*c**5 - 106*c**3 + 8*c**4 + 101*c**3 - 15*c**2 = 0?
-3, -1, 0, 1
Let a(p) be the third derivative of p**8/6720 + p**7/840 - p**6/720 - p**5/40 + 7*p**4/24 + 11*p**2. Let b(q) be the second derivative of a(q). Factor b(d).
(d - 1)*(d + 1)*(d + 3)
Suppose 0*a - 16/3*a**2 - 4/3*a**4 + 0 + 16/3*a**3 = 0. What is a?
0, 2
Let u(d) be the second derivative of 4*d**7/105 + 17*d**6/75 - 12*d**5/25 - 143*d**4/30 - 26*d**3/3 - 24*d**2/5 + 6*d + 10. Find r such that u(r) = 0.
-4, -2, -1, -1/4, 3
Let k(a) be the third derivative of 0*a + 0*a**3 + 1/780*a**6 + 10*a**2 - 1/156*a**4 + 0 + 0*a**5. Suppose k(r) = 0. Calculate r.
-1, 0, 1
Let i = -197/171 + 24/19. Let s(f) be the first derivative of 2/9*f**5 + 0*f**3 + 0*f**2 + 1/9*f**6 + i*f**4 - 1 + 0*f. Determine j so that s(j) = 0.
-1, -2/3, 0
Let r(c) be the third derivative of -c**6/60 - 2*c**5/15 + 11*c**4/12 - 2*c**3 + 155*c**2. Factor r(u).
-2*(u - 1)**2*(u + 6)
Let t(l) be the third derivative of l**7/10080 + l**6/2880 - l**5/240 - l**4/4 + 11*l**2. Let r(m) be the second derivative of t(m). Let r(k) = 0. What is k?
-2, 1
Let k(i) = 2*i - 3. Let v be k(2). Let l be -1 + (v - 4)/(-1). Determine w so that 3*w**2 + 3*w**2 - 5*w**3 - 3*w**5 - 4*w**3 + 9*w**4 - 3*w**l = 0.
0, 1
Suppose 3*r - 12 = -3*p - 0*p, -5*r + 5*p + 100 = 0. Factor 72 + 1/2*a**2 - r*a.
(a - 12)**2/2
Suppose 5*o - 6 = v + 3*o, 0 = 2*v - o - 3. Factor r**2 - 4*r - 2*r**v - 10*r**2 + 0*r - 8*r**3 - r**2.
-2*r*(r + 1)**2*(r + 2)
Let v(i) be the first derivative of -3*i**5/35 - 15*i**4/14 + 3*i**3/7 + 48*i**2/7 + 60*i/7 + 596. Determine a, given that v(a) = 0.
-10, -1, 2
Let a(j) = 2*j**4 + 11*j**3 - 24*j**2 + 13*j + 1. Let w(x) = x**4 + x**2 + 1. Let t(v) = 3*a(v) - 3*w(v). Factor t(h).
3*h*(h - 1)**2*(h + 13)
Let q = -1137 - -1141. Factor 1/6*a**q - 1/3*a**2 + 1/6*a**3 + 0 + 0*a.
a**2*(a - 1)*(a + 2)/6
Let f(l) be the first derivative of -8*l**3/9 - 6*l**2 - 28*l/3 + 109. Solve f(o) = 0.
-7/2, -1
Suppose -5*s = 5, 4*w + 5*s - s = 4. Let -539*a**w + 0 + 536*a**2 + 3 = 0. What is a?
-1, 1
Let h be 80/25 - 4 - (-3)/(-15). Let w(t) = 10*t**2 + 66*t + 14. Let q(p) = p**2 - 1. Let i(x) = h*w(x) + 2*q(x). Solve i(b) = 0 for b.
-8, -1/4
Suppose a - 26 + 1 = 0. Factor -12*j**2 + 3*j + a - 13*j + 13*j**2.
(j - 5)**2
Suppose -f + 23 = -5*i, 0 = -5*f + 2*i + 11 + 81. Determine o so that 4*o - f*o**2 - 3*o - 21*o**3 - 18*o**2 + 11*o = 0.
-2, 0, 2/7
Let x(k) be the first derivative of 1/12*k**3 - 1 - 3/4*k - 1/4*k**2. Factor x(i).
(i - 3)*(i + 1)/4
Let b(p) be the first derivative of 3 - 3*p**2 + 0*p**3 + 4*p + 1/2*p**4. Let b(s) = 0. What is s?
-2, 1
Let q(r) = 21*r + 21. Let t be q(-1). Let m(b) be the second derivative of 0 + 0*b**4 - 1/10*b**3 + 3/100*b**5 + 4*b + t*b**2. Solve m(x) = 0 for x.
-1, 0, 1
Let u(b) be the first derivative of -3*b**4/4 + 6*b**3 + 45*b**2/2 + 24*b + 215. Let u(n) = 0. What is n?
-1, 8
Let l be 0 + -2 + -2 - -7. Let c**l + 3*c**3 + 4*c**2 - c**5 - 58*c**4 + 54*c**4 - 3*c**5 = 0. Calculate c.
-1, 0, 1
Factor 4/5*n - 2/15*n**2 + 32/15.
-2*(n - 8)*(n + 2)/15
Let f(t) = t**3 - 3*t**2 - 2*t. Let y be f(3). Let b be ((-3)/y)/((-236)/88 + 3). Find u, given that -2/7 - 4/7*u**4 - 16/7*u**3 - 3*u**2 - b*u = 0.
-2, -1, -1/2
Let j(i) be the first derivative of -i**9/1512 - i**3/3 + 17. Let k(t) be the third derivative of j(t). What is h in k(h) = 0?
0
Let z(f) be the second derivative of f**7/105 + f**6/15 + 7*f**5/50 + f**4/10 - 47*f - 2. Factor z(q).
2*q**2*(q + 1)**2*(q + 3)/5
Let z(h) = -h + 2. Let w be z(2). Suppose -2*u - 5*p - 1 = 0, -5*u + w*u = 3*p - 7. What is k in -2/11*k**u - 8/11*k - 8/11 = 0?
-2
Let j(l) be the third derivative of -l**7/42 - 2*l**6/3 - 25*l**5/12 + 35*l**4/4 + 96*l**2 + 2*l. Factor j(y).
-5*y*(y - 1)*(y + 3)*(y + 14)
Let z be (-4)/(-6) + 8/6. Let c = -118 - -118. Suppose 5 + 1 + 4*w - 4 + c*w + z*w**2 = 0. Calculate w.
-1
What is l in 1/12*l**2 + 4/3*l + 0 = 0?
-16, 0
Let m = 222 + -139. Let s = m + -81. Factor 0 + 1/4*v**s + 1/2*v.
v*(v + 2)/4
Let d(y) be the third derivative of y**8/168 - y**7/21 - y**6/12 + 5*y**5/6 + 10*y**4/3 + 16*y**3/3 - 20*y**2 + 1. What is a in d(a) = 0?
-1, 4
Let c(q) be the third derivative of -q**5/30 - 247*q**4/60 - 98*q**3/15 - 881*q**2. Find r such that c(r) = 0.
-49, -2/5
Let f(q) be the third derivative of q**5/120 + q**4/3 - 11*q**2 + 6. Factor f(t).
t*(t + 16)/2
Let o(k) be the second derivative of k**4/36 + k**3/18 - k**2/3 + 2*k - 4. Factor o(h).
(h - 1)*(h + 2)/3
Suppose -5*n = -3*n - 2*t, 4*t + 2 = 5*n. Suppose -w + n = -0*w. What is z in 31*z**3 - 2*z**w - 8*z**2 - 39*z**3 - 4*z - 2*z**4 = 0?
-2, -1, 0
Let s = -4/1969 + 7888/5907. Factor s - 1/3*j**2 + 0*j.
-(j - 2)*(j + 2)/3
Suppose 9 = 3*q - 3*m, 2*m - 5*m = 0. Suppose 2*o - 8 = -3*h, 0*h - 4*h - 12 = -q*o. Let 2/13*p**4 + 2/13*p**3 - 2/13*p**2 + 0*p - 2/13*p**5 + h = 0. What is p?
-1, 0, 1
Factor -2*q - 7*q**2 - 383 + q**3 + 395 + 6*q.
(q - 6)*(q - 2)*(q + 1)
Let d be (-6*(-5)/18)/((-2)/(-6)). Factor -5*k - 49 + d*k**2 + 49.
5*k*(k - 1)
Suppose 5*y + 24 = 9*y. Factor 210 - 218 + 2*h**2 + 0*h**2 - y*h.
2*(h - 4)*(h + 1)
Factor 3/2*n**2 + 0 - 1/4*n**4 + 2*n - 3/4*n**3.
-n*(n - 2)*(n + 1)*(n + 4)/4
Let d = -269/30090 - 1/354. Let u = d - -18/85. Solve 3/5*q**2 + u*q**3 + 2/5*q + 0 = 0.
-2, -1, 0
Let c = -20 - -22. Find g, given that -g**c - g**2 - 16*g**2 - 8*g - 2*g**2 = 0.
-2/5, 0
Suppose -21*x = -15*x - 516. Let n = x + -83. Factor -3/5*h**n - 6/5 - 12/5*h**2 - 3*h.
-3*(h + 1)**2*(h + 2)/5
Let i(x) be the second derivative of 0 + 35*x + 25/12*x**4 + 3/5*x**5 + 0*x**2 + x**3 - 7/30*x**6. Find m, given that i(m) = 0.
-1, -2/7, 0, 3
Let f(x) = 2 + 1 - 11 - x. Let d be f(-10). Let -1/4*a**4 + 0 - 5/4*a**d + a**3 + 1/2*a = 0. Calculate a.
0, 1, 2
Let p(h) = 8*h**5 - 39*h**4 + 203*h**3 - 486*h**2 + 562*h - 243. Let a(c) = -c**5 - c**3 + c. Let d(y) = -5*a(y) - p(y). Factor d(g).
-3*(g - 3)**4*(g - 1)
Factor 0*h + 12*h**3 - 1/3*h**4 + 0 - 108*h**2.
-h**2*(h - 18)**2/3
Let c = 0 - 0. Let a(t) = -t**3 + 4*t**2 - 6*t + 4. Let n be a(2). Let n*h**3 + h**2 + h**4 - 2*h**3 + 0*h**3 + c*h**4 = 0. Calculate h.
0, 1
Let r(j) be the second derivative of -3/8*j**4 + 9/2*j**2 + j + 17/4*j**3 + 0. Find i such that r(i) = 0.
-1/3, 6
Let z(p) be the third derivative of p**5/75 + 2*p**4/15 + 8*p**3/15 - 856*p**2. Factor z(c).
4*(c + 2)**2/5
Let f be 352/160 + (-2)/10. Let u be (2/6)/(f - 87/54). Factor -u*z**2 + 4/7*z + 0 + 2/7*z**4 + 0*z**3.
2*z*(z - 1)**2*(z + 2)/7
Let d(i) = 7*i**2 + 3*i. Let f be d(-1). Factor -g**5 + 3*g**4 + 3*g**5 - 3*g**5 + 0*g**4 - f*g**2.
-g**2*(g - 2)**2*(g + 1)
Factor 1/5*z**3 - 7/5*z**2 - 9/5 + 3*z.
(z - 3)**2*(z - 1)/5
Factor 4*r + 23*r**2 - 24*r**2 + 4*r + 2 - 9.
-(r - 7)*(r - 1)
Find b such that 54/13*b**3 + 34/13*b**2 + 0 + 8/13*b + 10/13*b**5 + 38/13*b**4 = 0.
-1, -4/5, 0
Let m be 4*1 + (-4 - -5) + -2. Suppose 12 = m*q - 0. Factor 6/7 + 3*c + 3/7*c**q + 27/7*c**2 + 15/7*c**3.
3*(c + 1)**3*(c + 2)/7
Le