/9
Let j(c) be the second derivative of c**4/4 + 7*c**3/2 - 12*c**2 + 6*c + 12. Factor j(u).
3*(u - 1)*(u + 8)
Suppose -2*d**3 - 256*d**2 - 4*d**4 + 8*d + 4 + 259*d**2 + 3*d**4 = 0. What is d?
-2, -1, 2
Suppose -13*t + 2 + 37 = 0. Let q(a) be the second derivative of -11/21*a**3 + t*a + 0 + 5/84*a**4 + 4/7*a**2. Find k, given that q(k) = 0.
2/5, 4
Let m = 8218 - 8215. Find y, given that -1/4*y**m + 0*y + y**2 + 0 = 0.
0, 4
Let u(a) be the second derivative of -38*a + 0 - 3/10*a**3 + 0*a**2 + 1/60*a**4. Let u(f) = 0. What is f?
0, 9
Suppose -15 - 21 = -18*l. Suppose -6/7*b + 4/7 + 2/7*b**l = 0. Calculate b.
1, 2
Let g(k) be the second derivative of 0 - 6/7*k**2 + 3/140*k**5 - 5/28*k**4 + 4*k + 4/7*k**3. Factor g(z).
3*(z - 2)**2*(z - 1)/7
Factor -2/7*a**2 - 172/7*a + 174/7.
-2*(a - 1)*(a + 87)/7
Let y(p) be the first derivative of -p**5/30 + 5*p**4/18 + 9*p - 3. Let q(j) be the first derivative of y(j). Suppose q(v) = 0. Calculate v.
0, 5
Find w such that 0*w**3 - 160 + 324*w + 134 + 90*w**2 - 324 + 5*w**3 - 69*w = 0.
-14, -5, 1
Let s(p) be the first derivative of p**6/720 - p**5/120 + p**4/48 - 5*p**3/3 - 12. Let d(v) be the third derivative of s(v). Factor d(w).
(w - 1)**2/2
Let m(p) be the second derivative of 5*p**4/12 - 5*p**3/6 - 15*p. Factor m(u).
5*u*(u - 1)
Let m be (12/14)/(1/(-7)). Let l be (-22)/(-88)*m/(-2). Determine v, given that -1/2 - 1/4*v**2 - l*v = 0.
-2, -1
Suppose -4*i = p, 2*i - 7*p = -9*p. Factor 0 - 4/7*c**2 + 0*c**3 + i*c + 4/7*c**4.
4*c**2*(c - 1)*(c + 1)/7
Let c be (-7 + (-72)/(-10))*16. Factor 4/5*y**2 - 12/5*y - c.
4*(y - 4)*(y + 1)/5
Let y(i) = i**3 + 2*i**2 - 3*i + 3. Let q be y(-3). Find j such that -11*j - 8*j + 4*j**3 + 9*j + 5*j**2 + j**q = 0.
-2, 0, 1
Suppose 1533 = 4*a + 1521. Factor -1/2*q - q**2 + 0 - 1/2*q**a.
-q*(q + 1)**2/2
Let y(h) = h**3 - 299*h**2 - 587*h - 322. Let v(j) = -100*j**2 - 196*j - 106. Let d(u) = -7*v(u) + 2*y(u). Factor d(o).
2*(o + 1)**2*(o + 49)
Let c(q) = -q**3 + 6*q**2 - 5*q + 3. Let x be c(5). Factor -5*v**x - 3*v**4 + 4*v**4 + 0*v**4.
v**3*(v - 5)
Let d(t) = -t**4 + t**3 + t**2 + t. Let i(h) be the second derivative of -h**6/6 + 3*h**5/20 + h**4/2 + 2*h**3/3 + h. Let q(y) = -4*d(y) + i(y). Factor q(b).
-b**2*(b - 1)*(b + 2)
Suppose -15 - 6 - 3*c**3 + 21 + 12*c = 0. What is c?
-2, 0, 2
Let 72*g**2 - 1775*g**4 + 876*g**4 - 2*g**5 + 865*g**4 + 40*g**3 = 0. What is g?
-18, -1, 0, 2
Let u be 2/1*-2 + (-3)/((-72)/222). Let 3 + 12*t + u*t**2 = 0. What is t?
-2, -2/7
Suppose -s + 15 = 13. Factor -8*q - q**5 + 2*q**5 + 9*q**3 - 4 - q**2 + 12*q**4 - 7*q**4 - s*q**3.
(q - 1)*(q + 1)**2*(q + 2)**2
Let p(i) be the first derivative of -i**6/2 - 3*i**5/5 + 9*i**4/4 + 5*i**3 + 3*i**2 + 82. Factor p(y).
-3*y*(y - 2)*(y + 1)**3
Suppose 2*a - 1 = 1. Let x be 9/6*2*a. Factor 106*r**2 + 2*r**4 + 6*r - 34*r**2 - r**3 - 114*r - 19*r**x + 54.
2*(r - 3)**3*(r - 1)
What is l in -2*l - l**2 - 3*l + 4 - 7 + 3 = 0?
-5, 0
Let z(b) be the second derivative of -1/96*b**4 + 7*b + 1/48*b**3 + 0 + 1/8*b**2. Solve z(m) = 0 for m.
-1, 2
Let z(t) be the first derivative of 2/5*t**2 + 4/5*t + 4/25*t**5 - 2/5*t**4 - 8/15*t**3 + 2/15*t**6 - 17. Find p, given that z(p) = 0.
-1, 1
Let w(o) be the first derivative of -o**7/210 + o**6/10 - 23*o**5/30 + 5*o**4/2 - 25*o**3/6 - o**2 + 26. Let j(x) be the second derivative of w(x). Factor j(z).
-(z - 5)**2*(z - 1)**2
Let h(k) = 2*k**2 - 2*k + 6. Let a be h(5). Factor -9 + a - 12*t + 4*t**3 + 35 + 2*t**2 - 18*t**2.
4*(t - 3)**2*(t + 2)
Let k be -1 + -2 + 16/1. Let x = -10 + k. Factor 2*t**5 - 3*t - 5*t**x + t**3 + 5*t.
2*t*(t - 1)**2*(t + 1)**2
Let m(r) = -r**2 - r + 6. Let d be m(-5). Let j be d/35 - (-12)/5. Factor 3*o**2 + o - 3*o + o**j + 3*o.
o*(4*o + 1)
Let s = 60293/5 + -12058. Let b = 707/30 + -109/6. What is f in -s*f**2 - b - 18/5*f = 0?
-3
Suppose l = 4*g - 8, 2 - 1 = -l - 3*g. Let z be -4*(1 + 7/l). Determine u, given that -3*u**4 - 3*u**2 - 1 + 5*u**3 + u**z + 1 = 0.
0, 1
Let w(x) be the third derivative of x**8/1176 - x**7/105 + x**6/420 + 9*x**5/70 + 3*x**4/14 + 14*x**2 - 28*x. Suppose w(n) = 0. What is n?
-1, 0, 3, 6
Let v(n) be the third derivative of 0*n + 7*n**2 + 2/15*n**3 + 1/15*n**4 - 2/525*n**7 - 1/75*n**6 + 0 + 0*n**5. Factor v(f).
-4*(f - 1)*(f + 1)**3/5
Let p(j) be the first derivative of -j**6/30 - 3*j**5/20 + j**4/4 + 7*j**3/6 - 3*j**2 - 40*j + 43. Let g(c) be the first derivative of p(c). Factor g(r).
-(r - 1)**2*(r + 2)*(r + 3)
Solve -9/2*v - 15 + 3/2*v**2 = 0 for v.
-2, 5
Let u be (-166)/(-172) - (5 + -4). Let h = 667/602 - u. Determine g so that 6/7*g**4 + 0 - h*g**3 + 0*g + 2/7*g**2 = 0.
0, 1/3, 1
Let g = 1935/4277 - -3/329. Let f = g - 17/65. Factor 2/5*l - 3/5 + f*l**2.
(l - 1)*(l + 3)/5
Let q(j) = j**2 + j. Suppose -2 = 2*z + 4. Let r(t) = -3*t**3 + 18*t**2 - 18*t + 9. Let k(h) = z*q(h) + r(h). Factor k(m).
-3*(m - 3)*(m - 1)**2
Suppose 5*y + 32*i = 37*i + 5, -2*y + 14 = 4*i. What is d in 0*d + 3/8*d**y - 3/8*d**2 + 0 = 0?
0, 1
Let n(m) be the first derivative of m**5/80 + m**4/48 - m**3/24 + 5*m**2 + 2*m + 5. Let g(a) be the second derivative of n(a). Determine r so that g(r) = 0.
-1, 1/3
Let m(s) be the third derivative of 0*s**3 - 7/6*s**6 - 2/3*s**4 + 36*s**2 + 0*s + 22/15*s**5 + 5/21*s**7 + 0. Solve m(v) = 0 for v.
0, 2/5, 2
Let x(g) be the third derivative of -20*g**2 + 2*g - 27/32*g**4 - 13/8*g**3 + 0 - 1/40*g**5. Factor x(p).
-3*(p + 13)*(2*p + 1)/4
Let 1854*z**3 - 44*z + 60 + 19*z**2 + 108*z - 1853*z**3 = 0. What is z?
-15, -2
Let s(x) = -3*x - 1. Let i be s(-1). Suppose -16*g + i*g**3 - 34*g**2 + 0*g**3 + 0*g**3 + 12*g**4 - 16*g - 8 = 0. What is g?
-1, -2/3, -1/2, 2
Let n be 16 + -16 - (24/9 - 4). Find h, given that -n*h + 4/3 + 4/3*h**3 - 1/3*h**4 - h**2 = 0.
-1, 1, 2
Let w(z) be the second derivative of 1/9*z**4 + 0 + 4*z**2 - 14/9*z**3 - 27*z. Find s, given that w(s) = 0.
1, 6
Let n be (-4)/((2/3)/((-3)/9)). Let z(s) be the first derivative of 0*s**2 + 1/4*s**4 + 0*s - n + 1/3*s**3. Factor z(c).
c**2*(c + 1)
Let i(y) be the third derivative of 1/80*y**6 + 0*y**5 - 3/16*y**4 - 1/2*y**3 - 18*y**2 + 0*y + 0. Solve i(k) = 0 for k.
-1, 2
Factor 45 + 77*b - 77 + 62*b**3 + 23*b - 28 - 5*b**2 - 77*b**3.
-5*(b - 2)*(b + 3)*(3*b - 2)
Suppose b + 3*f - 8 = 0, -4*b + 7*f - 2*f = 2. Let q(h) be the first derivative of 5 + 2/15*h**3 - 1/5*h**b - 4/5*h. Factor q(j).
2*(j - 2)*(j + 1)/5
Let y(c) be the third derivative of 26*c**2 - 1/90*c**5 - 64/9*c**3 + 0*c + 0 - 4/9*c**4. Factor y(k).
-2*(k + 8)**2/3
Suppose -2*b - 19 = -3*c, -5*c - b - 2 = -25. Suppose 3*i - 14 = -c. Solve 3*u**5 - 3*u**i + 27*u**2 - 27*u**2 = 0 for u.
-1, 0, 1
Suppose 3*n - 5*d - 8 = 0, -4*d - 6 = -4*n + 2. Let m(w) be the first derivative of 2/3*w**3 + 1/4*w**4 + 0*w + 1/2*w**2 - n. Let m(l) = 0. What is l?
-1, 0
Suppose 2*j + 2*j = -z + 14, 0 = 5*j - 15. Factor z*i**2 - 6*i**3 - 3*i**4 - 5*i**2 - 4*i**4 + 4*i**4.
-3*i**2*(i + 1)**2
Let p(y) = 12*y - 2. Let t be p(1). Factor -b**2 + 20*b**5 - t*b**4 - 12*b**3 + 9*b**2 + 16*b - 22*b**5.
-2*b*(b - 1)*(b + 2)**3
Suppose -3*f + 7 = -3*k - 53, 0 = -5*f + k + 84. Let z be 4*(22/(-33))/(f/(-18)). Factor 0 - 3/7*c**z + 3/7*c**2 + 0*c.
-3*c**2*(c - 1)/7
Suppose 0 = -4*m + 3*a - 7, 5*m - 3*m = -2*a. Let n be 1/10*m*(-8 + 0). Factor 3/5 + 7/5*p + n*p**2.
(p + 1)*(4*p + 3)/5
Let w(c) be the second derivative of -c**5/20 - c**3/6 - 2*c. Let h be w(-1). Find x such that -2/7*x**3 + 6/7*x + 0*x**h - 4/7 = 0.
-2, 1
Let g(i) = -i**3 - 4*i**2 + i + 9. Let z be g(-4). Let p = 6 + -3. Factor -p*c**2 + 6*c - 3 + z + 7.
-3*(c - 3)*(c + 1)
Let u(j) = -8*j**3 + 85*j**2 + 421*j + 448. Let k(c) = -12*c**3 + 128*c**2 + 632*c + 672. Let a(d) = -5*k(d) + 8*u(d). Suppose a(i) = 0. What is i?
-2, 14
Let z(j) be the third derivative of 0*j - 1/30*j**4 - 10*j**2 + 0 + 1/525*j**7 + 0*j**5 + 1/150*j**6 - 1/15*j**3. Solve z(q) = 0.
-1, 1
Factor 19*p - 1/2*p**2 + 0.
-p*(p - 38)/2
Let r(c) be the third derivative of -c**5/30 - 31*c**4/12 + 32*c**3/3 - 5*c**2 + 106*c. Factor r(x).
-2*(x - 1)*(x + 32)
Let i = -1/5632 - -22535/39424. Solve -32/7 + 48/7*l + i*l**3 - 24/7*l**2 = 0 for l.
2
Let k(u) be the third derivative of 25*u**7/14 - 115*u**6/6 + 8*u**5/3 + 110*u**4/3 - 40*u**3 + 57*u**2 + 1. Let k(o) = 0. What is o?
-2/3, 2/5, 6
Let z be 1/((-19)/(-475)) + 