**2/10 - 11. Factor d(f).
-f*(f - 1)*(f + 1)/5
Let d be (-8)/6 + -9 + (-6 - -17). Factor -1/3*b**2 - d*b + b**3 + 0.
b*(b - 1)*(3*b + 2)/3
Let r(y) be the first derivative of -2*y**3 + y**2 + 6. Factor r(c).
-2*c*(3*c - 1)
Suppose -8*l + 13*l = -6*l. Factor -2/9*d**5 - 4/9*d**2 + 0 + l*d - 10/9*d**3 - 8/9*d**4.
-2*d**2*(d + 1)**2*(d + 2)/9
Factor -4/7*i**3 + 0 + 5/7*i**2 + 1/7*i**4 - 2/7*i.
i*(i - 2)*(i - 1)**2/7
Solve 5*o**5 - 10*o**2 + 9*o**5 - 20*o**3 + 5*o**3 - 9*o**5 = 0 for o.
-1, 0, 2
Let u be ((-2)/5)/((16/(-10))/2). What is c in u*c**3 + 1/6*c + 1/2*c**2 + 1/6*c**4 + 0 = 0?
-1, 0
Let p(s) = 2*s - 6. Let r be p(4). Suppose r*c = c. Suppose -x**3 + 5*x**2 + 0 - 2*x**2 + c*x + 1 - 3*x = 0. What is x?
1
Let o(f) be the third derivative of 0 + 0*f**3 - 2*f**2 - 1/24*f**4 - 1/40*f**6 - 1/20*f**5 - 1/210*f**7 + 0*f. Suppose o(h) = 0. What is h?
-1, 0
Let v = 1/30 + -1/102. Let h = 176/255 - v. Determine s so that -2/3*s**2 + 0*s + h = 0.
-1, 1
Let j(d) be the first derivative of -3/5*d**2 + 2/15*d**3 - 4/5*d + 2 + 2/25*d**5 + 3/10*d**4. Factor j(s).
2*(s - 1)*(s + 1)**2*(s + 2)/5
Let i(j) be the second derivative of -j + 0*j**2 + 1/12*j**4 - 1/540*j**6 + 1/3*j**3 + 0 + 1/90*j**5. Let n(y) be the second derivative of i(y). Factor n(m).
-2*(m - 3)*(m + 1)/3
What is i in -15/2*i**5 + 3/4*i**2 - 9/2*i**4 + 9/8*i**3 + 0 + 0*i = 0?
-1/2, 0, 2/5
Suppose 35*m - 12 = 29*m. Factor 2/3*n**3 - 1/3*n**m - 5/3*n - 2/3.
(n - 2)*(n + 1)*(2*n + 1)/3
Solve g + 4*g**2 + 2*g + 4*g - 3*g = 0.
-1, 0
Let 8/3*t - 2/3*t**2 + 0 = 0. What is t?
0, 4
Solve 0*s - 1/4*s**2 + 0 = 0.
0
Let a = -34 - -103/3. Factor a + 1/3*w**2 - 2/3*w.
(w - 1)**2/3
Let c(h) be the third derivative of -1/84*h**8 + 4/3*h**3 + 8/15*h**5 + 0*h + 2*h**2 + 0 - 4/105*h**7 + 7/6*h**4 + 1/15*h**6. Solve c(o) = 0.
-1, 2
Suppose 148 - 28 = 3*z. Suppose 4*x = -5*b - 7 + z, -b - 5 = -5*x. Factor 2*l + 2*l**2 - x*l**4 + l - 4*l + l**5.
l*(l - 1)**3*(l + 1)
Suppose 3*h + 1 = 7. Let q(l) be the first derivative of -4/3*l**3 + 7/2*l**2 - h + 2*l. Determine n so that q(n) = 0.
-1/4, 2
Factor -9*j + j + 24*j**2 - 19*j - 4*j**3 - 9*j + 16.
-4*(j - 4)*(j - 1)**2
Let x(v) = -3 - 5*v**2 + 3*v**2 - 2*v + v**2 - 2*v**2. Let q(y) = 4*y**2 + 2*y + 4. Let i(a) = -4*q(a) - 5*x(a). Find h, given that i(h) = 0.
1
Let y be (6/5)/((-1)/10). Let b = -10 - y. Factor 0 - 4/7*z**2 + 0*z - 16/7*z**4 + b*z**3 + 6/7*z**5.
2*z**2*(z - 1)**2*(3*z - 2)/7
Suppose -105 + 4*g**3 + 2*g - 5*g**2 - g**4 + 105 = 0. What is g?
0, 1, 2
Suppose 0 + 2/3*y**2 + 1/3*y + 1/3*y**3 = 0. What is y?
-1, 0
Let l(s) = 2*s**3 + 6*s**2 + 8*s. Let a = 15 + -12. Let q(v) = 2*v**3 + 6*v**2 + 9*v - 1. Let h(b) = a*l(b) - 2*q(b). Let h(y) = 0. Calculate y.
-1
Let m(n) be the first derivative of -n**6/600 + n**4/120 - n**2 - 2. Let j(l) be the second derivative of m(l). Factor j(y).
-y*(y - 1)*(y + 1)/5
Let -2/15 - 2/15*h + 2/15*h**2 + 2/15*h**3 = 0. Calculate h.
-1, 1
Suppose -7 = 8*v - 31. Let x(r) be the third derivative of 0 - 1/3*r**3 + 1/3*r**4 - v*r**2 - 2/15*r**5 + 0*r. Find t, given that x(t) = 0.
1/2
Factor 70*r**4 + 17*r**3 + 4*r + 17*r**2 + 11*r**2 + 52*r**3 + 25*r**5.
r*(r + 1)**2*(5*r + 2)**2
Let c be (-4 + 0)*(-2)/4. Suppose 0 = -2*l - 5*a + 20, 4*l - c*l = 5*a. Let -v**l - 2*v**4 + v**4 + 2*v**4 = 0. What is v?
0, 1
Factor -14 + 8*t + 14 + 16*t**2 + 10*t**3 + 2*t**4.
2*t*(t + 1)*(t + 2)**2
Let w(j) = -5*j**3 - 5*j**2 - 11*j - 3. Let f(q) = -19*q**3 - 21*q**2 - 43*q - 11. Let g(c) = 6*f(c) - 22*w(c). Let g(s) = 0. Calculate s.
-2, 0
Suppose -3*o = 5*b - 24, -2*b + 4*o = 3*o - 3. Let -10/7*g**b - 8/7*g + 0 - 16/7*g**2 - 2/7*g**4 = 0. Calculate g.
-2, -1, 0
Let w = 248/5 + -49. Determine v, given that 0 + w*v**3 + 1/5*v**4 + 3/5*v**2 + 1/5*v = 0.
-1, 0
Suppose 3*p - 16 = -7. Suppose 0 = -b - 2*b. Find z such that b - 2*z**p + 0*z + 1/3*z**2 + 3*z**4 = 0.
0, 1/3
Let g(t) = t**2 - 4*t - 3. Let w(h) = -2*h**2 + 9*h + 7. Let a(u) = -7*u. Let f be a(-1). Let z(v) = f*g(v) + 3*w(v). Determine i so that z(i) = 0.
0, 1
Factor 0 - 3/7*q + 5/7*q**3 - 2/7*q**4 + 4/7*q**2.
-q*(q - 3)*(q + 1)*(2*q - 1)/7
Let c(v) = -v**3 + 5*v**2 + 8*v - 2. Let j be c(6). Suppose 0*u - 5*u + j = 0. Factor -2/7*p**4 + 2/7*p**5 - 2/7*p**3 + 2/7*p**u + 0 + 0*p.
2*p**2*(p - 1)**2*(p + 1)/7
Factor -3*o**3 - 2*o**3 + 20 + 35*o - 31 - 19.
-5*(o - 2)*(o - 1)*(o + 3)
Factor -10/3*k**3 - 2/3 - 14/3*k - 22/3*k**2.
-2*(k + 1)**2*(5*k + 1)/3
Let k(d) = -3*d**3 + 8*d**2 + 6*d. Suppose -4*b + 17 = p, 0 = 2*b + 3*p - p - 4. Let s(w) = 3*w**3 - 7*w**2 - 6*w. Let u(l) = b*s(l) + 4*k(l). Factor u(i).
3*i*(i - 2)*(i + 1)
Suppose -18/17*t + 16/17 + 2/17*t**2 = 0. What is t?
1, 8
Let l(g) = g**2 - 6*g - 5. Let r be l(7). Suppose x - r*x + 9 = -a, 5*x - 36 = 2*a. Factor 2 - 2*b**3 - 3*b**2 - 4*b + b**2 + x*b.
-2*(b - 1)*(b + 1)**2
Let 1/2*i**2 + 0*i**3 + 1/4*i**5 + 0 - 1/4*i - 1/2*i**4 = 0. What is i?
-1, 0, 1
Let g(j) be the second derivative of -1/195*j**6 + 0*j**2 + 0*j**3 + 1/130*j**5 + 0*j**4 + 0 + j. Determine v so that g(v) = 0.
0, 1
Let t(v) be the second derivative of v**5/10 - 4*v**4/3 + 5*v**3/3 + 14*v**2 + 33*v. Factor t(m).
2*(m - 7)*(m - 2)*(m + 1)
Let d(b) be the third derivative of -b**5/30 + 5*b**4/6 - 25*b**3/3 - 6*b**2. Factor d(j).
-2*(j - 5)**2
Factor 8/9*m**3 + 8/9*m - 4/3*m**2 - 2/9 - 2/9*m**4.
-2*(m - 1)**4/9
Let q(p) = -p - 1. Let i(g) = g**3 + 2*g**2 - 8*g - 5. Let x = 2 + 3. Let y(k) = x*q(k) - i(k). Suppose y(t) = 0. Calculate t.
-3, 0, 1
Suppose f - 4*f + 18 = 0. What is g in 36*g + 1 - 16*g**2 - 3 - f = 0?
1/4, 2
Let m(w) be the third derivative of -3*w**6/40 - 13*w**5/20 - 5*w**4/3 - 2*w**3 - 23*w**2. Solve m(o) = 0.
-3, -2/3
Let k(n) be the third derivative of 7*n**5/45 + 37*n**4/18 + 20*n**3/9 + 23*n**2. Factor k(w).
4*(w + 5)*(7*w + 2)/3
Let h(u) be the first derivative of 6*u**5/35 - u**4/28 - 8*u**3/21 + u**2/14 + 2*u/7 + 27. Find o such that h(o) = 0.
-1, -1/2, 2/3, 1
Let c be 1183/52 - 2/(-8). Let i = -112/5 + c. Find u such that 3/5*u**2 - i*u + 0 = 0.
0, 1
Let c(l) = l**3 + 4*l**2 - 2*l + 2. Let n be (2/6)/((-3)/(-54)). Let z(h) = 2*h**3 + 5*h**2 - 3*h + 3. Let p(a) = n*c(a) - 4*z(a). Suppose p(t) = 0. What is t?
0, 2
Factor 9/2*u**5 - 2*u**3 - 5/2*u + 1 + 8*u**4 - 9*u**2.
(u - 1)*(u + 1)**3*(9*u - 2)/2
Let c(j) be the third derivative of -j**7/315 + j**6/30 - 2*j**5/15 + 5*j**4/18 - j**3/3 + 8*j**2. Solve c(k) = 0.
1, 3
Let w = 1/62 + 35/1674. Let m(d) be the second derivative of -1/135*d**6 - d + 0 - 1/189*d**7 - 1/9*d**2 - w*d**3 + 1/27*d**4 + 1/45*d**5. Factor m(j).
-2*(j - 1)**2*(j + 1)**3/9
Suppose -2*u + 4 + 4 = 0. What is q in 0*q**3 + 16*q**2 - 4*q**5 + 16*q**u - 24*q**3 - 4*q + 0*q = 0?
0, 1
Let c = -467/14 - -67/2. Let z(a) be the second derivative of -1/7*a**3 + c*a**2 + 2*a + 0 - 2/21*a**4. Factor z(j).
-2*(j + 1)*(4*j - 1)/7
Let u be ((-6)/8)/(84/(-32)). Let l = 7 - 4. Factor -2/7*b**2 + 0 + 0*b + u*b**l.
2*b**2*(b - 1)/7
Let h(r) be the first derivative of 4*r**3/3 + 8*r**2 - 3. Factor h(s).
4*s*(s + 4)
What is a in 2/11*a - 2/11*a**3 + 8/11 - 8/11*a**2 = 0?
-4, -1, 1
Factor 9 - 3/2*p**2 + 3/2*p.
-3*(p - 3)*(p + 2)/2
Suppose -4*d + 1 = -11, c + 4*d - 11 = 0. Let r(p) = p**2 - p + 1. Let b(z) = -2*z**2 - z + 4. Let f(v) = c*r(v) + b(v). Determine k so that f(k) = 0.
-1, 1
Let b(w) = -w**3 + w + 1. Let t(m) = -9*m**3 + 40*m**2 - 101*m + 94. Let a(p) = 4*b(p) - t(p). Solve a(g) = 0 for g.
2, 3
Let 0 + 0*x**3 - 6/13*x**2 + 4/13*x + 2/13*x**4 = 0. What is x?
-2, 0, 1
Let 0 + 6/11*z + 2/11*z**2 = 0. What is z?
-3, 0
Determine g so that -12/11 - 14/11*g**3 - 34/11*g**2 - 2/11*g**4 - 34/11*g = 0.
-3, -2, -1
Let w(i) be the third derivative of i**5/60 + i**4/12 + i**3/6 - 10*i**2. Factor w(t).
(t + 1)**2
Let x(c) be the second derivative of c**7/126 - c**6/90 - 4*c. Factor x(k).
k**4*(k - 1)/3
Suppose 5*j + 1 + 49 = 0. Let p = 12 + j. Factor -3 - 1 + q + 1 + 1 + q**p.
(q - 1)*(q + 2)
Let a(z) be the first derivative of -1/8*z**2 + 1/6*z**3 + 0*z - 1/16*z**4 - 6. Factor a(m).
-m*(m - 1)**2/4
Let m be 1 - (-1 + -2 - 0). Let -49*z**m + 486*z**3 - 68*z**5 + 44*z + 288*z**2 + 6 + 25*z + 211*z**4 - 175*z**5 = 0. Calculate z.
-1/3, 2
Let a(p) be the third derivative of 45*p**8/224 + 289*p**7/140 + 41*p**6/5 + 15*p**5 + 11*p**4 + 4*p**3 - 3*p**2. What is k