 - 5 = -2*q, 5*q = -3*u + 20. Factor -1/4 + 27/4*o**z + 45/2*o**3 + 11/4*o - 23/2*o**2 - 81/4*o**q.
(o - 1)**2*(3*o - 1)**3/4
Determine h so that 8/7*h + 2/7*h**2 + 8/7 = 0.
-2
Solve 8/9*g**2 + 10/9*g + 2/9*g**3 + 4/9 = 0 for g.
-2, -1
Let n(r) be the first derivative of -r**7/210 + r**6/30 - r**5/10 + r**4/6 - 8*r**3/3 - 7. Let s(v) be the third derivative of n(v). Factor s(q).
-4*(q - 1)**3
Let d(w) = -4*w**2 - 2*w**3 - 5*w + 4 - 1 + 1 + 3*w**3. Let b be d(5). Solve 2/5*v**3 - 2/5*v**2 + 0 - 2/5*v + 2/5*v**b = 0.
-1, 0, 1
Let s = 1 + -2. Let b be -1 + 2 + s/3. What is i in 2/3*i**2 - 4/3*i + b = 0?
1
Let x(w) be the third derivative of w**6/420 - w**4/84 - 20*w**2. Factor x(v).
2*v*(v - 1)*(v + 1)/7
Factor 0 + 2/7*b + 0*b**2 - 2/7*b**3.
-2*b*(b - 1)*(b + 1)/7
Let u = -4 + 8. Suppose -s**4 + 8*s**5 - 4*s**3 + 0*s**4 + 2*s**2 - s**u - 4*s**3 = 0. What is s?
-1, 0, 1/4, 1
Let m(i) be the third derivative of -i**5/15 + i**4/2 + 3*i**2. Suppose m(x) = 0. Calculate x.
0, 3
Let v(x) be the second derivative of x**7/231 - x**5/110 - x. Factor v(u).
2*u**3*(u - 1)*(u + 1)/11
Let y(s) be the first derivative of s**4/16 - 4*s**3/3 + 8*s**2 + 3. Solve y(o) = 0.
0, 8
Suppose 3*t - 5 = 2*t. Let s(a) be the first derivative of -1 + 1/5*a**t - 1/3*a + 1/18*a**6 - 2/9*a**3 + 1/6*a**4 - 1/2*a**2. Factor s(q).
(q - 1)*(q + 1)**4/3
Let p be -2 + 6 - (-28)/(-7). Factor p + 0*c + 1/5*c**4 + 0*c**3 + 0*c**2.
c**4/5
Let o(s) be the third derivative of s**5/150 - s**4/15 - 5*s**2 + 2. Factor o(i).
2*i*(i - 4)/5
Let h be -3 + -6*(-9)/21 - -3. Suppose h + 12/7*u + 2/7*u**2 = 0. Calculate u.
-3
Let a(w) be the second derivative of -3*w**5/20 - 3*w**4/4 + 6*w**2 + 53*w. Solve a(i) = 0.
-2, 1
Factor 3/4*q**4 + 0 + 9/4*q - 15/4*q**2 + 3/4*q**3.
3*q*(q - 1)**2*(q + 3)/4
Let c(m) be the second derivative of 5*m**5/18 + 5*m**4/27 + m**3/27 - 4*m. Solve c(n) = 0 for n.
-1/5, 0
Let y(j) be the second derivative of 4/15*j**6 + 2*j**2 - 3*j + 1/7*j**7 - 2/5*j**5 + 0 + 1/3*j**3 - j**4. Determine s, given that y(s) = 0.
-1, 2/3, 1
Suppose 0 = -5*f - 0*f + 5. Factor -f - 3 + 0 + t + 2 + t**2.
(t - 1)*(t + 2)
Find n such that 0*n - 2/11*n**2 + 2/11 = 0.
-1, 1
Let u be -3*4/(-3) - 2. Let a(g) be the first derivative of -u + 0*g**2 - 2/3*g**3 + 1/3*g**6 + 2/5*g**5 + 0*g - 1/2*g**4. Suppose a(v) = 0. What is v?
-1, 0, 1
Let x(d) be the second derivative of -d**7/840 - d**6/360 + d**5/120 + d**4/24 - d**3/3 + 2*d. Let t(a) be the second derivative of x(a). Factor t(h).
-(h - 1)*(h + 1)**2
Find s, given that 2*s**3 + 1 - 13 + 6*s**2 - 36 - 26*s**2 + 56*s = 0.
2, 6
Let a be 1/10*8*20. Determine p, given that -48*p**3 + 4*p + a*p**3 - 20*p**2 + 12*p**4 + 20*p = 0.
-1, 0, 2/3, 3
Let m(d) = -d + 13. Let p be m(9). What is n in p - 2*n**3 - 4 + 0*n**3 = 0?
0
Suppose 0*b + 2*c + 12 = -2*b, b + 10 = -2*c. Let v(o) = -2*o - 2. Let g be v(b). Factor -3 - 3/2*a + 3/2*a**3 + 3*a**g.
3*(a - 1)*(a + 1)*(a + 2)/2
Let a(j) = -j**2 + j + 1. Let b(c) = 5*c**2 - 7*c - 4. Let d(n) = -12*a(n) - 3*b(n). Determine g so that d(g) = 0.
0, 3
Let m(g) = -4*g**2 + 13*g + 7. Let q(x) = -3*x**2 + 12*x + 7. Let s(o) = -4*m(o) + 5*q(o). Suppose s(w) = 0. What is w?
-7, -1
Let n be 6/(0 + 12)*(-2)/(-2). Find j such that -1/6 + 1/2*j - n*j**2 + 1/6*j**3 = 0.
1
Let g = -266 + 270. Factor -1/2*k**g + 0 - 1/2*k**2 + 0*k + k**3.
-k**2*(k - 1)**2/2
Suppose 16 = -2*l + l + 4*w, -5*l - w - 17 = 0. Let j be ((-6)/9)/(l/18). Let -2*p**2 + 3 + 2*p - 2*p**j + 1 - 4 + 2 = 0. Calculate p.
-1, 1
Factor 0*b**4 + 2/15*b + 0*b**2 + 2/15*b**5 - 4/15*b**3 + 0.
2*b*(b - 1)**2*(b + 1)**2/15
Let d(b) be the first derivative of -1/3*b**3 + 0*b - 3 + b**2. Determine n, given that d(n) = 0.
0, 2
Factor -4*a - 5*a**3 + 9*a**3 + 4*a - 4*a**5.
-4*a**3*(a - 1)*(a + 1)
Let v be 3/12 - 111/448. Let o(p) be the third derivative of 0*p**4 + 0*p**3 - v*p**8 - 1/240*p**6 + 0*p**5 + 0*p + 0 - 1/168*p**7 + p**2. Factor o(b).
-b**3*(b + 1)*(3*b + 2)/4
Let d be (-10)/(-4)*(-112)/70. Let i be d/10 + 663/170. Factor 1 - 7/2*n**3 - n**2 + i*n.
-(n - 1)*(n + 1)*(7*n + 2)/2
Let k(a) be the second derivative of 5/2*a**3 + 3*a**2 + 1/5*a**6 + 5/14*a**7 - a**4 + 0 - 3*a - 3/2*a**5. Suppose k(z) = 0. What is z?
-1, -2/5, 1
Let n = 25 + -23. Let -4*c**5 + 2*c**4 + 2 - c**2 + 3*c**5 - 4*c**3 - 6*c**4 + 3*c**n + 5*c = 0. Calculate c.
-2, -1, 1
Let o(s) = s**3 - 8*s**2 - 7*s - 13. Suppose 3*h - 18 = -2*l + 19, -14 = -h - l. Let b be o(h). Solve 5*q**3 - 5*q**2 - 3*q**3 - b*q**3 - 2*q = 0.
-1, -2/3, 0
Let b(q) = 27*q**2 - 12*q - 6. Suppose 3*m = 10 + 8. Let n(s) = -s - 1. Let i(z) = m*n(z) - b(z). Factor i(v).
-3*v*(9*v - 2)
Suppose -32/3*u + 1/3*u**2 + 256/3 = 0. Calculate u.
16
Let q(w) be the third derivative of w**8/896 + w**7/112 - w**6/64 - 5*w**5/32 + 5*w**4/8 - w**3 - 9*w**2. Suppose q(v) = 0. What is v?
-4, 1
Let b(p) = -8 + 3 + 5 + 8*p. Let h be b(1). Let -44*c**3 - 9/2*c**5 + 24*c**4 - h*c + 0 + 32*c**2 = 0. Calculate c.
0, 2/3, 2
Let x = -8 + 12. Find j, given that -6*j**3 - 10*j**x + 2*j**4 - 7*j**4 + 8*j + 16*j**2 - 3*j**4 = 0.
-2/3, 0, 1
Solve f**2 + 0*f + 0 + 1/2*f**3 = 0.
-2, 0
Factor -2/3 + 2/9*w**2 - 4/9*w.
2*(w - 3)*(w + 1)/9
Factor 47*w**2 - 15*w**2 - 17*w**2 - 16 + 16*w - 19*w**2.
-4*(w - 2)**2
Determine s, given that 3/8*s**4 + 3*s**2 - 27/8 - 9/4*s + 9/4*s**3 = 0.
-3, -1, 1
Suppose -3*h + 2 = -2*t, -5*h - 2*t = -22 - 8. Suppose h*c + 18 + 10 = 4*a, -2*c = 10. Solve 2*b**2 - a*b - 6*b**2 + b**2 - 4*b = 0 for b.
-2, 0
Suppose 0 = -3*h - 12 - 0. Let v(b) = b**2 + b + 1. Let r(j) = j**3 + 3*j**2 + 5. Let y(l) = h*r(l) + 12*v(l). Factor y(a).
-4*(a - 1)**2*(a + 2)
Let b(u) be the third derivative of -u**6/120 + 7*u**5/180 - u**4/36 - u**2. Find p, given that b(p) = 0.
0, 1/3, 2
Factor -37*q**2 + 40*q**2 - 3*q**3 + 0 + 0.
-3*q**2*(q - 1)
Let s(a) be the first derivative of -2 + 1/6*a**4 - 2/3*a**3 + a**2 - 2/3*a. Suppose s(m) = 0. What is m?
1
Let f(k) = -7*k**2 - k + 13. Let j(v) = -11*v**2 - v + 20. Let y(x) = -8*f(x) + 5*j(x). Factor y(r).
(r - 1)*(r + 4)
Let h(i) be the first derivative of -i**4/4 + 2*i**3/3 + i**2/2 - 2*i + 2. Suppose h(z) = 0. Calculate z.
-1, 1, 2
Suppose -5*o + 3 = 3*m, 0*m - m = 2*o - 2. Let b be (6 - 3)/(33/6 + -4). Determine u, given that 0*u**b + 2/5*u - 2/5*u**o + 0 = 0.
-1, 0, 1
Let i(f) be the first derivative of 2/3*f**3 - 3 + 0*f**2 - 1/5*f**5 + 1/4*f**4 + 0*f. Suppose i(q) = 0. What is q?
-1, 0, 2
Let o = 140 - 137. Find b, given that -3/4*b**4 + o*b**3 - 9/2*b**2 - 3/4 + 3*b = 0.
1
Let j be (-5)/(105/(-24))*(-63)/(-90). Solve j*s**2 + 2/5 + 6/5*s - 6/5*s**4 - 2/5*s**5 - 4/5*s**3 = 0 for s.
-1, 1
Let f(t) be the second derivative of -t**5/120 - t**4/12 - t**3/3 - 2*t**2/3 - 31*t. Solve f(a) = 0 for a.
-2
Suppose 3*u - 5*u = -2. Let m be 20/5 + u + -2. Let -1 + 8*c + 49/4*c**m - 77/4*c**2 = 0. What is c?
2/7, 1
Let h(n) = 85*n**4 - 80*n**3 - 80*n**2. Let i(d) = 21*d**4 - 20*d**3 - 20*d**2. Let c(p) = 6*h(p) - 25*i(p). Let c(t) = 0. What is t?
-2/3, 0, 2
Suppose 2*i + 5*o = 4*o, -5*o - 18 = i. Factor 0*f**i + 0 - 2/5*f**3 + 2/5*f.
-2*f*(f - 1)*(f + 1)/5
Let s(z) be the third derivative of -z**7/840 + z**5/120 - z**3/24 + 2*z**2. Suppose s(o) = 0. What is o?
-1, 1
Let p = 147/125 + 3/125. Let w(d) be the first derivative of 1 - 5/8*d**4 - d**2 + 0*d + 3/4*d**6 + 2*d**3 - p*d**5. Suppose w(k) = 0. What is k?
-1, 0, 2/3, 1
Let u(z) = 3*z**3 - 4*z**2 + z. Let h(o) = -2*o**3 + 3*o**2 - o. Let a(n) = -4*h(n) - 3*u(n). Factor a(p).
-p*(p - 1)*(p + 1)
Let g = -1321/7 - -189. Let h = 1578 - 11042/7. Find l, given that 0 + h*l + g*l**2 - 6/7*l**3 = 0.
-2/3, 0, 1
Factor 0*h**2 + 0*h**2 - 125 + 50*h - h**2 - 4*h**2.
-5*(h - 5)**2
Let a = -3 - -7/2. Factor -1/4*z + 0 - a*z**4 + 1/2*z**2 + 0*z**3 + 1/4*z**5.
z*(z - 1)**3*(z + 1)/4
Let z(w) be the second derivative of -w**7/2100 - w**6/225 - w**5/60 - w**4/30 - 5*w**3/6 - 6*w. Let x(h) be the second derivative of z(h). Factor x(g).
-2*(g + 1)**2*(g + 2)/5
Let c(s) be the third derivative of 3*s**2 + 1/110*s**5 + 1/33*s**3 + 0 + 0*s - 1/44*s**4 - 1/660*s**6. Let c(k) = 0. Calculate k.
1
Let c(x) = x**3 + 2*x**2 - x + 7. Let o(y) = y**3 + 3*y**2 + 8. Let h(a) = 4*c(a) - 3*o(a). Factor h(s).
(s - 2)*(s - 1)*(s + 2)
Let w(b) be the first derivative of -3*b**4/28 - b**3/7 - 5. Factor w(