that s(b) = 0.
-1, 0, 1
Let x(b) be the first derivative of -2*b**3/3 + 5*b**2 - 12*b + 21. Factor x(u).
-2*(u - 3)*(u - 2)
Let h = 251 - 6023/24. Let a(r) be the second derivative of h*r**3 + 3*r + 1/4*r**2 + 0 - 1/48*r**4. What is y in a(y) = 0?
-1, 2
Let a(f) = -3*f + 28. Let x be a(8). What is t in 7/4*t**3 - 5/4*t**x + 1 + 1/4*t**5 + 1/4*t**2 - 2*t = 0?
-1, 1, 2
Determine q so that 0 - 2/5*q - 128/5*q**5 + 24/5*q**2 + 192/5*q**4 - 104/5*q**3 = 0.
0, 1/4, 1/2
Let d be 8/2*(-2)/(-4). Let o(h) be the second derivative of 1/84*h**7 + 3/40*h**5 - 1/24*h**4 + 0 + 0*h**3 - 1/20*h**6 - 3*h + 0*h**d. Factor o(u).
u**2*(u - 1)**3/2
Let i(o) be the second derivative of 0*o**3 + 0 + 0*o**2 + 0*o**4 - 1/30*o**6 - o + 1/20*o**5. Factor i(y).
-y**3*(y - 1)
Let i(w) = 1 - w**2 - w + w**2 + 5*w**2 + 4*w. Let v(p) = -p**2 - p - 1. Let n(a) = -i(a) - 3*v(a). Determine q, given that n(q) = 0.
-1, 1
Let l(z) be the second derivative of -3*z - 1/6*z**3 + 0 + 0*z**2 + 1/20*z**5 - 7/60*z**6 + 7/24*z**4. Factor l(k).
-k*(k - 1)*(k + 1)*(7*k - 2)/2
Let n(u) be the first derivative of -u**3/12 - u**2/4 - u/4 + 5. Suppose n(s) = 0. What is s?
-1
Let r(m) be the second derivative of -m**4/42 - 2*m**3/21 + 3*m**2/7 + 4*m. Factor r(x).
-2*(x - 1)*(x + 3)/7
Let y = -1/32 - -19/96. Factor 1/6*t + 0 - y*t**2.
-t*(t - 1)/6
Let o(k) = 2*k**2 + 3*k. Let u be o(-2). Suppose -2*z + y + 0*y + u = 0, -2*y = -2*z. Determine v so that -v**2 + z + v - 2 = 0.
0, 1
Let r = 1095/286 - 57/26. Solve 12/11*u**2 + r*u + 2/11*u**3 + 0 = 0.
-3, 0
Let p = 12 + -10. Let c be (p/25)/((-1)/(-30)). Factor 2/5*x**3 - c*x**2 + 24/5*x - 16/5.
2*(x - 2)**3/5
Let b = 9 - 8. Let m be b/((-1)/(14/(-2))). Find w, given that 145*w**2 + 49*w**5 + 166*w**3 + 4 + 175*w**4 + m*w + 69*w**3 + 33*w = 0.
-1, -2/7
Let x(c) be the first derivative of c**4/28 - 2*c**3/21 - 3*c**2/14 - 5. Factor x(j).
j*(j - 3)*(j + 1)/7
Let s(f) be the second derivative of -5*f**7/42 - 3*f**6 - 61*f**5/4 + 75*f**4 - 250*f**3/3 - 2*f - 2. What is m in s(m) = 0?
-10, 0, 1
Let y(k) be the second derivative of k**6/105 + 3*k**5/70 + k**4/42 - k**3/7 - 2*k**2/7 - 17*k. Factor y(n).
2*(n - 1)*(n + 1)**2*(n + 2)/7
Suppose 13 = 2*b - g - 0*g, -23 = -2*b + 3*g. Factor b*w**2 + 2*w**5 - w - w - 2*w**4 - 2*w**4.
2*w*(w - 1)**3*(w + 1)
Let q = 1575/13 + -121. Factor 0 - 2/13*o**5 + 0*o**2 + 4/13*o**3 + 0*o + q*o**4.
-2*o**3*(o - 2)*(o + 1)/13
Let d(r) be the first derivative of 0*r**2 + 2 - r**3 - 1/360*r**6 + 0*r**4 + 0*r + 1/120*r**5. Let h(a) be the third derivative of d(a). Factor h(x).
-x*(x - 1)
Let r(a) = -a + 7. Let g be r(7). Suppose 2*p - 3 - 1 = g. Solve 1/4*k**p - 1/2*k + 1/4 = 0.
1
Let l be 68/51 - 13/3. Let m be 2/6 - l/(-36). Factor 1/4*j**2 - m*j**3 + 1/4*j - 1/4.
-(j - 1)**2*(j + 1)/4
Let t(p) be the third derivative of -p**5/15 + p**4/3 + 2*p**3 + 4*p**2. Let t(b) = 0. Calculate b.
-1, 3
Let n = 598/5 - 119. Factor 2/5 + 0*p**2 + n*p - 1/5*p**3.
-(p - 2)*(p + 1)**2/5
Let d(h) be the first derivative of -3*h**5/35 - 3*h**4/14 + 3*h**3/7 + 24. Suppose d(n) = 0. Calculate n.
-3, 0, 1
Let k(w) be the third derivative of -w**6/40 + 3*w**4/8 + w**3 + 8*w**2. Find f, given that k(f) = 0.
-1, 2
Let j = -8 - -13. Suppose -w = 3*g + 3*w, -5*w + 5 = j*g. Let 2/3*q**3 + 0 + 0*q + 1/3*q**2 + 1/3*q**g = 0. What is q?
-1, 0
Let w(l) be the second derivative of l**6/30 - l**5/20 - l**4/4 + l**3/6 + l**2 + 13*l. Solve w(z) = 0 for z.
-1, 1, 2
Let c(g) be the first derivative of 9 + 0*g**3 + 0*g**2 - 1/6*g**4 + 0*g. Find b such that c(b) = 0.
0
Suppose -2*f - 5*p + 4 = 0, -f = -4*f + 3*p + 6. Find j such that -2/5 - 2/5*j**f - 4/5*j = 0.
-1
Suppose 8 = -4*y + 4*a, 5*a - 10 = -3*y - 0*a. Let x(v) be the first derivative of -2 - 1/3*v**3 + 0*v + y*v**2. What is j in x(j) = 0?
0
Let h = 695 + -3463/5. Factor 2*y**2 + h*y + 2/5.
2*(y + 1)*(5*y + 1)/5
Suppose 0 = -0*s + s - 5. Let j = 13 - 11. Suppose -s*b + 1 - 7*b**j + 2 - 4 + 3 = 0. Calculate b.
-1, 2/7
Let k(p) be the third derivative of p**6/420 + p**5/210 - p**4/84 - p**3/21 - 65*p**2. Factor k(c).
2*(c - 1)*(c + 1)**2/7
Let v(f) be the second derivative of -5*f + 1/3*f**3 + 4/45*f**6 - 2/3*f**2 + 1/2*f**5 + 8/9*f**4 + 0. Suppose v(x) = 0. Calculate x.
-2, -1, 1/4
Let b be 4/14 - (4 - (-156)/(-42)). Factor b*d + 0*d**2 + 0 - 1/4*d**3 + 1/4*d**4.
d**3*(d - 1)/4
Let f(c) = c**3 - 5*c**2 + 4. Suppose -24 = -3*b - 9. Let u be f(b). Determine w so that 2/9*w + 0*w**3 - 2/9*w**5 + 4/9*w**2 - 4/9*w**u + 0 = 0.
-1, 0, 1
Let a(d) be the first derivative of -d**9/6048 + d**7/1680 + d**3/3 - 10. Let c(f) be the third derivative of a(f). Factor c(z).
-z**3*(z - 1)*(z + 1)/2
Let n(g) = -g**3 - 29*g**2 - g - 24. Let z be n(-29). Suppose 2/7*u**z - 2/7*u**2 + 0*u - 6/7*u**4 + 0 + 6/7*u**3 = 0. Calculate u.
0, 1
Let k(o) be the second derivative of o**7/420 - o**6/120 + o**5/120 + o**2 + o. Let t(u) be the first derivative of k(u). Factor t(d).
d**2*(d - 1)**2/2
Let z(m) = m**3 + 7*m**2 - m - 5. Let i be z(-7). Factor 4*n**3 - n**2 + 7*n**2 - 2*n**i.
4*n**2*(n + 1)
Suppose -4*l - 277 = -3*j, 6*l - l = 4*j - 346. Let d = 634/9 + l. Find z, given that 2/9*z + 2/9*z**2 - d = 0.
-2, 1
Let y be (-2 - -3 - 0) + -3. Let i = y - -4. Find t such that 3*t**2 - t**2 - 4*t**i = 0.
0
Let l = 1 + 1. Factor q**l + 5*q**2 - 2 + 18*q**2 + 2*q.
2*(3*q + 1)*(4*q - 1)
Let c be (2/7)/(1/7). Find p, given that 3*p**c - 5*p**3 - 9*p - 6*p**2 + 7*p**2 + 8*p**2 + 2 = 0.
2/5, 1
Let p(t) be the third derivative of t**5/240 + t**4/48 + 2*t**2. Find z, given that p(z) = 0.
-2, 0
Factor 3/2 - 1/2*r**4 - r**2 - 2*r + 2*r**3.
-(r - 3)*(r - 1)**2*(r + 1)/2
Let y(t) be the first derivative of t**6/15 - 6*t**5/25 - t**4/10 + 2*t**3/5 + 20. Find w such that y(w) = 0.
-1, 0, 1, 3
Let h(y) be the second derivative of y**5/30 - 2*y**4/9 + 5*y**3/9 - 2*y**2/3 - 4*y. Solve h(s) = 0.
1, 2
Let b(v) be the first derivative of -3*v**2 + 0*v**3 + 2 - 4*v + 1/2*v**4. Factor b(n).
2*(n - 2)*(n + 1)**2
Let y(o) be the second derivative of -o**4/4 - o**3/2 - 2*o. Determine z so that y(z) = 0.
-1, 0
Let i(t) be the first derivative of -t**3 + 12*t**2 - 48*t - 2. Let i(u) = 0. Calculate u.
4
Let t(p) = p**2 - 8*p + 9. Let z be t(7). Suppose -7*w + w = 0. Find m, given that 10/11*m**z + 4/11*m + w = 0.
-2/5, 0
Let n(y) be the first derivative of -1 - 4/15*y**3 + 2*y + 1/5*y**2 + 1/10*y**4. Let d(h) be the first derivative of n(h). Factor d(a).
2*(a - 1)*(3*a - 1)/5
Let m = -263 - -6313/24. Let j(b) be the third derivative of -1/120*b**5 - m*b**4 + 0*b + 0 - 1/12*b**3 - b**2. Factor j(w).
-(w + 1)**2/2
Let l(f) = f**3 + 6*f**2 + 7*f + 5. Let m be l(-4). Let g = -5 + m. Solve 2/3*y**2 + 0 + 0*y**3 - 2/3*y**g + 0*y = 0.
-1, 0, 1
Let u(j) = -j**3 + 14*j**2 + j - 20. Let l be u(14). Let i be 2 - (10/l - -3). Factor 0 + i*o + 2/3*o**2.
2*o*(o + 1)/3
Let a = 159 + -156. Factor 1/3*q**2 + 0 + 1/3*q**a + 0*q.
q**2*(q + 1)/3
Suppose -4*p - 3*g + 132 = 0, 0 = p - 2*g - 0*g - 33. What is h in -3*h**5 + 0*h**5 + 24*h**2 - 36*h**3 - 15*h**4 + p*h**4 = 0?
0, 2
Let x(b) = 7*b**2 + 76*b - 9. Let q be x(-11). Let -8/9*p**4 + 2/3*p**5 - 2/9*p + 8/9*p**q - 4/9*p**3 + 0 = 0. Calculate p.
-1, 0, 1/3, 1
Let -20*s + 145/2*s**2 - 49/2*s**5 + 175/2*s**4 - 235/2*s**3 + 2 = 0. Calculate s.
2/7, 1
Let y(r) = -4*r**3 - 2*r**2 - 2. Let x be y(-2). Let f = x - 19. Find c such that 1/4 - 1/2*c**f + 1/4*c + 1/4*c**5 + 1/4*c**4 - 1/2*c**2 = 0.
-1, 1
Let n(q) be the first derivative of -5*q**6/6 + 5*q**4/4 + 15. Suppose n(z) = 0. What is z?
-1, 0, 1
Let s(r) be the second derivative of 1/18*r**4 + 1/5*r**5 - r + 0 + 1/45*r**6 + 0*r**2 - 2/63*r**7 - 2/9*r**3. Solve s(u) = 0.
-1, 0, 1/2, 2
Suppose 2*h - 6 = -0*h. Suppose 5*b**h - 13*b**2 - 2*b**4 + 4*b**3 - 4 - 3*b**3 + 12*b + b**4 = 0. What is b?
1, 2
Factor 2/9*n**4 - 2/3 - 4/3*n**2 + 16/9*n + 0*n**3.
2*(n - 1)**3*(n + 3)/9
Factor -1/8*f**3 - 5/8*f**2 - 3/8*f + 9/8.
-(f - 1)*(f + 3)**2/8
Let l = -36 + 150. Let m = l + -338/3. Factor -10/3*f**5 + m*f**2 - 16/3*f**4 + 0 + 0*f - 2/3*f**3.
-2*f**2*(f + 1)**2*(5*f - 2)/3
Let d(p) be the third derivative of 0*p + 0 + 2*p**2 + 0*p**3 + 1/90*p**5 - 1/18*p**4. Let d(n) = 0. Calculate n.
0, 2
Let z(p) be the second derivative of p**7/21 - p**6/30 - 3*p**5/20 + p**4/12 + p**3/6 - 18*p. Factor z(s).
s*