*q**2 + 3*q + 3. Let l(a) = -3*v(a) - 5*x(a). Factor l(i).
-i**2*(i + 1)*(5*i + 2)
Suppose 0 = -5*i + 4*k + 23, k - 4*k + 23 = 2*i. Suppose -i*l + 8 = -3*l. Factor -2*x**3 - 7*x**3 - 4*x + 7*x**3 - 6*x**l.
-2*x*(x + 1)*(x + 2)
Suppose -9*m = -3*m - 18. Factor 0*a - 6/13*a**2 - 4/13*a**m + 2/13.
-2*(a + 1)**2*(2*a - 1)/13
Let f be (-37)/(-13) - (-2)/13. Suppose -1 + 10 = f*y. What is c in 2/3 + 2/3*c**y + 2*c + 2*c**2 = 0?
-1
Let p(u) be the first derivative of 0*u**2 + 0*u + 4/9*u**3 - 7/9*u**6 + 32/15*u**5 - 11/6*u**4 - 2. Factor p(v).
-2*v**2*(v - 1)**2*(7*v - 2)/3
Let z(n) be the first derivative of -n**2 + 1 + 1/2*n**4 + 2*n**3 - 4*n - 2/5*n**5. Let z(x) = 0. What is x?
-1, 1, 2
Let j(a) be the first derivative of 2*a**3/9 + a**2/9 - 4*a/9 - 47. Suppose j(q) = 0. Calculate q.
-1, 2/3
Let i(f) = -9*f**3 + 4*f**2 - 5*f + 3. Let v(z) = -4*z**3 + 2*z**2 - 2*z + 1. Let j(u) = -3*i(u) + 7*v(u). What is s in j(s) = 0?
-1, 1, 2
Let w = 2551/2 + -1275. Find i such that -w*i**3 - 3/2*i + 3/2*i**2 + 1/2 = 0.
1
Let j = 16 + -12. Let r(u) be the second derivative of 1/2*u**2 - 1/12*u**j + 0 + u + 0*u**3. Factor r(q).
-(q - 1)*(q + 1)
Let f(x) be the first derivative of x**6/6 - 4*x**5/5 + 3*x**4/4 + 4*x**3/3 - 2*x**2 - 19. Solve f(y) = 0.
-1, 0, 1, 2
Let l = 115 + -352/3. Let c = l - -3. Solve 8/3*z - 8/3 - c*z**2 = 0.
2
Let g be -2 - -3 - 88/9. Let r = g + 9. Factor 4/9 + r*x**2 - 2/3*x.
2*(x - 2)*(x - 1)/9
Suppose -m - 1 = -4. Determine o, given that 4*o + 0*o - 2*o**4 - 5*o + o**m + 2*o**2 = 0.
-1, 0, 1/2, 1
Let r(k) be the second derivative of -3*k**7/14 - k**6/10 + k**5/4 - k**4/12 - k. Factor r(h).
-h**2*(h + 1)*(3*h - 1)**2
Let z = 12 + -9. Suppose -z*f = f. Solve 1/2 - 1/2*o**2 + f*o = 0.
-1, 1
Suppose 0 = -3*o + 2*l - 0*l + 17, 6 = 2*o + 4*l. Find g such that -16*g**2 + 6*g**3 + 8*g**4 + 8 + 3*g**3 + 4*g**3 - 4*g - 4*g**5 - o*g**3 = 0.
-1, 1, 2
Suppose -2*g + 10 = -10. Let r be (-15)/g + 14/4. Determine q, given that -3/2*q**r + 3*q - 18*q**3 - 27/2*q**4 + 0 = 0.
-1, -2/3, 0, 1/3
Let n be 33/55 + 14/10. Let z(t) be the first derivative of 2/9*t - 2/9*t**n - 2 + 2/27*t**3. Find v, given that z(v) = 0.
1
Let q(c) = -12*c - 4. Let w be q(-3). Factor 0*m + 10*m + 8*m**3 - w*m**3 - 4 - 2*m**2 + 8*m.
-2*(m + 1)*(3*m - 2)*(4*m - 1)
Let x = 6 - 6. Let t be x*(-3)/((-3)/1). Factor t*c + 2/5*c**3 + 0 + 2/5*c**2.
2*c**2*(c + 1)/5
Let n(a) = -27*a**4 + 42*a**3 - 18*a**2 - 12*a. Let z(c) = c**4 - c**3 + c. Let m(b) = n(b) + 15*z(b). Suppose m(d) = 0. Calculate d.
0, 1/4, 1
Let a(k) = -k**2 + 6*k - 3. Let c be a(5). Determine i, given that -2*i - 2*i - c*i - i**2 - 9 = 0.
-3
Suppose 42 + 8 = 10*y. Let -3/4*r**4 + 0*r + 0 + 1/4*r**y + 1/2*r**3 + 0*r**2 = 0. What is r?
0, 1, 2
Let f be (-12*10/1350)/(1/(-10)). Find d, given that 8/9 + 2/9*d**2 - f*d = 0.
2
Let w(p) = 99*p**3 - 156*p**2 + 60*p - 24. Let i(b) = 20*b**3 - 31*b**2 + 12*b - 5. Let a(u) = 24*i(u) - 5*w(u). Determine k, given that a(k) = 0.
0, 2/5, 2
Factor -2/15*m - 4/15*m**4 + 0 + 4/15*m**2 + 0*m**3 + 2/15*m**5.
2*m*(m - 1)**3*(m + 1)/15
Let m(g) be the third derivative of g**6/480 + g**5/240 - g**4/24 - g**3/6 + 2*g**2. Factor m(p).
(p - 2)*(p + 1)*(p + 2)/4
Factor -3/4*y**3 - 9/4 - 21/4*y - 15/4*y**2.
-3*(y + 1)**2*(y + 3)/4
Suppose 0*x + 4*x - 16 = 0. Factor 14*b**x + b**5 + 8*b**4 + 2*b**2 - 24*b**4 - b.
b*(b - 1)**3*(b + 1)
Factor 0*k - 3/2*k**3 + 0 + 9/2*k**4 - k**2.
k**2*(3*k - 2)*(3*k + 1)/2
Let h(s) be the third derivative of s**7/210 + 7*s**6/120 + 2*s**5/15 - 2*s**4/3 + 15*s**2. Let h(l) = 0. Calculate l.
-4, 0, 1
Let h be ((-1)/5)/((-32)/20). Let j(o) be the first derivative of 1/6*o**3 + h*o**4 - 1 - 1/4*o**2 - 1/2*o. Factor j(b).
(b - 1)*(b + 1)**2/2
Let c(p) = -p**2 + 6*p + 12. Let t be c(9). Let q be 2/((-9)/t + -1). Let k(d) = -d**2 + d + 1. Let m(g) = 8*g**2 - 3. Let y(b) = q*k(b) - m(b). Solve y(s) = 0.
-1, -2/3
Let r(f) be the third derivative of -1/42*f**4 - 2*f**2 + 0*f**3 - 1/735*f**7 + 1/210*f**6 + 1/210*f**5 + 0 + 0*f. Factor r(t).
-2*t*(t - 2)*(t - 1)*(t + 1)/7
Determine q so that -113*q**4 + 223*q**4 - 113*q**4 + 3*q**5 - 3*q**3 + 3*q**2 = 0.
-1, 0, 1
Let g(c) be the first derivative of 1/14*c**4 - 1/7*c**2 + 0*c + 0*c**3 + 3. Factor g(b).
2*b*(b - 1)*(b + 1)/7
Let b = -114 + 1141/10. Let y(i) be the third derivative of 1/3*i**3 + b*i**5 - i**2 - 1/4*i**4 + 0*i - 1/60*i**6 + 0. Find c, given that y(c) = 0.
1
Let g = -413 - -413. Solve g*v**3 + 2/7*v**4 + 32/7 - 16/7*v**2 + 0*v = 0 for v.
-2, 2
Let s(n) = 16*n + 80. Let m be s(-5). Let j(a) be the second derivative of 1/10*a**5 + m - a**2 - 1/2*a**4 + a**3 - 2*a. Determine i so that j(i) = 0.
1
Let g(b) = -9*b**2 + 36*b - 114. Let w(y) = -y**2 - 1. Let q(n) = -g(n) + 6*w(n). Determine i, given that q(i) = 0.
6
Factor -3/2*b**3 + 5*b**2 + 1 - 9/2*b.
-(b - 2)*(b - 1)*(3*b - 1)/2
Suppose 3*y + 2*h - 15 = 0, 24 = 4*y + 2*h + 2*h. Determine w so that 0*w**2 + y*w**2 + 2*w**3 + 3*w**4 - 8*w**3 = 0.
0, 1
Let r(v) = v + 2. Let d be r(0). Let z(t) be the second derivative of 0 - 4/3*t**d - 1/18*t**4 + t + 4/9*t**3. Find l such that z(l) = 0.
2
Let n(p) = 2*p**2 + 7 - 9*p - 1 + 9. Let m(i) = -6*i**2 + 26*i - 44. Let l(t) = 2*t**2 + 19*t - 13. Let w be l(-10). Let b(j) = w*m(j) - 10*n(j). Factor b(r).
-2*(r - 3)**2
Let p(v) be the second derivative of 0*v**2 + 1/6*v**3 + 1/80*v**5 + 0 + 1/12*v**4 - v. Let p(d) = 0. Calculate d.
-2, 0
Let z(r) be the second derivative of 0*r**2 + 0*r**3 + 1/30*r**5 + 0 + r - 1/18*r**4. Factor z(x).
2*x**2*(x - 1)/3
Factor -2/3*i**2 + 1/3*i**4 + 0*i + 0 - 1/3*i**3.
i**2*(i - 2)*(i + 1)/3
Factor 3 + 1 + 2*z**4 + 4*z - 2 - 4*z**3 - 4.
2*(z - 1)**3*(z + 1)
Let l be -6 + 3 + (-134)/(-40). Let y(n) be the second derivative of 0*n**3 + 0 - 2*n + 0*n**2 + l*n**5 + 1/14*n**7 - 4/15*n**6 - 1/6*n**4. Factor y(j).
j**2*(j - 1)**2*(3*j - 2)
What is d in -2/3*d**3 + 0 + 0*d + 1/3*d**4 + 1/3*d**2 = 0?
0, 1
Let h(b) be the first derivative of b**7/280 - 3*b**5/40 - b**4/4 - 2*b**3/3 - 4. Let a(c) be the third derivative of h(c). Factor a(m).
3*(m - 2)*(m + 1)**2
Let u(m) be the third derivative of m**8/26880 + m**7/5040 - m**6/2880 - m**5/240 + m**4/6 - 2*m**2. Let q(t) be the second derivative of u(t). Factor q(y).
(y - 1)*(y + 1)*(y + 2)/4
Let f(b) be the third derivative of 0*b + 1/30*b**5 + 0 - 1/60*b**6 + 0*b**3 + 1/168*b**8 - b**2 + 0*b**4 - 1/105*b**7. Factor f(v).
2*v**2*(v - 1)**2*(v + 1)
Let k be (15/275)/(6/60). Suppose 2/11*z**4 + 4/11*z**2 + 0 + 0*z - k*z**3 = 0. Calculate z.
0, 1, 2
Let x(q) = -66*q**2 - 234*q + 300. Let f(w) = -5*w**2 - 18*w + 23. Let o(s) = -27*f(s) + 2*x(s). Suppose o(r) = 0. What is r?
-7, 1
Let h(k) be the second derivative of -k**7/56 - k**6/10 - 3*k**5/20 - 12*k - 1. Factor h(c).
-3*c**3*(c + 2)**2/4
Let t(f) be the first derivative of f**6/30 - f**5/10 + f**4/12 - 2*f + 2. Let b(a) be the first derivative of t(a). Factor b(v).
v**2*(v - 1)**2
Let x(w) be the first derivative of w**6/3 + 2*w**5/5 - w**4/2 - 2*w**3/3 - 4. Factor x(h).
2*h**2*(h - 1)*(h + 1)**2
Let -4/15*m**2 + 0 - 2/15*m**3 - 2/15*m = 0. Calculate m.
-1, 0
Let x(a) be the first derivative of -a**6/60 + a**5/30 + a**4/12 - a**3/3 + a**2/2 + 1. Let s(v) be the second derivative of x(v). Factor s(o).
-2*(o - 1)**2*(o + 1)
Let w = 2847/2 - 1394. Let r = 31 - w. Factor r*j - j**3 + 1/2 - 3/2*j**4 - 1/2*j**5 + j**2.
-(j - 1)*(j + 1)**4/2
Let t(z) be the first derivative of 1/5*z**5 - 1 + 1/16*z**4 + 0*z + 0*z**2 + 0*z**3. Factor t(r).
r**3*(4*r + 1)/4
Let m be (-1)/(2/(-4)*10). Factor m*n + 1/5 - 2/5*n**2.
-(n - 1)*(2*n + 1)/5
Suppose 10 = 13*x - 16. Let h(m) be the second derivative of -1/4*m**x + 1/80*m**5 + 0*m**4 - 1/8*m**3 - 2*m + 0. Solve h(k) = 0 for k.
-1, 2
Suppose -8 - 4 = 2*j - 4*i, -3*i + 16 = 2*j. Let o(a) be the third derivative of 0 + 0*a**3 - 1/120*a**5 + 0*a + 1/24*a**4 + 2*a**j. Let o(q) = 0. What is q?
0, 2
Let n(o) be the third derivative of 1/30*o**5 + 0*o + 0 + 0*o**4 - 2*o**2 + 0*o**3. Factor n(q).
2*q**2
Factor 216/5*j - 432/5 - 36/5*j**2 + 2/5*j**3.
2*(j - 6)**3/5
Let n(i) be the second derivative of 0 - 6*i**2 + 6*i + 8/3*i**3 - 1/3*i**4. Factor n(t).
-4*(t - 3)*(t - 1)
Let b(o) be the third derivative of 0*o**4 + 0 + 0*o**3 - 4*o**2 + 1/350*o**7 + 1/300*o**5 + 1/150*o**6 + 0*o. Factor b(