1
Let b(t) be the third derivative of -t**5/40 + t**4/16 - t**2. Factor b(n).
-3*n*(n - 1)/2
Let x(z) be the third derivative of 7*z**5/120 - z**4/24 - z**2. What is y in x(y) = 0?
0, 2/7
Let d(n) be the second derivative of -n**4/30 + n**3/5 - 8*n. Factor d(v).
-2*v*(v - 3)/5
What is y in 2/5*y**5 + 18/5*y**3 + 0 - 14/5*y**2 + 4/5*y - 2*y**4 = 0?
0, 1, 2
Let t(z) = -z + 1. Let g(w) = 10*w**2 + 4*w + 5. Let r(d) = d**2 + 1. Let q(o) = -2*g(o) + 18*r(o). Let a(x) = q(x) - 8*t(x). Find j such that a(j) = 0.
0
Let b = 11 + -7. Let n be b/26 + 36/104. Factor 0 + 1/2*c + c**2 + n*c**3.
c*(c + 1)**2/2
Let p(a) be the second derivative of 11*a**7/14 - 13*a**6/10 - 93*a**5/20 + 61*a**4/4 - 16*a**3 + 6*a**2 + 18*a. Suppose p(h) = 0. What is h?
-2, 2/11, 1
Let l = 10 - 6. Let k be 0 - 1*10/(-2). Factor k*q + 0*q**2 - l*q - q**2.
-q*(q - 1)
Factor 2/17*q + 0 - 2/17*q**2.
-2*q*(q - 1)/17
Let n(z) be the second derivative of 0*z**3 + 0*z**4 - 2/105*z**7 + 0 + 1/25*z**6 - 1/50*z**5 + 6*z + 0*z**2. Find b, given that n(b) = 0.
0, 1/2, 1
Let i(k) be the third derivative of k**7/70 - k**5/10 + k**3/2 - 7*k**2. What is q in i(q) = 0?
-1, 1
Let q be 14*(3 - 2 - 0). Factor -24*p + 1 + q*p**2 - 7 - 7 + 5.
2*(p - 2)*(7*p + 2)
Find f such that -3*f**2 - f**3 + 4*f**2 - f + f**2 - 4*f**2 = 0.
-1, 0
What is p in 117 - 4*p**2 - 2*p - 117 - 2*p**3 = 0?
-1, 0
Let m(i) be the first derivative of -i**6/100 + i**5/75 + 7*i**4/60 + 2*i**3/15 - 3*i**2 - 5. Let r(p) be the second derivative of m(p). What is v in r(v) = 0?
-1, -1/3, 2
Let l(z) = 2*z**3 + 5*z**2 - 11*z**2 + 2*z**3 - 3*z**3. Let r be l(6). Factor -1/4*c**3 - 1/4*c - 1/2*c**2 + r.
-c*(c + 1)**2/4
Let l be ((-24)/10 - (-8)/20) + 4. Solve 9/2*i**5 + 0 - 3/2*i + 12*i**4 + 0*i**l + 9*i**3 = 0 for i.
-1, 0, 1/3
Let x(z) = 21*z**4 + 33*z**3 - 9*z**2 - 33*z - 3. Let g(h) = 5*h**4 + 8*h**3 - 2*h**2 - 8*h - 1. Let n(v) = 9*g(v) - 2*x(v). Let n(m) = 0. Calculate m.
-1, 1
Determine f, given that 24/5*f**2 + 0 + 6/5*f**3 - 3/5*f**4 + 0*f = 0.
-2, 0, 4
Let h(t) = t**3 + 4*t**2 + 2*t + 1. Let q be h(-3). Determine y, given that 4*y**2 + q*y**2 + 0*y**3 - 32*y**3 + 50*y**5 + 10*y**4 = 0.
-1, 0, 2/5
Let j(b) = 9*b**3 - 39*b**2 + 42*b - 6. Let k(o) = 18*o**3 - 78*o**2 + 83*o - 13. Let a(m) = 5*j(m) - 3*k(m). Solve a(t) = 0.
1/3, 1, 3
Let f = -13 + 17. Let 16*c**3 - c**4 - 3*c**f + 0*c**4 - 16*c**5 + 4*c**2 = 0. What is c?
-1, -1/4, 0, 1
Let t(d) be the second derivative of -3/10*d**5 - 1/112*d**7 - 8*d - 1/4*d**4 + d**3 + 3*d**2 - 7/80*d**6 + 0. Factor t(a).
-3*(a - 1)*(a + 2)**4/8
Let v(r) be the first derivative of -7*r**6/33 + 122*r**5/55 - 185*r**4/22 + 430*r**3/33 - 48*r**2/11 - 72*r/11 + 38. Solve v(x) = 0.
-2/7, 1, 2, 3
Let m(i) = i - 2. Let l be m(8). Factor -2*z**2 - l*z**3 + 1 - 1 + 4*z.
-2*z*(z + 1)*(3*z - 2)
Let x(a) = -a**3 + 3*a**2 - a. Let t be x(2). Let n = 4 - t. Suppose 8/7*y + 8/7 + 2/7*y**n = 0. What is y?
-2
Let v(j) be the second derivative of j**6/2 - 21*j**5/10 + 11*j**4/5 - 4*j**3/5 - 4*j. Determine b, given that v(b) = 0.
0, 2/5, 2
Let n = 362/207 - 30/23. Suppose 3*j = -2*i - 0*j - 12, -5*i + 4*j = -16. Determine c, given that i + n*c + 2/9*c**2 = 0.
-2, 0
Let n = 68393/70 - 977. Let c(q) be the third derivative of -q**2 + 1/2*q**3 - 1/5*q**5 + 0 + 1/20*q**6 + n*q**7 - 1/4*q**4 + 0*q. Let c(f) = 0. What is f?
-1, 1/3, 1
Let t(m) = -m**3 - 9*m**2 - 8*m + 2. Let h be t(-8). Factor 2 + 3*i - 3*i**3 + h*i**3 + 0.
-(i - 2)*(i + 1)**2
Suppose 4*z + i + 35 + 47 = 0, -5*i = -2*z - 30. Let v be z/25*5/(-2). Let 0*p + 0 - 2/5*p**v + 2/5*p**5 - 2/5*p**3 + 2/5*p**4 = 0. Calculate p.
-1, 0, 1
Let i be (-9 - -12) + 0 + 3. Suppose 6*s - 3/2*s**2 - i = 0. Calculate s.
2
Let v(f) be the first derivative of 0*f**3 - 3*f + 1 + 0*f + f**3. Suppose v(h) = 0. Calculate h.
-1, 1
Let o(y) = -6*y**2 + 7*y**2 - 9 + 8 - y**3. Let p be 2*(3/2 - 1). Let b(i) = 2*i**3 - 6*i**2 + 4. Let l(k) = p*b(k) + 4*o(k). Factor l(j).
-2*j**2*(j + 1)
Let z(f) = -3*f - 38. Let y(j) = j + 13. Let t(g) = -17*y(g) - 6*z(g). Let l be t(-5). Factor -5 + 2*d**l - 3 + 4 - 2*d.
2*(d - 2)*(d + 1)
Let w(v) be the first derivative of 11/10*v**4 - 8/5*v**3 + 4/5*v**2 + 3 - 6/25*v**5 + 0*v. Determine q, given that w(q) = 0.
0, 2/3, 1, 2
Let m be 3 + 2 - 2 - 1. Let u(c) be the second derivative of 1/25*c**5 + 0*c**4 + 0 + m*c - 1/15*c**3 + 0*c**2 - 1/105*c**7 + 0*c**6. Factor u(b).
-2*b*(b - 1)**2*(b + 1)**2/5
Let p(h) = 3*h**4 + 12*h**3 + 15*h**2 + 6*h - 8. Let j(f) = 2*f**4 + 8*f**3 + 10*f**2 + 4*f - 5. Let c(o) = 8*j(o) - 5*p(o). Factor c(u).
u*(u + 1)**2*(u + 2)
Let c(w) be the second derivative of 0 - 13/30*w**6 + 0*w**2 + 3*w + 9/20*w**5 + 5/42*w**7 - 1/3*w**3 + 1/12*w**4. Solve c(h) = 0.
-2/5, 0, 1
Let j(z) be the second derivative of -7*z**5/4 - 55*z**4/4 - 15*z**3 + 20*z**2 + z - 6. Let j(i) = 0. Calculate i.
-4, -1, 2/7
Let u(v) be the first derivative of 2/3*v + 3 - 2/9*v**3 + 0*v**2. Factor u(o).
-2*(o - 1)*(o + 1)/3
Let s be 0/((36/(-3))/(-4)). Factor 1/2*j**4 + s*j**2 - j - 1/2 + j**3.
(j - 1)*(j + 1)**3/2
Suppose 0 + 2/9*j**2 + 1/3*j - 1/9*j**3 = 0. Calculate j.
-1, 0, 3
Factor 1/5*n**2 - 1/5*n**3 + 3/5 + n.
-(n - 3)*(n + 1)**2/5
Let s be -2 + (2 - (3 - -1)). Let r be (4/2)/((-2)/s). Let -2*c + 1 + 2*c**3 + 1 + 2*c**2 - r*c**2 = 0. What is c?
-1, 1
Suppose -m**2 - m + 3*m**2 - m**2 - 7*m + 16 = 0. What is m?
4
Let r = -22/5 + 93/20. Let u(k) be the first derivative of -r*k**4 + 0*k + 0*k**2 - 3 - 2/3*k**3. Factor u(h).
-h**2*(h + 2)
Let h(c) be the first derivative of -c**6/12 + 7*c**5/5 - 73*c**4/8 + 86*c**3/3 - 44*c**2 + 32*c + 34. Factor h(l).
-(l - 4)**3*(l - 1)**2/2
Let j(u) be the second derivative of -u**4/66 + 4*u**3/11 - 36*u**2/11 + 17*u. Factor j(y).
-2*(y - 6)**2/11
Let q be (-601)/(-300) - 2/1. Let b(w) be the third derivative of 0*w - q*w**6 - 1/50*w**5 - w**2 - 1/20*w**4 + 0 - 1/15*w**3. Factor b(o).
-2*(o + 1)**3/5
Let t(x) = x**4 + 3*x**3 - x**2 + 3*x + 2. Let m(v) = 2*v**4 + 3*v**3 + 4*v + 3. Let y(b) = 4*m(b) - 6*t(b). Find w such that y(w) = 0.
0, 1
Let u = 2 + 2. Let l be 40/32 - (-3)/4. Factor 4*n - 2*n**u - 4*n + 4*n**3 - 2*n**l.
-2*n**2*(n - 1)**2
Let d(l) = -l**2 + 2*l + 3. Let h(o) = o + 1. Suppose 5*j + 3*z - 2*z + 23 = 0, -6 = -3*z. Let r(a) = j*h(a) + 2*d(a). Factor r(k).
-(k + 1)*(2*k - 1)
Let z(g) be the second derivative of g**8/168 - 2*g**7/105 + g**5/15 - g**4/12 + 3*g**2/2 - g. Let i(b) be the first derivative of z(b). Solve i(o) = 0.
-1, 0, 1
Determine p so that -11*p**4 + 120*p**2 - 5*p**4 - 32*p - 26*p**3 + 62*p**3 = 0.
-2, 0, 1/4, 4
Let p(y) be the third derivative of -y**6/45 + y**5/45 + 11*y**2. Find b such that p(b) = 0.
0, 1/2
Let x(m) = -3*m**2 - 2*m - 2. Let a(d) = 4*d**2 + d + 1. Let w(g) = -2*a(g) - 3*x(g). Determine h so that w(h) = 0.
-2
Let r(v) = -24*v**2 - 101*v - 29. Let z(q) = 25*q**2 + 100*q + 30. Let b(x) = -5*r(x) - 4*z(x). Determine f so that b(f) = 0.
-5, -1/4
Let v(b) = 2*b**2 + 3*b + 1. Let z be v(-2). Find i, given that -3*i + 2*i**2 - 8 + 11*i - 81*i**z + 79*i**3 = 0.
-2, 1, 2
Let q(h) be the third derivative of -h**11/110880 - h**10/50400 + h**9/10080 + h**5/15 + 5*h**2. Let d(x) be the third derivative of q(x). Factor d(l).
-3*l**3*(l - 1)*(l + 2)
Let m = 667/5 - 133. What is k in -2/5*k**3 + m*k**5 + 0*k - 4/5*k**4 + 4/5*k**2 + 0 = 0?
-1, 0, 1, 2
Let b(n) be the second derivative of n**6/60 + n**5/10 + n**4/4 + n**3/3 + n**2/4 + 24*n. Let b(m) = 0. What is m?
-1
Suppose -3*z + 24 = 4*y, 4*y - 4*z = -5 + 1. Let d(q) be the first derivative of -2*q**2 - q + 2 - 1/5*q**5 - q**4 - 2*q**y. Solve d(w) = 0.
-1
Solve -5*t - t + 10*t**2 - 4 + 0*t = 0 for t.
-2/5, 1
Let n(o) = -5*o**2 + 11*o - 2. Let j = -4 + 7. Let h(c) = 16*c**2 - 32*c + 6. Let u(p) = j*h(p) + 8*n(p). Factor u(s).
2*(2*s - 1)**2
Suppose 3/5*t**4 - 11/5*t**3 - 4/5*t + 0 + 12/5*t**2 = 0. What is t?
0, 2/3, 1, 2
Let v(n) be the second derivative of n + 0*n**3 + 0*n**2 - 1/5*n**5 + 0 + 1/3*n**6 + 0*n**4 + 1/3*n**7. Factor v(c).
2*c**3*(c + 1)*(7*c - 2)
Let i = -67 + 69. Find n, given that 2/7*n**4 + 2/7*n**3 - 2/7*n + 0 - 2/7*n**i = 0.
-1, 0, 1
Determine y, given that 5*y**5 + 13*y - 23*y - 10*y**3 + 15*y = 0.
-1, 0, 1
Let b be (-261)/(-54) - (-2)/12. Let n(p) be the first derivative of -8*p**3 - 4 + 5*p**4 - 2*p - 6/5*p*