e 0 = 4*w - 9 + b. Factor 0*z + 1/2*z**w - 1/2.
(z - 1)*(z + 1)/2
Let q be (3/10)/(18/24). Factor 0 - 1/5*r**2 + q*r.
-r*(r - 2)/5
Suppose 3*n - 100 = -2*n. Let b be 8/90*n/8. Determine i, given that 0 + 0*i - 4/9*i**3 - b*i**2 - 2/9*i**4 = 0.
-1, 0
Let c(y) = -y**2 - y + 4. Let f be c(0). Suppose -m - f*m = 0. Factor 0*j + m + 1/3*j**2 + 1/3*j**3.
j**2*(j + 1)/3
Let m(a) be the first derivative of -3*a**7/70 + a**6/40 + a**5/12 + a**4/24 - a**2/2 - 3. Let u(k) be the second derivative of m(k). What is r in u(r) = 0?
-1/3, 0, 1
Let c(p) be the first derivative of p**4/2 - 7*p**3/3 + 7*p**2/2 - 2*p + 1. Suppose c(z) = 0. What is z?
1/2, 1, 2
Let j(c) be the second derivative of 0*c**2 - 1/18*c**4 - 2*c + 0*c**3 + 2/15*c**6 + 1/20*c**5 + 1/18*c**7 + 0. Suppose j(n) = 0. What is n?
-1, 0, 2/7
Let n(j) = -4*j**2 + 5*j - 4. Let s be n(3). Let r be (-10)/s - (-8)/5. Factor -3*d + d**r + 2*d - d**4 + 3*d**3 - 2*d**3.
-d*(d - 1)**2*(d + 1)
Suppose 3 + 1 = -p. Let y(w) = -3*w**2 - 2*w - 9. Let d(s) = 2*s**2 + 2*s + 8. Let j(u) = p*y(u) - 5*d(u). Let j(q) = 0. Calculate q.
-1, 2
Let v(j) be the third derivative of -j**7/42 - j**6/12 + 5*j**4/12 + 5*j**3/6 + 13*j**2. Factor v(t).
-5*(t - 1)*(t + 1)**3
Let w(o) be the first derivative of 0*o**2 - 1/9*o**3 + 1/3*o - 2. Find y such that w(y) = 0.
-1, 1
Let m(l) be the second derivative of 0*l**3 + 0 + 1/2*l**2 - 1/60*l**6 + 0*l**5 - 2*l + 1/12*l**4. Let j(f) be the first derivative of m(f). Factor j(c).
-2*c*(c - 1)*(c + 1)
Determine p, given that -1/7*p**3 - 3/7*p - 3/7*p**2 - 1/7 = 0.
-1
Determine d so that -8 - 2/3*d**2 + 26/3*d = 0.
1, 12
Let n(z) = -7*z**3 + 7*z**2 + 7*z - 2. Let v(u) be the first derivative of -7*u**4/4 + 2*u**3 + 7*u**2/2 - 2*u + 1. Let r(b) = 4*n(b) - 5*v(b). Factor r(g).
(g - 1)*(g + 1)*(7*g - 2)
Let j(z) be the first derivative of -5*z**3/3 + 25*z**2/2 - 32. Determine f, given that j(f) = 0.
0, 5
Let g be 3*(8/(-3))/(-4). Find y, given that -y + g*y**2 + 0*y + 2*y - 3*y = 0.
0, 1
Determine n so that -22 + 6*n**3 + 16*n**2 - 120*n - 62 + 3*n**4 - 12 - 52*n**2 = 0.
-2, 4
Let c(i) = -i**2. Let r(m) = 3*m**3 - 4*m**2 + 9*m - 3. Let w(b) = 5*c(b) + r(b). Find u, given that w(u) = 0.
1
Let r = 1043 - 1038. Find i such that 3/2*i + 0 + 3*i**3 - 6*i**2 + 6*i**4 - 9/2*i**r = 0.
-1, 0, 1/3, 1
Let q(w) be the second derivative of w**5/20 + w**4/4 - w**3/6 - 3*w**2/2 + 24*w. Solve q(v) = 0 for v.
-3, -1, 1
Let v(z) be the second derivative of z**5/35 - 13*z**4/21 + 46*z**3/21 - 22*z**2/7 - 21*z + 1. Find j, given that v(j) = 0.
1, 11
Let b = 757/10 - 376/5. Find x, given that -b*x**5 + 1/2*x + 0*x**3 - x**2 + 0 + x**4 = 0.
-1, 0, 1
Suppose -5*o = -4 - 11. Factor -2*h**2 - 2*h**4 + 0*h**4 + 2*h**4 - 2*h**4 + 4*h**o.
-2*h**2*(h - 1)**2
Let s(u) be the first derivative of -u**6/12 - 3*u**5/5 - 7*u**4/4 - 8*u**3/3 - 9*u**2/4 - u - 1. Let s(q) = 0. What is q?
-2, -1
Let j(t) be the first derivative of t**6/4 - 21*t**5/10 + 45*t**4/8 - 9*t**3/2 + 56. Factor j(w).
3*w**2*(w - 3)**2*(w - 1)/2
Suppose -10*n + 48 = 6*n. Suppose 5/4*h**2 - 1/2*h - h**n + 1/4*h**4 + 0 = 0. Calculate h.
0, 1, 2
Let m = -6 - -6. Let g be 13/3 - 9/3. Let g*j**2 + 0 - 10/3*j**3 + m*j = 0. What is j?
0, 2/5
Let a be ((-4)/16*6)/((-2)/4). Suppose -15 = 4*m - m - 5*b, 0 = b - 3. Factor 2/3*d**a + 0 + 0*d + m*d**2 + 2/3*d**4.
2*d**3*(d + 1)/3
Let v = -3 + 5. Suppose v*j - 2 = 5*z - 2*j, -j = -3. Factor -2*p**4 + 4*p**2 + 4*p**z - 6*p**2.
-2*p**2*(p - 1)*(p + 1)
Let n(v) be the third derivative of v**6/360 - v**5/90 + v**4/72 - 8*v**2. Factor n(d).
d*(d - 1)**2/3
Let m(z) be the second derivative of -z**4/12 + z**3/2 - z**2 + 3*z. Factor m(l).
-(l - 2)*(l - 1)
Factor 1/7*g**3 - 2/7*g**2 + 0 + 0*g.
g**2*(g - 2)/7
Let x(g) be the second derivative of g**6/150 + 3*g**5/100 + g**4/20 + g**3/30 + g - 8. Determine m, given that x(m) = 0.
-1, 0
Let x be (1*-1)/(5/(-10)). Suppose -25 = -7*b + x*b. What is j in 7*j**2 + 2*j + b*j**2 + 8*j**4 + 0*j**2 + 18*j**3 = 0?
-1, -1/4, 0
Let o(r) be the second derivative of r**5/40 + r**4/12 - r**3/4 - 2*r. Solve o(z) = 0 for z.
-3, 0, 1
Let r(z) = z**2 - z - 1. Let d(c) = 7*c**2 - 9*c - 3. Let v(f) = d(f) - 5*r(f). Factor v(n).
2*(n - 1)**2
Let m(x) be the third derivative of x**8/2240 + 5*x**3/6 + 6*x**2. Let a(t) be the first derivative of m(t). Factor a(s).
3*s**4/4
Let f(z) be the second derivative of -z**5/50 + z**3/15 + z. Let f(m) = 0. What is m?
-1, 0, 1
Let l(n) be the third derivative of -n**8/84 + 2*n**7/105 + n**6/30 - n**5/15 + n**2. Factor l(z).
-4*z**2*(z - 1)**2*(z + 1)
Let p(k) = k**2 - 10*k + 4. Let m be p(10). Factor -51*w**4 - 5*w**3 + 2*w + 47*w**4 + m*w**2 + 3*w**3.
-2*w*(w - 1)*(w + 1)*(2*w + 1)
Let m(s) = 3 - 3 - 1. Suppose -t = -4*t - 3*g, 4*t = -g - 3. Let l(o) = -7*o**2 + 2*o + 3. Let f(w) = t*l(w) - 3*m(w). Find q, given that f(q) = 0.
0, 2/7
Let s(r) be the third derivative of 2*r**7/105 + r**6/3 + 28*r**5/15 + 4*r**4 + 2*r**2 + 4. Let s(x) = 0. Calculate x.
-6, -2, 0
Let g(t) be the second derivative of 4/13*t**2 + 5*t + 0 - 11/78*t**4 + 20/39*t**3. Factor g(r).
-2*(r - 2)*(11*r + 2)/13
Suppose 1 + 1 = v. Determine t so that -18*t - v*t**3 - 2*t**2 + 18*t - t**4 + t**2 = 0.
-1, 0
Factor 0*i**2 + 0 + 6/5*i**5 - 21/5*i**4 + 0*i - 12/5*i**3.
3*i**3*(i - 4)*(2*i + 1)/5
Suppose 0 = -5*l + 3*r - r, -27 = -l - 5*r. Suppose -5*k + 4 = l*c, k = 5*c + 1 - 11. Determine t so that 2*t**4 + 0 + 18/5*t**c + 4/5*t + 24/5*t**3 = 0.
-1, -2/5, 0
Suppose -3*c - 6 = -3*j, -j + 2*c = -2*j + 8. Factor 3*b**2 + j*b**3 - 4*b**2 + b**4 - 3*b**5 + 2*b**5 - 3*b**3.
-b**2*(b - 1)**2*(b + 1)
Let z(c) be the third derivative of 1/30*c**5 + 1/30*c**6 + 0*c**3 + 0*c + 0 + c**2 + 0*c**4 + 1/105*c**7. Factor z(x).
2*x**2*(x + 1)**2
Let p be (-18)/(-12)*10/3. Suppose -c = -p + 3. Determine h, given that 0*h + 2/9*h**c - 2/9 = 0.
-1, 1
Determine i, given that -45*i**3 + 42*i**3 + i**2 + 2*i**2 - 3*i**4 + 3*i**5 = 0.
-1, 0, 1
Solve -22/3*a**2 + 20/3*a + 2/3*a**3 + 0 = 0.
0, 1, 10
Let z = -165 - -1157/7. Solve 2/7 + 4/7*u**3 - 4/7*u + 0*u**2 - z*u**4 = 0 for u.
-1, 1
Let t be -3 + 4 + 0 + 2. Find l, given that 3*l - 4*l**2 - 4 - t*l - 8*l = 0.
-1
Let v(q) = q**2 + 2*q. Let a be v(1). What is t in -2/5*t**4 - 6/5*t**a - 6/5*t**2 + 0 - 2/5*t = 0?
-1, 0
Let m(y) be the third derivative of 121*y**5/300 + 11*y**4/30 + 2*y**3/15 + 2*y**2. Solve m(n) = 0 for n.
-2/11
Let k be ((-9)/(-4))/((-30)/(-32)). Factor -18/5*i**2 + 27/5*i - k + 3/5*i**3.
3*(i - 4)*(i - 1)**2/5
Let j be 3 + ((-3)/(-3) - 2). Let o(h) be the third derivative of -1/72*h**4 + 0 + 0*h - 1/180*h**5 + 0*h**3 - j*h**2. Factor o(s).
-s*(s + 1)/3
Suppose 3*x = -5*x + 24. Let n(i) be the first derivative of 2/7*i - 1/14*i**4 - 1 + 2/7*i**x - 3/7*i**2. Find z, given that n(z) = 0.
1
Let u(l) = 2*l**2 - 7*l + 3. Let t be u(3). Find i such that t*i - 1/5*i**4 + 0 - 1/5*i**3 + 1/5*i**5 + 1/5*i**2 = 0.
-1, 0, 1
Factor j - 6*j + 1 + 8*j + 2*j**2.
(j + 1)*(2*j + 1)
Let v(h) be the second derivative of h**5/15 + h**4/6 - 4*h**3/3 - 7*h**2/2 + 5*h. Let p(x) be the first derivative of v(x). Find k such that p(k) = 0.
-2, 1
Suppose 0 = -2*i - 0 + 4. Suppose 4*z**2 - 2*z**i - 4*z**3 + 2*z**3 = 0. Calculate z.
0, 1
Let a(q) be the third derivative of -1/270*q**5 + 0 + 0*q**3 - 7*q**2 + 0*q - 1/189*q**7 + 0*q**4 - 1/90*q**6. Determine d, given that a(d) = 0.
-1, -1/5, 0
Let h(f) be the second derivative of f**4/15 - 2*f**3/5 + 21*f. Factor h(v).
4*v*(v - 3)/5
Let a(d) be the first derivative of -1/6*d**4 + 1/3*d**2 - 4/3*d + 4/9*d**3 + 1. Let a(v) = 0. What is v?
-1, 1, 2
Let b(n) = -n**3 + 7*n**2. Let u(t) = 6*t**2 - 19*t - t**3 + 0*t**2 + 19*t. Let k(r) = 6*b(r) - 7*u(r). Factor k(y).
y**3
Let k(a) = 2 - 1 - a**2 - 2*a**4 + 3*a**4 + 0*a**4. Let t(h) = -2*h**4 + h**3 + 3*h**2 - 1. Let j(n) = -k(n) - t(n). Find y, given that j(y) = 0.
-1, 0, 2
Determine d, given that 0*d + 0*d**2 + 2/3*d**5 + 0*d**4 + 0 - 2/3*d**3 = 0.
-1, 0, 1
Let o(w) = -2*w + 13. Let b be o(5). Let 1/3*h - 2/3*h**2 - 1/3*h**b + 2/3 = 0. What is h?
-2, -1, 1
Let s(z) be the first derivative of z**4/2 + 14*z**3/3 + 16*z**2 + 24*z - 17. Determine t so that s(t) = 0.
-3, -2
Suppose -2*i = i. Suppose -2*l = 4*h - i*h - 2, -5*l = h + 13. Factor -f - 2*f**2 - f + h*f**3 + 2*f**2.
2*f*(f - 1)*(f + 