r + 1)/2
Suppose 0 = -2*l + 5*w - 17, -3*l = -4*l + 5*w - 21. Let q(a) be the first derivative of 0*a + 1/2*a**l + a**2 + 4/3*a**3 - 2. Determine t, given that q(t) = 0.
-1, 0
Suppose 0*k - 9 = -3*k. Suppose -4*m = -k*m - 5*g - 25, -4*g - 41 = -5*m. Solve -2*y**2 + 3*y**5 - y + 0*y - 2*y**m + 2*y**4 = 0 for y.
-1, 0, 1
Let i = 2 - -1. Suppose 2*j = o - 1, i*o + 3*j - 16 + 4 = 0. Let 5*k - 2*k**2 - o*k + 4*k**2 - 6 + 2 = 0. What is k?
-2, 1
Let c(d) = -2*d**5 + 13*d**4 - 13*d**3 + 2*d**2 + 7*d + 7. Let n(t) = -t**5 + 7*t**4 - 7*t**3 + t**2 + 4*t + 4. Let g(a) = 4*c(a) - 7*n(a). Factor g(p).
-p**2*(p - 1)**3
Let b(k) = -k - 49. Let g be b(-51). Let 1 + 1/2*n - 3/2*n**g = 0. Calculate n.
-2/3, 1
Let p(q) be the second derivative of q**6/30 - q**5/4 + 3*q**4/4 - 7*q**3/6 + q**2 - q. Factor p(o).
(o - 2)*(o - 1)**3
Let c be (132/(-55))/((-4)/10). Suppose 2*q**2 + 6*q**2 - 2*q**2 - 4*q**2 + c*q = 0. What is q?
-3, 0
Let l(z) = 2*z**4 - 3*z**2 + 4*z. Let c(d) = -4*d**4 + 5*d**2 - 8*d. Let g(a) = 3*c(a) + 7*l(a). Suppose g(o) = 0. Calculate o.
-2, 0, 1
Let o(s) = 8*s**4 + 96*s**3 - 87*s**2 - 17*s. Let a(f) = -f**4 - 12*f**3 + 11*f**2 + 2*f. Let r(t) = 51*a(t) + 6*o(t). Factor r(l).
-3*l**2*(l - 1)*(l + 13)
Suppose 3*l - 6 = -2*v + 3, -5*l + 15 = -5*v. Suppose -l*n = 7 - 13. Factor 2/9*t**4 + 4/9*t**3 + 0*t**n - 2/9 - 4/9*t.
2*(t - 1)*(t + 1)**3/9
Let y be ((-1)/(-3))/((-3)/(-27)). Factor -4*o - 4 - 23*o**y - 12*o - 24*o**2 - 4*o**4 + 7*o**3.
-4*(o + 1)**4
Let i(b) = b + 1. Let k(c) = -c**2 - 4*c - 5. Let n(l) = 5*i(l) + k(l). Solve n(f) = 0 for f.
0, 1
Let g(a) be the third derivative of -a**8/672 + a**7/140 - a**6/80 + a**5/120 + 6*a**2. Factor g(j).
-j**2*(j - 1)**3/2
Suppose -11*t + 12 = -8*t. Factor -2*l**5 + 4*l**3 + 4*l**2 - t*l**4 + 0*l**4 - 2*l**5.
-4*l**2*(l - 1)*(l + 1)**2
Suppose -3*y = 2*g + 15, 3*g + 7 = -4*y - 13. Suppose g = -2*o + o. Factor l**2 + o*l**2 - 4*l**2 + l**2.
-2*l**2
Let c(x) be the second derivative of -5*x**5/12 + 35*x**4/36 - 5*x**3/9 - 7*x + 4. Suppose c(h) = 0. What is h?
0, 2/5, 1
Suppose -14 + 130 = -4*m - 4*n, -5*m - 154 = -4*n. Let h be (5/m)/((-1)/3). Factor -h*c**2 - 1/2 - c.
-(c + 1)**2/2
Factor 3*l**2 - 2*l - 6*l - 7*l.
3*l*(l - 5)
Let k(v) be the second derivative of v**5/130 - 4*v**3/39 + 18*v. Let k(a) = 0. What is a?
-2, 0, 2
Let d(n) be the third derivative of -n**5/180 - n**4/36 - n**3/18 + 19*n**2. Factor d(l).
-(l + 1)**2/3
Let t = 7 + -6. Let b be (-2)/(-5) + 3/30. Factor -3/2*i + b*i**2 + t.
(i - 2)*(i - 1)/2
Factor -o - 1/2 - 1/2*o**2.
-(o + 1)**2/2
Let r = 28 + -139/5. Let w(y) be the first derivative of 0*y**2 + 1/8*y**4 + 0*y + 0*y**3 - r*y**5 + 1/12*y**6 + 2. Determine o so that w(o) = 0.
0, 1
Let x = 1 + -1. Let d(a) be the second derivative of -2/3*a**3 + a - 3/2*a**4 + 0 - 7/10*a**5 + x*a**2. Let d(i) = 0. Calculate i.
-1, -2/7, 0
Find i such that 1/3*i**2 - 1/3*i**4 + 0 - 2/3*i + 2/3*i**3 = 0.
-1, 0, 1, 2
Let b(l) be the third derivative of -l**5/10 - l**4/8 - l**3 - 5*l**2. Let w(a) = -a**2 - a - 1. Suppose -5*v + 0 = 5. Let j(h) = v*b(h) + 5*w(h). Factor j(p).
(p - 1)**2
Factor -2/3*x**4 - 2/3*x**3 + 2/3*x**2 + 0 + 2/3*x.
-2*x*(x - 1)*(x + 1)**2/3
Suppose u + 6 = -2*u. Let m(i) = -i**4 - i**3 + 1. Let q(w) = 9*w**4 + 19*w**3 + 4*w**2 - 24*w - 29. Let s(z) = u*q(z) - 22*m(z). Factor s(a).
4*(a - 3)**2*(a + 1)**2
Suppose 3*x + 5 + 0 = 5*o, -4*x - 4 = -4*o. Suppose p - 1 - 1 = x. Factor -p*m**2 + m**3 + 4*m**4 - m**5 + 3*m**2 - 5*m**4.
-m**2*(m - 1)*(m + 1)**2
Let p be 1 + (2 - 4 - -3). Let 7*z - z**p + 2*z**3 - 9*z - 2*z**4 + 3*z**4 = 0. Calculate z.
-2, -1, 0, 1
Factor 9/7 + 12/7*z + 3/7*z**2.
3*(z + 1)*(z + 3)/7
Suppose 3*h = -2*m - 6, h + 7 = -3*m - 2. Let b(v) be the third derivative of 1/180*v**5 + 0 + h*v + 0*v**3 + 1/72*v**4 + 3*v**2. Determine c so that b(c) = 0.
-1, 0
Let j(r) be the second derivative of -r**4/36 + 11*r**3/18 - 8*r. Factor j(h).
-h*(h - 11)/3
Let h(j) be the second derivative of -j**4/66 + j**3/33 - 54*j. Determine x so that h(x) = 0.
0, 1
Suppose 9 = 4*c + 1. Suppose c*j + 2 - 8 = 0. Factor 2/7 + 0*w + 2/7*w**4 + 0*w**j - 4/7*w**2.
2*(w - 1)**2*(w + 1)**2/7
Suppose 2*c + 0*u + 4*u + 44 = 0, 4*u + 20 = 0. Let l be -2 - (2 - (-57)/c). Suppose -l*o**4 + 1/4*o**5 + 0*o + 0 - 1/4*o**2 + 3/4*o**3 = 0. Calculate o.
0, 1
Let r = 1121/230 - -15/46. Let t be 14/(-10) - 3/(-1). Solve -6*v**3 - t*v**5 + r*v**4 - 2/5*v + 0 + 14/5*v**2 = 0.
0, 1/4, 1
Let u be ((-60)/(-22) - 1) + -2. Let q = -7/66 - u. Factor -q*a - 1/6*a**2 + 0.
-a*(a + 1)/6
Let w be (-4)/8*-2*2. Factor -2 + w*r**3 + 3 + 0 - r**4 - 3*r + r.
-(r - 1)**3*(r + 1)
Let q(b) = b**3 - b + 1. Let k(o) = -5*o**4 - 12*o**3 + 25*o**2 + 12*o - 17. Let u(j) = k(j) - 3*q(j). What is w in u(w) = 0?
-4, -1, 1
Suppose 32 = -4*m + 4*h, -3*h - 20 = 2*m - 6*h. Let i = m - -10. Suppose -i*q**2 - 2*q + 3 + 2*q**2 + 4*q**2 - q**2 = 0. Calculate q.
-3, 1
Suppose 4*z = 4*l - 36, 14 = -0*l + 2*l - z. Let c(x) be the third derivative of 0 + 1/60*x**l - 1/24*x**4 + 0*x + 2*x**2 + 0*x**3. Find s, given that c(s) = 0.
0, 1
Let c(d) = d**2 - 2*d + 6. Let s(x) = -x**2 + x - 1. Let u(i) = -2*i**2 + 3*i - 8. Let g(z) = -s(z) + u(z). Let o(l) = 7*c(l) + 6*g(l). Factor o(m).
m*(m - 2)
Let h be -10*((-24)/15)/4. Suppose j - h = -j. Factor -m**2 - 2 + m**4 - 4*m**3 + j + 4*m**5.
m**2*(m - 1)*(m + 1)*(4*m + 1)
Let k(d) = 3*d**3 + d + 2. Let w(z) = 7*z**3 + z**2 + 3*z + 4. Let o(u) = -5*k(u) + 2*w(u). Solve o(n) = 0 for n.
-1, 1, 2
Let w be (4*(-7)/35)/((-6)/5). Find j such that 1/3*j**3 - w*j**2 + 0 + 1/3*j = 0.
0, 1
Let r(k) be the third derivative of k**8/588 + 2*k**7/245 + k**6/105 - 2*k**5/105 - k**4/14 - 2*k**3/21 + 22*k**2. Factor r(g).
4*(g - 1)*(g + 1)**4/7
Let p(j) be the first derivative of 0*j**3 + 0*j + 0*j**2 - 3 + 3/32*j**4 + 3/40*j**5. Suppose p(t) = 0. Calculate t.
-1, 0
Let w = -5 + 6. Let n be (0/(-3))/(1 + w). Find o such that 4*o**4 + 4*o**3 - o**3 + 1 - 3*o - 5*o**2 + n*o**3 = 0.
-1, 1/4, 1
Factor 0 - y**2 - 1/3*y**3 - 2/3*y.
-y*(y + 1)*(y + 2)/3
What is h in 3/2*h**2 + 24 - 12*h = 0?
4
Factor -2/3*f**3 - 8*f + 16/3 + 4*f**2.
-2*(f - 2)**3/3
Let w(m) be the third derivative of 1/420*m**6 + 0*m**4 + 0 - 1/1176*m**8 + 0*m**3 - 2*m**2 - 1/210*m**5 + 1/735*m**7 + 0*m. Factor w(h).
-2*h**2*(h - 1)**2*(h + 1)/7
Let y(s) = -3*s. Let q be y(-1). Factor -q*v**4 + 20*v**3 - 32*v + 4*v**2 - v**5 + 16 - 3*v**5 - v**4.
-4*(v - 1)**3*(v + 2)**2
Let n = -25/6 - -187/42. Find y, given that -n*y**4 - 2/7*y**5 - 2/7 - 2/7*y + 4/7*y**2 + 4/7*y**3 = 0.
-1, 1
Let x(j) = j**2 - j - 7. Let u be x(0). Let i(f) = 2*f**2 + 6*f + 7. Let h(g) = -4*g**2 - 12*g - 15. Let z(o) = u*i(o) - 3*h(o). Factor z(l).
-2*(l + 1)*(l + 2)
Let m(b) = -b**2 + 2. Suppose -2*p = -2*a + 8, 5*a + 0 = -p - 4. Let w be m(a). Let -6*h**4 - 4*h**w - 8*h**3 + 2*h + h**4 + 3*h**2 = 0. Calculate h.
-1, 0, 2/5
Suppose 2*r = -0*r + 10. Suppose -2*h**4 + 0*h**4 + h**r + 3*h**5 - 2*h**5 = 0. What is h?
0, 1
Let h(m) be the third derivative of m**7/2520 + m**6/360 + m**5/120 + m**4/24 + 3*m**2. Let q(y) be the second derivative of h(y). Determine d so that q(d) = 0.
-1
Let a(q) be the third derivative of -q**5/330 + q**3/33 - 6*q**2. Factor a(r).
-2*(r - 1)*(r + 1)/11
Let z = -88 + 90. Factor 0 + 2/3*j**3 - 2/3*j**z + 0*j.
2*j**2*(j - 1)/3
Let u(z) be the third derivative of -7*z**6/8 - 23*z**5/10 + 11*z**4/2 - 4*z**3 + 3*z**2. Determine f, given that u(f) = 0.
-2, 2/7, 2/5
Let n = -12 + 14. Determine k so that 251*k**n - 16*k - 251*k**2 + 4*k**3 = 0.
-2, 0, 2
Suppose -8 + 4 = -2*s. Suppose 0 = -5*r - 12 + 27. Factor 10/9*t + 2/9 + 10/9*t**4 + 20/9*t**r + 20/9*t**s + 2/9*t**5.
2*(t + 1)**5/9
Suppose -5*u + 40 = -q, -2*u + 5*q + 32 = 2*u. Find i, given that -i**2 - 5*i**2 + 3*i - 3*i**3 + u - 2 = 0.
-2, -1, 1
Let f = -264 + 794/3. Suppose -3 = -z - 1. Factor 0*g**3 + 0 + f*g + 1/3*g**4 - g**z.
g*(g - 1)**2*(g + 2)/3
Suppose 5*t - 5*o = 1032 - 127, 0 = -2*o. Let w = 912/5 - t. Solve -9/5*b**2 + 2/5 - b + w*b**4 + b**3 = 0 for b.
-1, 2/7, 1
Let v(p) be the third derivative of -p**6/200 + p**5/50 + 5*p**2. Factor v(f).
-3*f**2*(f - 2)/5
Let j(p) = -p**2 - p. Let m(i) = 34*i**2 - 81*i + 20. Let y(z) = j(z) - m(z). Find v, given that y(v) = 0.
2/7, 2
Let i(w) = -w**2 - 5*w - 2. Let l be i(-4