*(2*i - 1)
Let l = -1224 + 2449/2. Factor -3/2 + y + l*y**2.
(y - 1)*(y + 3)/2
Let w(m) be the second derivative of 1/15*m**3 + 1/60*m**4 + m**2 - 1/150*m**5 - 2*m - 1/300*m**6 + 0. Let o(y) be the first derivative of w(y). Factor o(i).
-2*(i - 1)*(i + 1)**2/5
Let v be (2 + -1 + 0)*0. Find c, given that 3 - 4*c**2 + v - 9*c + 0*c - 5 = 0.
-2, -1/4
Let z(v) = -4*v**4 + 30*v**3 - 4*v**2 - 30*v - 34. Let a(j) = -j**4 + 6*j**3 - j**2 - 6*j - 7. Let q(g) = -28*a(g) + 6*z(g). Find o, given that q(o) = 0.
-2, -1, 1
Suppose -35*d + 15 = -30*d. Factor -7/3*k**3 - 2/3*k + d*k**2 + 0.
-k*(k - 1)*(7*k - 2)/3
Let i(y) be the second derivative of y**10/60480 - y**8/6720 + y**6/1440 + y**4/12 + 2*y. Let o(q) be the third derivative of i(q). Let o(m) = 0. Calculate m.
-1, 0, 1
Determine s, given that -623*s**3 + s + 622*s**3 + 0*s - s**4 - 2 + 3*s**2 = 0.
-2, -1, 1
Let z(h) be the first derivative of 27*h**5/20 - 21*h**4/16 - h**3/2 - 8. What is c in z(c) = 0?
-2/9, 0, 1
Let n(v) = 3*v - 10. Let r be n(6). Let g = 12 - r. Factor -1/2*f**g + 0*f - 1/2 + f**2 + 0*f**3.
-(f - 1)**2*(f + 1)**2/2
Suppose 3*t = w + 14, 5*w + 16 + 14 = 5*t. Factor -7*f - t + 4 + 16*f - 3*f**2.
-3*f*(f - 3)
Let n(a) be the first derivative of -a**3/3 - 7*a**2/6 - 2*a/3 - 1. Factor n(q).
-(q + 2)*(3*q + 1)/3
Suppose -36/7*a + 124/7*a**3 - 72/7*a**4 + 8/7 - 24/7*a**2 = 0. Calculate a.
-1/2, 2/9, 1
Suppose -4*z - 2*v + 8 = v, z - 2 = -v. Suppose 12 = z*t + t. Factor 7*h**4 - 4*h**2 - h**t + 4*h**2 + 3*h**5 + 3*h**3.
3*h**3*(h + 1)**2
Let n(a) = -a**3 + 9*a**2 + 9*a + 11. Let i be n(10). Suppose -i - 11 = -g. Determine h, given that 1/2*h**2 + 8*h**4 - 3*h + 1/2 + g*h**3 = 0.
-1, 1/4
Let n be -1*(0/(-2) - 5). Suppose f - 4*h - 6 = 0, -n*f + 3*h + 11 = -f. Determine r so that 1/2*r**3 + 0 - 5/2*r**4 + 3/2*r**5 + 0*r + 1/2*r**f = 0.
-1/3, 0, 1
Let h(y) be the second derivative of 2*y**6/15 + 3*y**5/5 + y**4/3 - 2*y**3 - 4*y**2 - 12*y. Suppose h(j) = 0. What is j?
-2, -1, 1
Let z(i) be the second derivative of -i**8/3360 - i**7/1680 + i**6/720 + i**5/240 - i**3/3 + 5*i. Let d(g) be the second derivative of z(g). Factor d(q).
-q*(q - 1)*(q + 1)**2/2
Factor -6/5*n**2 + 0 + 2/5*n**3 + 0*n.
2*n**2*(n - 3)/5
Let p = 5 - 0. Find z, given that 14*z + p*z**3 - 6 - 10*z**2 - 3*z**3 + 0*z**3 + 0*z**2 = 0.
1, 3
Let f = -207/35 - -31/5. Let c be (-60)/42 + 1*2. Suppose 0*j**2 + 2/7*j**4 + c*j - f - 4/7*j**3 = 0. What is j?
-1, 1
Let x = 249/100 + 1/100. Determine w, given that -1/2*w + 5/2*w**4 + 2*w**5 - x*w**2 - 3/2*w**3 + 0 = 0.
-1, -1/4, 0, 1
Let j(u) = u**4 + u**2 + u. Let q(n) = -2*n**5 - 7*n**4 + 4*n**3 - 7*n**2 - 9*n. Let a(b) = 14*j(b) + 2*q(b). Suppose a(c) = 0. What is c?
-1, 0, 1
Let l(c) = c**4 + c**2 - 2*c + 2. Let f(u) = u**2 - u + 1. Suppose -3*h - 13*h = 32. Let v = 0 - -1. Let y(d) = h*f(d) + v*l(d). Solve y(r) = 0 for r.
-1, 0, 1
Let l(u) be the first derivative of -u**6/420 - u**5/70 - u**4/28 - u**3/21 + u**2 + 4. Let g(n) be the second derivative of l(n). Let g(o) = 0. Calculate o.
-1
Let t(h) be the first derivative of -h**3/24 + h**2/8 + 7. Factor t(z).
-z*(z - 2)/8
Let k = -7 + 5. Let p(t) = -7*t + 48 - 6*t**2 + 2*t - 4*t**3 - 48. Let o(u) = 3*u**3 + 5*u**2 + 4*u. Let q(y) = k*p(y) - 3*o(y). Solve q(w) = 0.
-2, -1, 0
Solve 2*m**3 + 133*m - 60 + m**3 - 61*m - 27*m**2 = 0 for m.
2, 5
Let j(z) = -2*z**2 + 10*z + 4. Let p(k) = -4 + k**2 - 11*k - k**2 + 3*k**2 + 0*k**2. Let d(x) = 5*j(x) + 4*p(x). Factor d(w).
2*(w + 1)*(w + 2)
Let o(m) be the first derivative of 0*m**3 + 0*m**2 + 0*m - 1/21*m**6 + 2/35*m**5 - 10 + 1/7*m**4. Factor o(h).
-2*h**3*(h - 2)*(h + 1)/7
What is f in -10*f - 5*f**2 - 29 + 29 = 0?
-2, 0
Suppose -3/2*m**3 + 3*m**2 - 12 + 6*m = 0. Calculate m.
-2, 2
Let c = -720/11 + 216011/3300. Let t(a) be the third derivative of 0*a + c*a**6 + 1/150*a**5 + 0 + 0*a**3 + 0*a**4 + 2*a**2. Determine o so that t(o) = 0.
-1, 0
Let p = -77/30 - -25/6. Find i, given that -p*i**3 + 14/5*i**2 - 7/5*i + 1/5 = 0.
1/4, 1/2, 1
Let u(q) be the third derivative of q**7/3780 + q**4/24 + 2*q**2. Let x(i) be the second derivative of u(i). Find p, given that x(p) = 0.
0
Let m = 0 + 2. Let p be (9/(-18))/((-2)/8). Factor z**2 + 2*z**4 - 4*z**4 + z**2 - p*z + m*z**3.
-2*z*(z - 1)**2*(z + 1)
Factor 4/3 - 1/3*m**3 - m**2 + 0*m.
-(m - 1)*(m + 2)**2/3
Let j(y) = y**3 + 11*y**2 - 15*y + 3. Let a(b) = -16*b**2 + 3*b - 4 + 4*b - 2*b**3 + 15*b. Let g(n) = -5*a(n) - 8*j(n). What is u in g(u) = 0?
1, 2
Let w(v) be the second derivative of -v**7/420 - v**6/60 - v**5/30 - v**2 - 4*v. Let n(j) be the first derivative of w(j). Suppose n(s) = 0. What is s?
-2, 0
Factor -6 + 12 - 5*r**3 + 15*r**2 - 26.
-5*(r - 2)**2*(r + 1)
Suppose 0 = -2*u + 7*u. Let j(g) be the first derivative of -1 - 1/2*g**2 + 0*g + u*g**3 + 1/4*g**4. Find v such that j(v) = 0.
-1, 0, 1
Let j = -14 - -14. Let t(x) be the third derivative of -1/210*x**7 + 0 + 1/24*x**4 + j*x**3 + 0*x - 1/120*x**6 + 1/60*x**5 + 2*x**2. Factor t(f).
-f*(f - 1)*(f + 1)**2
Let a(s) be the first derivative of s**7/2520 + s**6/1080 - s**5/360 - s**4/72 + 2*s**3 + 6. Let z(y) be the third derivative of a(y). Factor z(g).
(g - 1)*(g + 1)**2/3
Let -6/7*b**2 - 4/7*b - 2/7*b**3 + 0 = 0. Calculate b.
-2, -1, 0
Let x(d) be the third derivative of -d**5/210 + 4*d**3/21 - 17*d**2. Factor x(t).
-2*(t - 2)*(t + 2)/7
Let y(x) be the second derivative of x**5/40 + x**4/8 + x**3/4 + x**2/4 - 12*x. Factor y(a).
(a + 1)**3/2
What is j in 48/5*j + 21/5*j**5 + 3/5*j**2 - 69/5*j**3 + 12/5 - 3*j**4 = 0?
-1, -2/7, 1, 2
Factor -45*k**2 - 16*k**3 - 3*k**4 - 10 - 35*k + 7*k**3 - 16*k**3 - 2*k**4.
-5*(k + 1)**3*(k + 2)
Let v(u) be the second derivative of -u**6/120 + u**4/16 - u**3/12 - 13*u. Solve v(y) = 0 for y.
-2, 0, 1
Factor 2*f**2 + 13 + 7 + 12*f + 5 - 7.
2*(f + 3)**2
Let a = 182 + -179. Let h(t) be the first derivative of -1/8*t**4 - 1/20*t**5 + 0*t - 3 - 1/12*t**a + 0*t**2. Suppose h(r) = 0. What is r?
-1, 0
Determine u, given that 0 + 4/5*u**4 + 4/5*u**5 - 4/5*u**2 - 4/5*u**3 + 0*u = 0.
-1, 0, 1
Suppose r = 2*p + 8, 2*r + 2*p = -2*p + 8. Let k = 8 - r. Solve -8*f**4 - 11*f**k - f + 4*f**2 + 4*f**3 - 18*f**3 = 0 for f.
-1, -1/2, -1/4, 0
Solve a - a**2 - 2 + a**2 + a**2 + 0*a**2 = 0.
-2, 1
Let w(l) be the second derivative of l**6/6 + l**5 + 25*l**4/12 + 5*l**3/3 - 17*l. Factor w(o).
5*o*(o + 1)**2*(o + 2)
Suppose 0 = -0*y - 4*y + 4, 0 = 3*m + 5*y - 14. Factor 2/5*x**m + 6/5*x - 2/5 - 6/5*x**2.
2*(x - 1)**3/5
Let t(w) be the third derivative of -w**6/120 - w**5/20 - w**4/8 - w**3/6 - 6*w**2. Factor t(n).
-(n + 1)**3
Let l = -473/3 + 159. Let -l + 1/3*h**3 + 0*h + h**2 = 0. Calculate h.
-2, 1
Let m(y) = -y**3 - 5*y**2 + 6. Let h(t) = t**3 + 6*t**2 - 7. Let n(q) = -4*h(q) - 6*m(q). Let n(c) = 0. Calculate c.
-2, 1
Let a(v) be the first derivative of v**4/20 + 4*v**3/15 + 2*v**2/5 + 32. Factor a(x).
x*(x + 2)**2/5
Let -21/4*j**3 - 3/4*j**4 - 6 - 27/2*j**2 - 15*j = 0. What is j?
-2, -1
Suppose -x + 6*x - 420 = 0. Let k be (-12)/x - 2/(-14). Factor 0*g**3 + 0*g + 2/9*g**4 + k - 2/9*g**2.
2*g**2*(g - 1)*(g + 1)/9
Let d(x) be the second derivative of -x**6/6 + 5*x**4/12 + 7*x. Determine o so that d(o) = 0.
-1, 0, 1
Factor 45/2*u**2 + 10*u**4 + 5/2*u - 5/2 + 55/2*u**3.
5*(u + 1)**3*(4*u - 1)/2
Let p(s) be the third derivative of 0 - 1/80*s**6 - 2*s**2 + 1/10*s**5 + 0*s + 1/2*s**3 - 5/16*s**4. Factor p(w).
-3*(w - 2)*(w - 1)**2/2
Let v(z) = z**5 + 3*z**4 + z**3 + 9*z**2 + 2*z - 4. Let p(c) = c**5 + 2*c**4 + 8*c**2 + c - 3. Let i(l) = 4*p(l) - 3*v(l). Factor i(s).
s*(s - 1)**3*(s + 2)
Suppose -15 = 5*l - 30. Let y(i) be the second derivative of 1/90*i**5 + 0 + 0*i**2 - 1/54*i**4 + 0*i**l - i. Let y(h) = 0. Calculate h.
0, 1
Let t(k) be the third derivative of 0*k**3 + 0*k - 6*k**2 + 1/10*k**6 + 0 - 2/105*k**7 - 2/3*k**4 + 0*k**5. Find m, given that t(m) = 0.
-1, 0, 2
Suppose 1/4*b**2 + 3/4*b**4 + 3/4*b**3 + 1/4*b**5 + 0*b + 0 = 0. Calculate b.
-1, 0
Suppose 2 + 2*a**4 - 5*a**4 - 6*a**3 + 3*a**5 + 3*a + a**2 - 5 + 5*a**2 = 0. What is a?
-1, 1
Let n(l) = l**2 + 3*l - 1. Suppose -g = 4*b + 17, -3 - 10 = 2*b + 5*g. Let y be n(b). Factor -c**2 - c**5 - c**3 + 4*c**5 - y*c**5 + c**5 + c**4.
c**2*(c - 1)*(c + 1)**2
Factor i**4 + 14*i**2 + i**3 - 5*i**3 - 8*i - 3*i**4 + 0*i**4.
-2*i*(i - 1)**2