4*f - 7, f + 2*i = -3*f + 18. Factor 2/5*w**4 + 6/5*w**f + 0 + 6/5*w**3 + 2/5*w.
2*w*(w + 1)**3/5
Suppose 0 = -6*t + 2*t - 24. Let d be 8/t*(-3)/2. Factor 4/3*x**d - 5/3*x + 1/3.
(x - 1)*(4*x - 1)/3
Let y(m) be the first derivative of -2*m**3/15 + 8*m/5 + 7. Factor y(k).
-2*(k - 2)*(k + 2)/5
Let p = -20/9 - -49/18. Let t(s) be the first derivative of 1/8*s**4 + 0*s**2 - p*s**3 + 2*s - 2. Let t(b) = 0. Calculate b.
-1, 2
Let k(x) = -x**3 + 4*x**2 + 2*x - 5. Let o be k(4). Let -q**3 + 4 + q**2 + 0*q**o - 4 = 0. Calculate q.
0, 1
Let k = 105/2 + -513/10. Suppose 0 - k*s**4 - 4/5*s**2 + 0*s + 2*s**3 = 0. What is s?
0, 2/3, 1
Let m = -419 + 2103/5. Determine c so that 0*c - 8/5*c**2 + m*c**3 - 2/5*c**4 + 0 = 0.
0, 2
Let o(t) be the first derivative of -t**4/6 + t**2 - 2*t + 3. Let x(d) be the first derivative of o(d). Suppose x(n) = 0. What is n?
-1, 1
Suppose j - 8 = -3*z + 2, -4*j - 28 = -5*z. Let -1/2*h**2 - 1/2*h**5 - h + 1/2*h**z + 3/2*h**3 + 0 = 0. What is h?
-1, 0, 1, 2
Let t(i) = -i + 1. Let y be t(-4). Let d(o) be the second derivative of -1/33*o**3 + 0 - 1/11*o**2 + 1/110*o**y + 1/66*o**4 - 2*o. Solve d(m) = 0 for m.
-1, 1
Suppose 4*m + y - 42 - 21 = 0, -15 = -5*y. Suppose m = -t + 4*t. Factor -1/2*v**2 + 1/4*v**t + 1/4*v - 1/2*v**3 + 1/4 + 1/4*v**4.
(v - 1)**2*(v + 1)**3/4
Let m(x) be the first derivative of -4*x**5/5 + 4*x**4 - 20*x**3/3 + 4*x**2 + 2. Determine p, given that m(p) = 0.
0, 1, 2
Let z(c) be the first derivative of c**4/6 - c**3 + 2*c**2 + 5*c - 2. Let l(b) be the first derivative of z(b). What is f in l(f) = 0?
1, 2
Factor 2 + 5/2*k + 1/2*k**2.
(k + 1)*(k + 4)/2
Suppose -2/5*s**3 - 4/5*s - 6/5*s**2 + 0 = 0. Calculate s.
-2, -1, 0
Let w = 1484 - 812. Let y be 2/16 + 492/w. Factor 0*t - 6/7*t**3 - 2/7*t**5 - 2/7*t**2 + 0 - y*t**4.
-2*t**2*(t + 1)**3/7
Let v be (-3)/(-18)*(3 - 2). Let n(f) be the second derivative of -f + 4/3*f**3 - 4*f**2 + 0 - v*f**4. Factor n(b).
-2*(b - 2)**2
Let m(h) be the first derivative of -2*h**3/9 - 2*h**2/3 + 7. Factor m(j).
-2*j*(j + 2)/3
Let j(d) be the second derivative of d**7/21 + d**6/5 + d**5/5 - 15*d + 1. What is x in j(x) = 0?
-2, -1, 0
Let g be (-12)/3 + (-100)/(-2). Let h = g + -26. Suppose h*l**2 + 16/9 - 88/9*l - 18*l**3 + 6*l**4 = 0. What is l?
2/3, 1
Let a(s) = -s**5 - s**4 + s. Let q(h) = 5*h**5 - 15*h**4 + 24*h**3 - 16*h**2 + 3*h. Let v(r) = a(r) + q(r). Factor v(y).
4*y*(y - 1)**4
Let t(i) = -2*i**2 + 4*i. Let q(c) = -c**2 + c. Suppose -3*y - p = -5, 5*y = -p - 0 + 7. Let v(k) = y*t(k) - 3*q(k). Factor v(r).
r*(r + 1)
Let m(x) be the third derivative of x**5/390 - x**3/39 - 23*x**2. Factor m(d).
2*(d - 1)*(d + 1)/13
Let a(z) be the third derivative of -z**6/24 - z**5/6 + 5*z**4/6 + 20*z**3/3 + 31*z**2. Factor a(u).
-5*(u - 2)*(u + 2)**2
Suppose -4*h = 3*x - 2*x - 7, 0 = 5*x + 2*h + 37. Let v = 13 + x. Find q, given that 2/7*q**2 + 2*q**v + 6/7*q**5 + 0 + 10/7*q**3 + 0*q = 0.
-1, -1/3, 0
Let m(b) = b**3 + 2*b**2 - 1. Let f be m(1). Let j be -4 + 78/18 + 0. Suppose 8/3 + j*t**3 + f*t**2 + 4*t = 0. What is t?
-2
Suppose -10 = 5*d + 5*q, 2*d + 2*q + 9 = -d. Let y be 2/d*2 + 2. Solve -9/5*b**3 + 0*b + 3/5*b**4 + y*b**2 + 0 = 0 for b.
0, 1, 2
Let z be 1 - (-39)/(-15) - (-4 + 2). Let 2/5*f**5 + 2/5*f**2 + 0*f - 2/5*f**3 - z*f**4 + 0 = 0. Calculate f.
-1, 0, 1
Let p(o) = 3*o**2 + 3*o. Let t be p(-3). What is m in -t*m**2 - 25*m**3 + 1 + 3*m + 73*m**2 - 42*m + 8 = 0?
3/5, 1
Let l(v) be the third derivative of 5*v**8/336 - v**7/21 + v**6/24 - 12*v**2. Solve l(m) = 0 for m.
0, 1
Let f(a) be the third derivative of 0*a - 3/40*a**6 + 1/8*a**4 + 1/5*a**5 + a**2 - a**3 + 0. Let f(q) = 0. What is q?
-2/3, 1
Let u be (-1 - 14)/(-9 + 6). Determine l, given that 2*l**3 + 0 - 6*l**4 - 20/3*l**u + 0*l + 4/3*l**2 = 0.
-1, -2/5, 0, 1/2
Let m(f) = -f**2 + 6*f - 2. Let g be m(4). Suppose -4*n + g = -n. Determine c so that 4/7 - 10/7*c**n + 6/7*c = 0.
-2/5, 1
Let -10/9*o + 0 - 2/9*o**2 = 0. Calculate o.
-5, 0
Let f(u) be the second derivative of -u**7/2520 - u**6/1080 - 4*u**3/3 + 8*u. Let s(y) be the second derivative of f(y). Determine x, given that s(x) = 0.
-1, 0
Let m = -4 + 6. Factor 2*g**2 - m*g - 5*g**3 + 0*g**2 + 5*g**2.
-g*(g - 1)*(5*g - 2)
What is x in 26/9*x**2 - 26/9*x**3 - 4/9*x + 0 - 56/9*x**4 = 0?
-1, 0, 1/4, 2/7
Let k(x) = -x**3 + 3*x**2 + 11*x - 24. Let u be k(2). Let 18/7*n + 3/7*n**u + 27/7 = 0. What is n?
-3
Let x(b) = b**3 - 9*b**2 - 11*b + 13. Suppose -4*q + q + 30 = 0. Let y be x(q). Solve 0 + 4/7*d - 10/7*d**2 - 4/7*d**y + 10/7*d**4 = 0.
-1, 0, 2/5, 1
Let d(s) = 6*s**5 - 4*s**4 - 10*s**3 + 32*s**2 + 24*s - 8. Let u(a) = -2*a**5 + a**4 + 3*a**3 - 11*a**2 - 8*a + 3. Let n(h) = 3*d(h) + 8*u(h). Factor n(l).
2*l*(l - 2)**2*(l + 1)**2
Let q(n) be the second derivative of -n**4/12 + 3*n**3 + 5*n**2/2 - 9*n. Let a be q(18). Factor 0*i - 2/9*i**3 - 4/9*i**2 + 0 + 8/9*i**4 + 2/3*i**a.
2*i**2*(i + 1)**2*(3*i - 2)/9
Let h be (-128)/(-80) - 6/(-15). Factor 2/9*b**h - 4/9 - 2/9*b.
2*(b - 2)*(b + 1)/9
Let g = -3445 - -68821/20. Let u = g - -21/5. Determine p, given that 1/2*p + 1/4*p**2 + u = 0.
-1
Suppose 4*y - 8 = -8. Factor y + 0*n + 2/7*n**2.
2*n**2/7
Factor 3*v**5 - 29 - 9*v**3 + 16*v**2 + 29 - 10*v**2.
3*v**2*(v - 1)**2*(v + 2)
Let o = 556/843 - -2/281. What is h in 0 + 0*h + o*h**5 + 0*h**2 + 0*h**4 - 2/3*h**3 = 0?
-1, 0, 1
Let c(g) be the second derivative of g**7/14 - g**6/5 + 3*g**5/20 + 2*g. Factor c(a).
3*a**3*(a - 1)**2
Let v(k) = k + 15. Suppose -2*d - 4*b - 14 = 2, -58 = 5*d + b. Let p be v(d). Factor 0 + 1/3*i**2 - 1/3*i**p - 1/3*i**4 + 1/3*i.
-i*(i - 1)*(i + 1)**2/3
Let k(m) be the second derivative of m**7/1680 - m**6/720 + m**3/3 + 2*m. Let w(r) be the second derivative of k(r). Suppose w(q) = 0. Calculate q.
0, 1
Let r be ((-24)/112)/((-12)/14). Find h, given that 1/4*h**4 + 1/4*h**5 - r*h**3 - 1/4*h**2 + 0*h + 0 = 0.
-1, 0, 1
Factor 29*x**3 + 25*x**2 - 43*x - 9*x**3 + 48*x.
5*x*(x + 1)*(4*x + 1)
Let u(b) = -4*b**5 - 20*b**4 - 24*b**3 - 8*b**2 - 4*b + 4. Let t(z) = -4*z**5 - 19*z**4 - 23*z**3 - 8*z**2 - 3*z + 3. Let c(f) = -4*t(f) + 3*u(f). Factor c(m).
4*m**2*(m + 1)**2*(m + 2)
Let z = -553 - -3877/7. Find x such that 0 + z*x**2 + 3/7*x + 3/7*x**3 = 0.
-1, 0
Suppose 2 - 12 = -5*z. Let j be -1 + (-2)/(z/(-1)). Solve 0 + 4/7*s**2 + j*s + 18/7*s**3 + 2*s**4 = 0 for s.
-1, -2/7, 0
Let o(r) be the third derivative of -r**7/210 - r**6/45 - r**5/30 + r**3/6 + 2*r**2. Let q(x) be the first derivative of o(x). Factor q(w).
-4*w*(w + 1)**2
Let r = -220/3 + 74. Let v = -21 - -65/3. Suppose 2/3*n**4 + 2*n**3 - r*n**5 + 0 - v*n**2 - 4/3*n = 0. Calculate n.
-1, 0, 1, 2
Let z(j) = -j**3 - 6*j**2 - 7*j - 4. Let k be z(-5). Determine c, given that k*c**3 + 14 - 3*c**2 - 14 = 0.
0, 1/2
What is w in 20*w - 5*w**2 - 12 + 9 - 10 - 2 = 0?
1, 3
Let p be 7/3 + (-9 - -10). Let m = 23/6 - p. Let 0 - 1/2*u**4 - 1/2*u**3 + m*u**2 + 1/2*u = 0. Calculate u.
-1, 0, 1
Let p be 3 - ((1 - -1) + -1). Let g = 5 - p. Factor 4*x**3 - x - g*x**2 + 5*x**2 - 5*x**3.
-x*(x - 1)**2
Let u(p) be the second derivative of -p**6/30 - p**5/4 - 3*p**4/4 - 8*p**3/3 - 11*p**2/2 + 6*p. Let f(o) = -o - 1. Let y(a) = -18*f(a) + 2*u(a). Factor y(x).
-2*(x + 1)**3*(x + 2)
Factor -5/2*h**2 + 0 + 5/2*h**3 - 5/2*h**5 + 0*h + 5/2*h**4.
-5*h**2*(h - 1)**2*(h + 1)/2
Suppose 233 = 5*t - 2*r, t - 2*t + 2*r + 53 = 0. Let g be (-36)/t*(-10)/28. Factor -6/7*o + 8/7*o**2 - g.
2*(o - 1)*(4*o + 1)/7
Let z be 19/(-38) - 7/(-12). Let x(m) be the first derivative of -1/9*m**3 + z*m**4 + 2 + 0*m + 0*m**2. Factor x(o).
o**2*(o - 1)/3
Let a be 4/(-14) - 111/(-21). What is t in -t**2 + t**4 - 8*t**5 - 3*t**3 + 9*t**a + 2*t**3 = 0?
-1, 0, 1
Let s(x) be the third derivative of -x**8/3360 + x**3/3 + 5*x**2. Let q(f) be the first derivative of s(f). Solve q(l) = 0.
0
Factor 1/3*z**4 + 1/3*z**2 - z**3 + z - 2/3.
(z - 2)*(z - 1)**2*(z + 1)/3
Let t(k) = k**3 - 7*k**2 - 9*k + 12. Let m be t(8). Determine p, given that -2*p**3 + 5*p + p + m*p**2 - 2*p - 2*p**2 = 0.
-1, 0, 2
Solve -16/3*t - 4/3*t**3 + 0 - 16/3*t**2 = 0 for t.
-2, 0
Let g(a) be the first derivative of 5*a**4/6 - 7*a**3/3 + 2*a**2 + a - 3. Let m(z) be the first derivative of g(z). Factor m(h).
2*(h - 1)*(5*h - 2)
Let a(p) = -129*p**3 - 460*p**2 - 411*p - 58. Let r(u) = 26*u**3 + 92*u**2 + 8