first derivative of 1/12*f**3 + 5 - 1/4*f + 0*f**2. Determine j so that r(j) = 0.
-1, 1
Let g(s) be the first derivative of s**6/57 + 18*s**5/95 + 13*s**4/19 + 68*s**3/57 + 21*s**2/19 + 10*s/19 - 42. Suppose g(w) = 0. Calculate w.
-5, -1
Let k(c) = -5*c - 80. Let g be k(-16). Let j(s) be the second derivative of -3/20*s**5 + 0*s**3 + g + 0*s**2 + 1/4*s**4 + s. What is a in j(a) = 0?
0, 1
Let l(d) = -d**2. Suppose -3*b + 32 = 3*x + x, 0 = -b + 4*x. Let n = b - 6. Let r(g) = g**4 + 3*g**2 + 1. Let u(v) = n*r(v) + 10*l(v). Factor u(q).
2*(q - 1)**2*(q + 1)**2
Let r(m) be the first derivative of 0*m**2 + 2/3*m**3 - 2*m - 3. Solve r(k) = 0 for k.
-1, 1
Let l be (-1)/(-5)*20/8. Let u = -76 - -153/2. Let l*y - 1/2*y**3 + u*y**2 - 1/2 = 0. What is y?
-1, 1
Let u(l) be the first derivative of -5*l**5 - 5*l**4/4 + 16*l**3/3 - 2*l**2 + 5. Factor u(f).
-f*(f + 1)*(5*f - 2)**2
Let r(b) = b**2 - b + 3. Let l be r(0). Let c(h) be the first derivative of 2/9*h**l + 0*h - 2/3*h**2 - 1. Factor c(m).
2*m*(m - 2)/3
Let a = 1/245 + 242/735. Factor a*p**2 + 0 - 2/3*p.
p*(p - 2)/3
Factor 0*w - 2/13*w**2 + 0 + 2/13*w**3.
2*w**2*(w - 1)/13
Let l(d) be the first derivative of -d**6/21 + 2*d**5/35 + d**4/14 - 2*d**3/21 + 1. Determine r, given that l(r) = 0.
-1, 0, 1
Suppose 25 = -o - 5*s + 10*s, 5*o - 5*s + 25 = 0. Suppose 3*i + 5*g = -19, 20 = i - 5*g - 7. Find y such that -2/9 + o*y + 2/9*y**i = 0.
-1, 1
Let s(q) = -q**2 + 7*q - 10. Let i be s(4). Factor 1/4*b**i - 1/4*b - 1/2.
(b - 2)*(b + 1)/4
Suppose f + 5*f - 12 = 0. Let t be 0*(-1)/2 - -2. Find l, given that 0*l**t - 4*l**2 - 2*l**2 - 3*l + 3*l**f + 6 = 0.
-2, 1
Let l(m) be the second derivative of -8*m + 0 + 0*m**3 + 1/12*m**4 + 0*m**2 - 7/30*m**6 - 2/21*m**7 - 1/10*m**5. Find x such that l(x) = 0.
-1, 0, 1/4
Let m be (-34)/(-4) - (-16 + 24). Factor m - 1/2*x - 1/2*x**2 + 1/2*x**3.
(x - 1)**2*(x + 1)/2
Suppose 0 = -4*j - 2*d + 2, 4*d - 3*d = -4*j + 3. Factor -2*v + 1 + v**2 - j + 4*v.
v*(v + 2)
Let 0*h + 0*h**3 - 2/9*h**4 + 10/9*h**2 - 8/9 = 0. What is h?
-2, -1, 1, 2
Let s(y) be the third derivative of -2*y**7/105 + y**6/15 - y**4/3 + 2*y**3/3 - 11*y**2. Suppose s(a) = 0. Calculate a.
-1, 1
Let k(w) = w + 3. Let r be k(-3). Let u = 5 - 9/2. Determine c, given that 0 - 3/4*c**5 + 3/4*c**3 + 1/2*c**2 + r*c - u*c**4 = 0.
-1, -2/3, 0, 1
Let o = -65545/44254 - -281/218. Let l = 11/29 - o. Solve -l - 2/7*t + 2/7*t**2 = 0 for t.
-1, 2
Let w(t) = 3*t - 1. Let b be w(2). Suppose -2*y + 5 = -s, -4*s = -b*y + 3 + 11. Suppose 2*f**3 - 2*f - 3*f**2 + f**2 + 2*f**4 + 0*f**y = 0. What is f?
-1, 0, 1
Let j(u) = -5*u**2 - 50*u. Let b be j(-10). Let a(z) be the first derivative of -1/4*z**3 + b*z - 3/8*z**2 + 9/8*z**4 - 1. Factor a(o).
3*o*(2*o - 1)*(3*o + 1)/4
Suppose -3*n - 3 = 0, p + 0*p = 5*n + 7. Solve 8*y**p - 3*y**2 - 3*y**2 = 0 for y.
0
Let u(d) = -74*d**3 - 148*d**2 - 104*d - 22. Suppose -7 = -f - 8. Let w(k) = -k**3 + k**2 + 1. Let s(g) = f*u(g) + 2*w(g). Let s(a) = 0. What is a?
-3/4, -2/3
Let v(d) be the first derivative of d**6/10 + 9*d**5/20 + 3*d**4/4 + d**3/2 + 5*d - 4. Let q(x) be the first derivative of v(x). What is p in q(p) = 0?
-1, 0
Factor 2/3*w**2 - 4/3 - 2/3*w.
2*(w - 2)*(w + 1)/3
Let b = -29/1387 + 8101583/5548. Let f = b + -1448. Suppose -1 + 7*i - f*i**2 = 0. Calculate i.
2/7
Let m(t) be the first derivative of -75*t**6 + 114*t**5 - 32*t**4 + 8*t**3/3 - 27. Determine l, given that m(l) = 0.
0, 2/15, 1
Suppose 4*v - 62 + 158 = 0. Let r(o) = -9*o**4 + 9*o**2 + 8*o + 8. Let c(l) = -l**4 + l**2 + l + 1. Let n(h) = v*c(h) + 3*r(h). Factor n(k).
-3*k**2*(k - 1)*(k + 1)
Let y(a) = 4*a**3 - a**2 - 5*a + 3. Let w(x) = 7*x**3 - 2*x**2 - 9*x + 5. Let z(m) = -3*w(m) + 5*y(m). Suppose z(o) = 0. What is o?
-1, 0, 2
Suppose 4*d + 6 - 18 = -c, -5*d - 4*c = -26. Suppose 14/9*j**3 - 2/9 - d*j**2 - 4/9*j**4 + 10/9*j = 0. What is j?
1/2, 1
Let k(u) = -u**2 + 4*u - 4. Let h be k(4). Let r be 8/27*(-3)/h. Factor 2/9*w**2 + r - 4/9*w.
2*(w - 1)**2/9
Let u be 1/(-2)*0/(-8). Let y(o) be the third derivative of -1/120*o**6 + 1/6*o**3 + o**2 + u*o + 0 + 1/24*o**4 - 1/60*o**5. Determine g so that y(g) = 0.
-1, 1
Factor 0 - 16/5*p**2 + 4/5*p**3 - 4*p.
4*p*(p - 5)*(p + 1)/5
Let b be 6/4 - (-3)/2. Let v(d) be the first derivative of 0*d - 4/15*d**b - 2 + 1/5*d**2 + 1/10*d**4. Determine m so that v(m) = 0.
0, 1
Let d(q) = q + 8. Let s(t) = t**2 - 3*t - 4. Let a be s(3). Let r be d(a). Factor 0 - 1/3*o**3 - 1/3*o**r + 0*o**2 + 0*o.
-o**3*(o + 1)/3
Let j be 891/36*6/9. Factor -63/2*z**3 - j*z**2 - 3*z + 0 - 51/2*z**4 - 15/2*z**5.
-3*z*(z + 1)**3*(5*z + 2)/2
Factor 1/2*i - 1/2*i**2 - 1/2*i**3 + 0 + 1/2*i**4.
i*(i - 1)**2*(i + 1)/2
Let f(l) be the second derivative of l**5/60 - 3*l**2/2 - 3*l. Let v(i) be the first derivative of f(i). Factor v(o).
o**2
Suppose 4*v - 48 = i, -2*i - 88 = -v - 3*v. Let h be (-6)/i + 3/12. Factor 2/5*l**2 + h*l + 0.
2*l*(l + 1)/5
Let w(y) = -4*y. Let p be w(-1). Let i = p + 0. Determine m so that -i - m**2 - 3*m + 5*m + 2*m = 0.
2
Let 3/7*y**3 + 3/7*y**2 + 1/7*y**4 + 0 + 1/7*y = 0. What is y?
-1, 0
Factor 9*f**4 + 32*f**3 + 3*f**4 + 3 - 7 + 24*f**2.
4*(f + 1)**3*(3*f - 1)
Let h(j) be the third derivative of 0 - 7/2*j**4 + 0*j + 3*j**3 - 3*j**2 + 5/6*j**5 - 1/15*j**6. Factor h(u).
-2*(u - 3)**2*(4*u - 1)
Let o(v) = -v**3 + 4*v**2 + 3*v + 3. Let s be 6/(-15) + (-6)/10. Let r(d) = d**2 + d + 1. Let z(i) = s*o(i) + 3*r(i). Factor z(y).
y**2*(y - 1)
Let r be (-161)/(-21) + -4 - 1. Factor -8/3*m**4 + 2/3*m**5 - r*m**2 + 0 + 2/3*m + 4*m**3.
2*m*(m - 1)**4/3
Let c(u) = u**3 - 9*u**2 - 9*u - 9. Let h be c(10). Let k = 3 - h. Factor 32*l + 13*l**2 + 2*l**5 - 14*l**4 + 38*l**3 - 36*l**k - 27*l**2 - 8.
2*(l - 2)**2*(l - 1)**3
Suppose -4*z + 24 = -z. Let l = z + -6. Factor -2/3*f**l + 4/3*f - 2/3.
-2*(f - 1)**2/3
Let z = 80/3 - 26. Factor 0*o**3 - z + 0*o - 2/3*o**4 + 4/3*o**2.
-2*(o - 1)**2*(o + 1)**2/3
Let n(m) = -m**5 + 13*m**4 - 17*m**3 + 5*m + 5. Let i(z) = -z**5 + 7*z**4 - 9*z**3 + 3*z + 3. Let c(f) = -10*i(f) + 6*n(f). Factor c(b).
4*b**3*(b - 1)*(b + 3)
Let f(w) be the first derivative of -3*w**6/8 + 3*w**5/4 + 41*w**4/16 - w**3/4 - 4*w**2 - 3*w - 4. Let f(t) = 0. Calculate t.
-1, -2/3, 1, 3
Let -3/2*u**2 - 3 + 9/2*u = 0. Calculate u.
1, 2
Let i(h) = -27*h**3 + 21*h. Let v(x) = 27*x**3 - x**2 - 22*x + 1. Let m(z) = -5*i(z) - 6*v(z). Factor m(j).
-3*(j - 1)*(j + 1)*(9*j - 2)
Let a = 3 + -1. Factor 0 + 4/7*k + 2/7*k**a.
2*k*(k + 2)/7
Let h(m) be the third derivative of 7*m**5/60 - m**4/12 + m**3/2 - m**2. Let j(t) = -t**2 + t. Let d(u) = h(u) + 6*j(u). Factor d(c).
(c + 1)*(c + 3)
Let j(r) = -7*r + 59. Let w be j(8). Factor 6*t - 6*t**2 + 3/2*t**w + 0.
3*t*(t - 2)**2/2
Let z be ((-3)/(-7))/((-3)/(-46)). Let y = 318 + -316. Suppose 26/7*p + z*p**3 - y*p**4 - 4/7 - 54/7*p**2 = 0. Calculate p.
2/7, 1
Suppose t - t - 4*t = 0. Let k(z) be the first derivative of 0*z + t*z**2 + 3 - 2/21*z**3 + 3/14*z**4. Find l such that k(l) = 0.
0, 1/3
Let u(f) = 3*f - 7. Let z be u(3). What is p in -p**2 + 2*p**2 + z*p**2 - 3 + 0 = 0?
-1, 1
Let x(r) = -2*r**3 - 15*r**2 - 7*r - 5. Let z(b) = 2*b**3 + 14*b**2 + 8*b + 4. Let o(p) = 4*x(p) + 5*z(p). Let o(t) = 0. What is t?
-3, -2, 0
Let m(s) be the second derivative of -s**7/168 + s**6/40 + s**5/80 - 7*s**4/48 + s**2/2 + 7*s. Find v, given that m(v) = 0.
-1, 1, 2
Let k = 88 - 88. Determine j so that 0 - 1/4*j**2 + k*j = 0.
0
Let q(w) be the first derivative of -9/20*w**5 - 1/2*w**3 + 0*w + 0*w**2 + 15/16*w**4 + 1. Let q(g) = 0. Calculate g.
0, 2/3, 1
Let y(p) be the first derivative of 2*p**7/21 + p**6/6 + p**5/20 + 3*p - 3. Let d(i) be the first derivative of y(i). Factor d(q).
q**3*(q + 1)*(4*q + 1)
Let x(p) = p + 14. Let z be x(-9). Factor -5*r + r + 0*r**2 + 4*r**3 + r**2 + z*r**2.
2*r*(r + 2)*(2*r - 1)
Let t(p) be the first derivative of p**6/1800 + p**5/300 - 4*p**3/3 - 1. Let n(o) be the third derivative of t(o). Factor n(z).
z*(z + 2)/5
Suppose 5*l + 51*m + 20 = 47*m, 3*l - 5*m - 25 = 0. What is y in 0 - 16/3*y**3 - 5/3*y**5 + 4/3*y**2 + l*y + 17/3*y**4 = 0?
0, 2/5, 1, 2
Let a(y) be the first derivative of 3*y**2/2 + 1. Let f be a(1). Let -6*k - 2*k**f - 4*k**2 + 6*k = 0. What is k?
-2, 0
Suppose 0 - 2*v**2 - 3 - 12*v**2 + 32*v - 5 = 0. What is v?
2/7, 2
Let c(x) be the sec