 10*z. Let x(v) = 20*v**5 + 65*v**4 + 81*v**3 + 47*v**2 + 11*v. Let n(u) = -3*a(u) - 2*x(u). Factor n(o).
4*o*(o + 1)**3*(5*o + 2)
Let 0*a - 2/9 + 2/9*a**2 = 0. Calculate a.
-1, 1
Suppose 4*d + 0*t - 4*t = 12, d + 2*t = 0. Suppose d*y - b = -2*y - 5, 0 = y + 4*b - 20. Factor 0 + 0*v + 1/4*v**3 + y*v**2 - 3/4*v**4.
-v**3*(3*v - 1)/4
Let g = -7 + 12. Let y(a) be the first derivative of -1/7*a**2 - 2/35*a**g + 1 + 2/21*a**3 + 0*a + 1/14*a**4. Factor y(m).
-2*m*(m - 1)**2*(m + 1)/7
Let d(s) be the second derivative of -s**7/189 + 2*s**6/135 + s**5/90 - s**4/27 + 2*s. Let d(c) = 0. What is c?
-1, 0, 1, 2
Let t(i) be the first derivative of 5*i**4/4 + 5*i**3/3 - 15*i**2 + 7. Suppose t(a) = 0. What is a?
-3, 0, 2
Let j = -26 - -26. Let f(d) be the second derivative of -2/75*d**6 + 2/15*d**3 - d + 0 + 1/50*d**5 + j*d**2 + 1/6*d**4. Suppose f(v) = 0. What is v?
-1, -1/2, 0, 2
Let s(y) be the first derivative of 1/3*y**3 + 0*y**2 - 7 - y. Factor s(v).
(v - 1)*(v + 1)
Solve -4*p**3 + 2 + 5*p**3 + 0*p**3 - 3*p = 0 for p.
-2, 1
Let y(b) be the second derivative of -3*b**5/140 + b**4/14 + 3*b. Factor y(c).
-3*c**2*(c - 2)/7
Factor -6/5 - 8/5*g - 2/5*g**2.
-2*(g + 1)*(g + 3)/5
Let c(q) be the second derivative of -1/36*q**4 + 1/6*q**3 + 0 - 1/3*q**2 + q. Solve c(a) = 0.
1, 2
Let z(j) = -j**3 - 8*j**2 + 11*j + 5. Let y be z(-9). Let d(s) = 3*s**2 - 12*s. Let i(q) = -6*q**2 + 25*q. Let m(n) = y*d(n) - 6*i(n). Let m(p) = 0. What is p?
0, 2
Let y(o) be the first derivative of -128/15*o**5 - 1 - 16/3*o**3 - 1/6*o + 32/3*o**4 + 4/3*o**2. Find r such that y(r) = 0.
1/4
Suppose 17*a - 57 + 6 = 0. Find x such that -2/13*x**a - 54/13 - 18/13*x**2 - 54/13*x = 0.
-3
Let a(f) be the third derivative of 0 + 1/180*f**6 + 0*f**4 + 0*f**3 + 0*f**7 - 5*f**2 + 0*f**5 - 1/504*f**8 + 0*f. Factor a(v).
-2*v**3*(v - 1)*(v + 1)/3
Let a(v) be the third derivative of v**6/120 + v**5/15 + v**4/8 + v**3/2 - v**2. Let m be a(-3). What is r in -r - 3 + 2 - r**2 + m = 0?
-2, 1
Solve 2 + 4/3*k - 2/3*k**2 = 0.
-1, 3
Let g = -115 + 579/5. Suppose 4/5*y**3 - 2/5 - 6/5*y - g*y**2 + 6/5*y**4 + 2/5*y**5 = 0. Calculate y.
-1, 1
Let o(z) be the first derivative of -5*z**3/3 + 25*z**2/2 - 20*z + 26. Solve o(s) = 0 for s.
1, 4
Suppose -2*j = -3*m + 2, m - 4 = -43*j + 42*j. Factor -2/13*v + 2/13*v**5 - 4/13*v**j + 0 + 0*v**3 + 4/13*v**4.
2*v*(v - 1)*(v + 1)**3/13
Let v be 4 + 1 + -2 + 5/(-2). Factor v*t**2 + 1/2*t + 0.
t*(t + 1)/2
Let p(b) be the third derivative of -b**6/960 + b**5/480 + b**4/96 + b**2. Factor p(g).
-g*(g - 2)*(g + 1)/8
Let p(v) = v**2 - v - 1. Let h(z) = -z**2 - 2*z + 6. Suppose -5*d = 2*l + 18, 2*d = -l - 2*l - 16. Let y(b) = d*h(b) - 4*p(b). Suppose y(q) = 0. Calculate q.
2
Suppose 0 = 7*t - 8*t - 2. Let o be (-2 - t)/(1 - -1). Factor o + 0*u**2 + 0*u + 0*u**3 + 2/9*u**4 - 2/9*u**5.
-2*u**4*(u - 1)/9
Let 13/2*o**2 - 6*o - 3*o**3 + 2 + 1/2*o**4 = 0. What is o?
1, 2
Let a(m) be the second derivative of m**5/40 + m**4/6 - 10*m. Suppose a(t) = 0. What is t?
-4, 0
Let n be (241*-1)/(25/5). Let j = -48 - n. Factor -j - 2/5*l - 1/5*l**2.
-(l + 1)**2/5
Let x(r) = 2*r**2 + 3. Let w be x(-3). Let y = -5 + w. Determine l so that -2 - 2*l**3 - y*l**2 - 6*l**3 + 0*l**3 - 10*l = 0.
-1, -1/2
Let j(a) be the second derivative of a**6/90 + a**5/12 + a**4/4 + 7*a**3/18 + a**2/3 - 11*a. Factor j(l).
(l + 1)**3*(l + 2)/3
Determine a so that 2*a**2 - 1 - 6 + 1 - 4*a + 0*a**2 = 0.
-1, 3
Let j(h) be the first derivative of 8*h**6/15 - h**5 + h**4/3 - 9*h + 9. Let w(b) be the first derivative of j(b). Factor w(y).
4*y**2*(y - 1)*(4*y - 1)
Find h, given that 3*h + 3*h**2 - 3*h**2 - 4*h**2 - 2*h = 0.
0, 1/4
Let q(l) be the second derivative of l**7/105 - l**6/60 - l**5/60 + l**3/2 - 2*l. Let x(c) be the second derivative of q(c). What is t in x(t) = 0?
-1/4, 0, 1
Let c(t) be the third derivative of t**6/840 - t**5/210 + t**4/168 - 20*t**2. Determine h so that c(h) = 0.
0, 1
Factor -4*a + a**2 + 2 + 2*a**2 - 2*a**2 + a**2.
2*(a - 1)**2
Let o = -70/9 - -8. Suppose -2/9*z**3 - o*z**2 + 2/9 + 2/9*z = 0. What is z?
-1, 1
Let k(f) be the second derivative of -f**4/48 - f**3/12 + f. Factor k(t).
-t*(t + 2)/4
Let p = -656/7 - -94. Factor 2/7*j**3 - 2/7*j**2 + 2/7 - p*j.
2*(j - 1)**2*(j + 1)/7
Suppose -4*h + 7 = -s - 5, 0 = 5*h - 3*s - 8. Factor 0 - 10/3*r**5 + 8*r**h - 6*r**3 + 4/3*r**2 + 0*r.
-2*r**2*(r - 1)**2*(5*r - 2)/3
Let k(x) be the third derivative of -1/72*x**4 - 1/360*x**6 + 0*x + 1/90*x**5 + 0 + 0*x**3 + 3*x**2. Factor k(s).
-s*(s - 1)**2/3
Let f(j) = -j**2 + 5*j - 3. Let q be f(2). Solve -4*s**2 + s**q + s**2 - 5*s**3 + s**2 - 2*s**4 = 0.
-1, 0
Let v = 394 - 1181/3. Find r such that 1/3 + v*r**2 - 2/3*r = 0.
1
Let i be (-2)/4 - 14/4. Let a(q) = 10*q**3 - 20*q**2 + 81*q - 88. Let d(x) = -3*x**3 + 7*x**2 - 27*x + 29. Let c(s) = i*a(s) - 14*d(s). Factor c(k).
2*(k - 3)**3
Find h such that 0 + 0*h**2 - 3/5*h**3 + 3/5*h = 0.
-1, 0, 1
Let x(r) = -r**3 - 3*r**2 - r - 1. Let s be x(-3). Determine v so that 2 + 6*v + 0*v - 2 + 21*v**s = 0.
-2/7, 0
Let g = -5 + 7. Factor y**4 + 2*y**4 - y**4 - 4*y**4 + 2*y**g.
-2*y**2*(y - 1)*(y + 1)
Suppose -w = -1, 0 = y + w - 5 - 0. Suppose 2*a + y*k - 16 = -0*a, 2*k = 6. Factor -s**2 + 2 + 5*s - s**a - 6*s + s**3.
(s - 2)*(s - 1)*(s + 1)
Let r be (-6)/(-5) - 91/130. Let -7/4*l - l**2 + r = 0. What is l?
-2, 1/4
Let w(m) be the first derivative of -m**6/9 - 4*m**5/15 + 4*m**3/9 + m**2/3 + 8. Factor w(f).
-2*f*(f - 1)*(f + 1)**3/3
Let t(w) be the third derivative of 7*w**5/300 + w**4/60 + 18*w**2. Factor t(z).
z*(7*z + 2)/5
Let c = -45 - -40. Let q(h) = 2*h**3 - 6*h + 2. Let t(u) = -5*u**3 + u**3 + u - u**2 + 12*u - 5. Let n(b) = c*q(b) - 2*t(b). Factor n(o).
-2*o*(o - 2)*(o + 1)
Suppose 5*v + 55 = -25. Let n = -6 - v. Let 11*c**3 + 15*c**3 + n*c**2 - 8*c**3 - 14*c**4 - 18*c + 4 = 0. Calculate c.
-1, 2/7, 1
Let c(n) = -3*n + 3. Let o be c(-5). Let 18*v + 10*v - 29 + 2*v**3 - 25 - o*v**2 + 26*v = 0. Calculate v.
3
Let h be (-2)/(-3) + 14/(-3). Let i be ((-9)/6)/(3/h). Factor -3*r**3 + r**i + 4*r**3 - 3*r**2 + r**2.
r**2*(r - 1)
Let a(h) be the third derivative of -h**5/12 - h**4/8 + h**3/3 - 3*h**2. Let r(g) = 6*g**2 + 4*g - 2. Let w(u) = -5*a(u) - 4*r(u). Find l such that w(l) = 0.
-1, 2
Let l(i) be the first derivative of -4 - 1/9*i**3 - 1/6*i**2 + 1/3*i + 1/12*i**4. Factor l(c).
(c - 1)**2*(c + 1)/3
Let p be 3/2*4/3. Factor 0*d**3 + d - 2*d**3 - d**3 + p*d.
-3*d*(d - 1)*(d + 1)
Let s(i) be the third derivative of -i**5/12 - 5*i**4/8 - 5*i**3/3 + 10*i**2 - 4. Determine k, given that s(k) = 0.
-2, -1
Factor 4/3*m + 0 - 14/3*m**4 + 2*m**2 - 2*m**3 - 2*m**5.
-2*m*(m + 1)**3*(3*m - 2)/3
Let z(u) = 6*u + 60. Let i be z(-10). Factor 2/5*d**2 + 3/5*d**4 + 0*d - d**3 + i.
d**2*(d - 1)*(3*d - 2)/5
Solve -46/5*a**2 - 8/5 + 28/5*a**3 + 32/5*a - 6/5*a**4 = 0.
2/3, 1, 2
Suppose -117 = -4*u + u. Factor -u + 2*d**3 + d**2 + 38 + d - 3*d**3.
-(d - 1)**2*(d + 1)
Let b be (-1 + 1)/((-2)/2). Let s(g) be the first derivative of -7/12*g**6 - 1 + 0*g + b*g**2 + 0*g**3 + 1/5*g**5 + 0*g**4. Solve s(c) = 0 for c.
0, 2/7
Let o(w) be the third derivative of w**10/604800 - w**9/241920 + w**5/60 + 7*w**2. Let q(h) be the third derivative of o(h). Find f, given that q(f) = 0.
0, 1
Suppose -17*o**2 + 44*o**2 + 20*o - 23*o**2 = 0. What is o?
-5, 0
Let q(z) be the third derivative of -z**6/600 - z**5/50 - z**4/10 - 4*z**3/15 + 36*z**2. Factor q(i).
-(i + 2)**3/5
Let r(i) be the third derivative of i**7/35 - 3*i**6/40 + i**5/20 - 17*i**2. Factor r(t).
3*t**2*(t - 1)*(2*t - 1)
Let q(o) be the second derivative of o**6/25 + o**5/10 + o**4/30 - o**3/15 + 16*o. Determine x, given that q(x) = 0.
-1, 0, 1/3
Suppose 0 = -4*p + 4*b + 20, 4*b + 13 + 9 = 5*p. Factor -3*k**2 + 24*k - 11*k**p + 6 + 2.
-2*(k - 2)*(7*k + 2)
Suppose 4 = o, m + 5*o = -3*m + 40. Suppose 0 = 3*t + 6, m*g - 5 = 5*t + 5. Let g*n + 0 + 1/3*n**3 - 1/3*n**2 = 0. What is n?
0, 1
Let p(n) = n**3 + 7*n**2 + 2*n. Let b be p(-6). Let 31*l - 330*l**4 - 45*l - 20*l - 69*l**3 + b + 306*l**2 + 225*l**5 - 122*l = 0. Calculate l.
-1, 2/5, 2/3, 1
Let x = -278/5 - -56. Let f(w) = w**2 - w. Let q be f(1). Let q*o**2 - x*o**3 + 2/5*o + 0 = 0. Calculate o.
-1, 0, 1
Let s(l) be the second derivative of -l**4/3 - 8*l**3 - 72*l**2 - 18*l. Determine u, given tha