+ k.
k*(k - 1)*(k + 1)
Let m(s) = s**3 - 6*s**2 - s + 8. Let z be m(6). Solve 6*g**2 - g**3 + 1 - g**4 + 0 - 3*g**3 - 4*g + z*g**4 = 0.
1
Suppose -869*h - 33036*h**2 + 173*h + 33039*h**2 = 0. Calculate h.
0, 232
Let y be (-2)/((70/765)/(-7)). Let o = 155 - y. Factor 2*s**3 + 16/3*s**o + 14/3*s + 4/3.
2*(s + 1)**2*(3*s + 2)/3
Factor -2/9*r**2 - 28/3 + 46/9*r.
-2*(r - 21)*(r - 2)/9
Let m(i) be the second derivative of -i**4/90 - 94*i**3/45 - 2209*i**2/15 + 297*i. Suppose m(f) = 0. What is f?
-47
Let h(o) be the third derivative of o**8/2688 + o**7/240 + o**6/80 - o**5/120 - o**4/12 - 47*o**2 - 2. Factor h(r).
r*(r - 1)*(r + 2)**2*(r + 4)/8
Let g(k) be the first derivative of 0*k**2 - 3 + 2*k**5 + 5/6*k**6 + 5/4*k**4 + 0*k + 0*k**3. Factor g(v).
5*v**3*(v + 1)**2
Let r(n) be the first derivative of -n**3/3 + n + 8. Let c(b) = 6*b**2 - 32*b + 22. Let o(y) = c(y) - 6*r(y). Find w, given that o(w) = 0.
2/3, 2
Let k be (11 - 11)/(-4 - -1). Let s(t) be the first derivative of k*t**4 + 0*t + 9 - 2/15*t**5 - 1/6*t**2 + 2/9*t**3 + 1/18*t**6. Factor s(q).
q*(q - 1)**3*(q + 1)/3
Let p be -1*2/(-5)*-30. Let d be -6 - (112/p - -3). Let -1/3*l**2 - d*l + 0 = 0. Calculate l.
-1, 0
Suppose 4*r - 10 = 2*f, -3*f - 11 = -4*r - 0*f. Let i(q) be the second derivative of 0*q**2 - 7*q - r*q**4 - q**5 + 0 - 2/3*q**3. Factor i(y).
-4*y*(y + 1)*(5*y + 1)
Let r(n) be the second derivative of 2*n**7/7 + 11*n**6/10 - 33*n**5/4 - 47*n**4/4 + 15*n**3/2 - 603*n. Determine u, given that r(u) = 0.
-5, -1, 0, 1/4, 3
Factor -132*o - 106*o - 381*o + 234*o - 803*o - 4*o**2.
-4*o*(o + 297)
Find n, given that -127*n**3 - 52*n + 29*n**3 + 38*n**4 - 64 - 28*n - 2*n**5 + 10*n + 26*n**2 + 170*n = 0.
-1, 1, 2, 16
Let h = -71 - -73. Factor -6*t + 7*t + 0*t**2 - 2*t**2 - t**3 + h.
-(t - 1)*(t + 1)*(t + 2)
Let k(x) = 789*x - 8676. Let a be k(11). Solve -69*q**2 - 243/2 + 216*q - 24*q**a - 3/2*q**4 = 0.
-9, 1
Suppose -1/7 + 0*o + 1/7*o**2 = 0. What is o?
-1, 1
Let h(k) = -103*k + 412. Let i be h(4). Suppose -4*w + 11 = c + 2*c, -1 = -c. Factor 4/9*v**w + i - 2/9*v.
2*v*(2*v - 1)/9
Let m(x) be the third derivative of 0*x - 1/15*x**5 + 0*x**3 + 2/105*x**7 + 1/6*x**4 - 1/30*x**6 + 0 - 2*x**2. Solve m(c) = 0.
-1, 0, 1
Suppose -16*f - 18*f = 0. Suppose -o = -2*o. Find y such that o*y - 5/2*y**2 + f = 0.
0
Let i(m) = -4*m**2 - 424*m - 11214. Let a(o) = 2*o**2 + 212*o + 5606. Let s(v) = -11*a(v) - 6*i(v). Factor s(n).
2*(n + 53)**2
Suppose 5*c - 7 = -r, 3*c - 43*r + 41*r = 12. Let f be 1 - 2*2/8. Factor 1/4*j**c + f*j - 3/4.
(j - 1)*(j + 3)/4
Suppose 32*z - 2*z**5 - 98*z + 4*z**4 + 216 + 20*z**3 - 520 - 16*z**2 + 268 = 0. Calculate z.
-2, -1, 3
Suppose -4*d - v + 493 = 4*v, 2*v - 375 = -3*d. Let o = d - 247/2. Factor 5/2*k**2 + 3/2*k**4 - 1/2*k - o*k**3 + 0.
k*(k - 1)**2*(3*k - 1)/2
Let l(u) be the third derivative of -u**8/840 + u**7/105 - 2*u**6/75 + 2*u**5/75 + 64*u**2. Factor l(q).
-2*q**2*(q - 2)**2*(q - 1)/5
Let k be ((-10)/5)/((-12)/(-3)) + 14. Let h = -13 + k. Solve 0 + h*i + 1/2*i**4 - 3/4*i**3 - 3/4*i**2 = 0.
-1, 0, 1/2, 2
Let p(a) be the second derivative of a**4/8 + a**3 + 9*a**2/4 + 17*a - 5. What is c in p(c) = 0?
-3, -1
Let d(p) be the second derivative of -p**8/7840 + p**7/882 - p**6/2520 - p**5/70 - p**4/2 - p**3 + 16*p. Let o(g) be the third derivative of d(g). Factor o(c).
-2*(c - 3)*(c - 1)*(3*c + 2)/7
Let k be ((4 + -4)/(-8))/(-1). Let v(p) be the first derivative of -3 + 0*p**4 - 4/25*p**5 + k*p - 1/15*p**6 + 1/5*p**2 + 4/15*p**3. Factor v(h).
-2*h*(h - 1)*(h + 1)**3/5
Let q(n) be the first derivative of 2*n**5/15 + 4*n**4/3 + 32*n**3/9 + 179. Suppose q(h) = 0. Calculate h.
-4, 0
Let m = 470/3 + -156. Let t(i) be the second derivative of 0 + m*i**3 + i + i**2 + 1/6*i**4. Solve t(z) = 0.
-1
Let m = 205/2493 - -8/277. Let z(x) be the first derivative of 0*x + 2/9*x**3 + 1/6*x**4 + m*x**2 + 2/45*x**5 + 2. Suppose z(v) = 0. Calculate v.
-1, 0
Let -75*u**2 + 6*u**4 - 2*u**5 + 10*u**3 - 8*u - 69*u**2 + 138*u**2 = 0. What is u?
-1, 0, 1, 4
Let h(t) be the third derivative of -t**6/420 + t**5/5 - 24*t**4/7 + 544*t**3/21 - 3*t**2 + 38*t. Solve h(y) = 0.
4, 34
Suppose 3*m + m = -p + 21, p - 9 = -m. Let y(t) = t**2 - 5*t + 3. Let i be y(p). Find v, given that -11*v + 0*v + 5*v + i*v**2 = 0.
0, 2
Let z be 1/(-78) - (-50)/125*(-15)/(-36). Factor -2/13*y + 0 - z*y**3 + 4/13*y**2.
-2*y*(y - 1)**2/13
Let k(q) = 4*q**4 + 7*q**3 - 4*q**2 + 5*q + 12. Let a(z) = 4*z**4 + 6*z**3 - 4*z**2 + 4*z + 10. Let u(v) = -6*a(v) + 5*k(v). Find t such that u(t) = 0.
-1, -1/4, 0, 1
Let i(y) be the third derivative of 5/2*y**3 - 19*y**2 + 0*y + 25/24*y**4 + 0 + 1/6*y**5. Factor i(d).
5*(d + 1)*(2*d + 3)
Let o(r) = 5*r**2 + 17*r + 20. Let y(u) = 10*u**2 + 35*u + 40. Let x = 2 + 1. Let b(i) = x*y(i) - 5*o(i). Factor b(w).
5*(w + 2)**2
Let m(a) = -a**3 - a**2 + 3*a - 1. Let c(g) = g**4 + 12*g**3 + 3*g**2 - 24*g + 8. Let w(l) = -3*c(l) - 24*m(l). Factor w(k).
-3*k**2*(k - 1)*(k + 5)
Determine v, given that 3 + 5*v**2 + 13 + 0*v**2 - 21 = 0.
-1, 1
Let j be (42/56)/(15*-5*(-1)/60). Factor 1/5*c**4 + 0*c**3 - 2/5*c - j*c**2 + 0.
c*(c - 2)*(c + 1)**2/5
Let h(r) be the second derivative of 5*r**4/12 - 40*r**3/3 + 75*r**2/2 + 4*r. Suppose h(k) = 0. Calculate k.
1, 15
Let m be ((-2)/(-3))/((-4)/18). Let a(l) = l**3 + 3*l**2 - l. Let i be a(m). Let -5*t**4 + i*t**4 - t**4 - t**5 - t**3 + t**4 = 0. Calculate t.
-1, 0
Let f(w) be the third derivative of -w**7/7560 - w**6/360 - w**5/40 - 7*w**4/24 - 11*w**2. Let v(n) be the second derivative of f(n). Factor v(m).
-(m + 3)**2/3
Let r(g) = 2*g**2 + 16*g + 4. Let m be r(-9). Suppose 5*v**2 - 3*v + m - 12*v - 42 = 0. What is v?
-1, 4
Let k = 1651/6 - 275. Let y(m) be the second derivative of 1/10*m**5 - 3*m - k*m**4 + 0*m**3 + 0 + 0*m**2. Factor y(g).
2*g**2*(g - 1)
Let t(w) be the second derivative of -w**6/120 - 4*w**5/5 - 181*w**4/8 - 248*w**3/3 - 961*w**2/8 + 642*w. Determine r so that t(r) = 0.
-31, -1
Let c(l) be the second derivative of l**5/80 + 13*l**4/8 + 507*l**3/8 + 79*l. Factor c(g).
g*(g + 39)**2/4
Let d(g) be the third derivative of -g**6/180 + 61*g**5/90 + 125*g**4/36 + 7*g**3 - 22*g**2. Factor d(r).
-2*(r - 63)*(r + 1)**2/3
Let r(b) be the third derivative of 13*b**2 + 1/4*b**4 + 0*b + 0 - 7/30*b**5 + 0*b**3. Let r(t) = 0. What is t?
0, 3/7
Let s(w) = w**2 - w. Let u(x) be the second derivative of -8*x**5/5 - 59*x**4/6 - 22*x**3/3 - 3*x**2 - 13*x. Let y(d) = 6*s(d) + u(d). What is r in y(r) = 0?
-3, -1/4
Let q(i) be the third derivative of -i**6/16 - i**5/40 + 101*i**2. Factor q(y).
-3*y**2*(5*y + 1)/2
Let w(l) be the third derivative of -17/150*l**5 - 15*l**2 + 0 - 1/60*l**6 - 1/10*l**4 + 0*l**3 + 0*l. Suppose w(x) = 0. What is x?
-3, -2/5, 0
Let t be (0 + (-18)/21)/(((-930)/168)/31). Factor -2/5*n**2 - 72/5 - t*n.
-2*(n + 6)**2/5
Let r(a) be the second derivative of a**4/18 - 50*a**3/9 + 49*a**2/3 - 84*a. Factor r(o).
2*(o - 49)*(o - 1)/3
Let u be 0*(-2 - 4)/6. Let k(c) be the second derivative of u*c**2 - 1/30*c**6 + 5*c + 0 + 0*c**3 - 1/12*c**4 - 1/10*c**5. Factor k(i).
-i**2*(i + 1)**2
Let l be ((-2)/(-12) - (-11)/33)*0. Suppose 2*k = -l*k - 4*m + 8, -2*m - 20 = -2*k. Solve -4/3*n**2 - 22/3*n**3 + k*n**4 + 0 + 2/3*n = 0 for n.
-1/3, 0, 1/4, 1
Let g(d) be the first derivative of -3*d**5 + 25*d**4/4 + 80*d**3/3 - 30*d**2 + 56. What is s in g(s) = 0?
-2, 0, 2/3, 3
Let c(h) be the third derivative of -h**8/63840 + h**7/5985 - 3*h**4/4 - 3*h**2. Let p(j) be the second derivative of c(j). Let p(g) = 0. What is g?
0, 4
Let s(h) be the third derivative of 0*h**3 - 7/12*h**5 + 5/8*h**6 + 0*h - 13/42*h**7 - 47*h**2 + 0 + 5/24*h**4 + 5/84*h**8. Suppose s(m) = 0. Calculate m.
0, 1/4, 1
Let p(q) be the third derivative of -20*q**2 + 0*q - 1/4*q**4 + 0 + 0*q**3 + 1/60*q**5 + 1/120*q**6. Determine g so that p(g) = 0.
-3, 0, 2
Let x(t) be the first derivative of t**5/4 - 5*t**4/12 - 5*t**3/6 + 5*t**2/2 + 11*t - 35. Let z(i) be the first derivative of x(i). Let z(a) = 0. What is a?
-1, 1
Let i be (-4)/(-6) - ((-20)/6 - -4). Suppose i = 7*j - 2*j - 20. Factor 0 + 0*b + 9/4*b**3 + 3/2*b**2 - 15/4*b**j.
-3*b**2*(b - 1)*(5*b + 2)/4
Let o(u) be the second derivative of 0*u**2 - 1/80*u**5 + 0 + 1/336*u**7 + 0*u**4 + 21*u + 1/48*u**3 + 0*u**6. Solve o(g) = 0.
-1, 0, 1
Let g(s) b