) = 56*r**3 - 116*r**2 + 40*r. Let d(x) = -11*x**3 + 23*x**2 - 8*x. Let f(p) = y*d(p) + 3*i(p). What is n in f(n) = 0?
0, 1/2, 2
Let p(d) be the first derivative of 2*d**3/3 - 5*d**2 + 29*d - 75. Let i(u) = u**2 + u + 1. Let v(m) = 2*i(m) - 2*p(m). Factor v(a).
-2*(a - 7)*(a - 4)
Let g(n) be the third derivative of -n**6/72 - 11*n**5/60 + 2*n**4/3 + 38*n**3/9 + 108*n**2. Solve g(o) = 0 for o.
-38/5, -1, 2
Find r such that -23/3*r**2 - 20*r - 1/3*r**3 + 0 = 0.
-20, -3, 0
Let v(z) be the first derivative of z**4/60 - 28*z**3/15 + 392*z**2/5 + 38*z - 153. Let b(m) be the first derivative of v(m). Factor b(i).
(i - 28)**2/5
Factor -22*w**2 + 25/4*w**3 - 28*w + 0 + 1/4*w**4.
w*(w - 4)*(w + 1)*(w + 28)/4
Let f(w) be the third derivative of -w**8/252 - 2*w**7/35 + 5*w**6/9 - 2*w**5/3 - 49*w**4/18 + 26*w**3/3 + 118*w**2 - w. Find k such that f(k) = 0.
-13, -1, 1, 3
Let a(y) be the first derivative of 4/3*y**3 + 53 - 18*y**2 - 40*y. What is b in a(b) = 0?
-1, 10
Let v(n) be the first derivative of -n**7/56 + n**6/20 + n**5/8 - 3*n**4/4 + 38*n**3 + n**2 + 124. Let r(a) be the third derivative of v(a). Factor r(d).
-3*(d - 1)*(d + 1)*(5*d - 6)
Let m(w) be the first derivative of 35/9*w**4 + 64/9*w - 104/27*w**3 + 94/45*w**5 - 108 + 7/27*w**6 - 104/9*w**2. What is j in m(j) = 0?
-4, -2, 2/7, 1
Let f = -6817/165 + 124/3. Let m(x) be the second derivative of 1/66*x**4 + 0 - f*x**5 + 0*x**2 - 8*x + 2/33*x**3 - 1/165*x**6. Solve m(q) = 0 for q.
-2, -1, 0, 1
Let b(j) be the second derivative of -j**7/63 - 13*j**6/90 - j**5/2 - 7*j**4/9 - 4*j**3/9 + 70*j - 20. Let b(v) = 0. Calculate v.
-2, -1/2, 0
Suppose 47*p = 42*p + 35. Suppose -17*w + p*w - 48*w**2 + 93*w**2 = 0. What is w?
0, 2/9
Factor 72*r + 53 + 891*r**2 - 20*r - 892*r**2.
-(r - 53)*(r + 1)
Let j be 27/((-4)/(16/3)) - -2. Let r be (-85)/j*(1/(-5) - -1). Find t, given that -r*t**2 - t**2 - 4*t**3 + 4*t**2 + 5*t**3 = 0.
-1, 0
Suppose 58*c = 6*c + 7*c. Let k(t) be the first derivative of c*t - 3 - 4/9*t**3 - 3/5*t**5 - 5/3*t**4 + 0*t**2. Factor k(a).
-a**2*(a + 2)*(9*a + 2)/3
Let c(g) be the first derivative of 5*g**4/12 - 65*g**3/2 + 95*g**2 + 227*g - 289. Let i(w) be the first derivative of c(w). Find x such that i(x) = 0.
1, 38
Let o be (11 - 1) + (59 - 65). Let j(f) be the third derivative of -1/6*f**o + 1/25*f**5 - 4/15*f**3 + 0*f + 0 + f**2. Find i, given that j(i) = 0.
-1/3, 2
Let r(m) be the first derivative of 28/9*m**2 + 2/27*m**3 + 6*m - 138. Suppose r(p) = 0. What is p?
-27, -1
Let j be 8 - (2 + 6 - 4). Let w = -2 + j. Factor -4/5 + 14/5*f + 18/5*f**w.
2*(f + 1)*(9*f - 2)/5
Let n(d) be the second derivative of d**6/90 - 11*d**5/30 + 5*d**4/3 - d**3/6 + 9*d**2/2 - 45*d. Let j(w) be the second derivative of n(w). Factor j(c).
4*(c - 10)*(c - 1)
Let w(o) = o**2 + 2*o - 16. Let c be w(0). Let t = -13 - c. Factor -4*b - t*b**2 + b + 3*b.
-3*b**2
Suppose -130*a + 84 - 1 = -177. Let h be (3/4)/((-60)/(-8)). Solve h*b**3 - 1/10*b**5 + 0*b**a + 0*b + 0 + 0*b**4 = 0 for b.
-1, 0, 1
Suppose -4*q - 4 = 0, 0 = 12*d - 15*d + 3*q + 12. Suppose 0 + 1/3*v**2 + 0*v + 1/9*v**4 - 4/9*v**d = 0. What is v?
0, 1, 3
What is h in 3415/7*h**2 - 4/7 - 1356/7*h = 0?
-2/683, 2/5
Let r(n) be the first derivative of 58564/3*n - 92 + 4/15*n**5 - 44/3*n**4 - 10648/3*n**2 + 968/3*n**3. Find i, given that r(i) = 0.
11
Let l(r) be the second derivative of 1/15*r**3 - 11 + 1/90*r**4 + 0*r**2 - 2*r. Suppose l(w) = 0. Calculate w.
-3, 0
Let w = -3125/18 - -22163/126. Let y be (-33)/(-14) + 3/6. Factor y - 4/7*x**2 - w*x.
-4*(x - 1)*(x + 5)/7
Let c(y) be the first derivative of 121*y**5/45 + 161*y**4/6 + 589*y**3/27 - 1010*y**2/3 + 100*y/9 - 9172. Determine w, given that c(w) = 0.
-5, 2/121, 2
Let q be ((-80)/(-15))/((-6)/(-309)). Let n = q + -4102/15. Solve -12/5*s**2 + 16/5*s + 2/5*s**4 + 0*s**3 - n = 0 for s.
-3, 1
Let l(p) = 2*p**2 - 14*p. Let x(d) = -5*d**2 - 136*d - 360. Let w(q) = 3*l(q) + x(q). Determine z so that w(z) = 0.
-2, 180
Let y(i) be the first derivative of -i**5/4 + 17*i**4/4 - 39*i**3/4 - 139*i**2/4 - 22*i - 5135. Find r, given that y(r) = 0.
-1, -2/5, 4, 11
Let k be 35*(-2)/((-10)/57). Factor 240*l**3 + 444*l**3 + 24*l**5 - 21*l**5 + 5184 - 9072*l + 102*l**4 + 2700*l**2 + k*l**3.
3*(l - 1)**2*(l + 12)**3
Let n be (-104)/215 + (-231)/(-385). Let l = n + 41/387. Factor -2/9*g**4 - 8/9*g**3 - 4/3*g**2 - l - 8/9*g.
-2*(g + 1)**4/9
Suppose -8 = 4*r, -106*l + 101*l - 2*r = 334. Let c be 7/(35/40)*(-3)/l. Factor -c*b - 2/11*b**3 + 0 - 6/11*b**2.
-2*b*(b + 1)*(b + 2)/11
What is l in 150/11*l**4 + 1944/11 - 9288/11*l + 10014/11*l**2 + 2580/11*l**3 = 0?
-9, 2/5
Let g(c) be the third derivative of -c**7/210 - 29*c**6/120 + 877*c**5/60 - 1663*c**4/24 + 136*c**3 + 7510*c**2. Solve g(k) = 0.
-48, 1, 17
Let h(u) be the third derivative of 0*u + u**2 + 0*u**3 + 2/105*u**7 - 70 + 0*u**4 - 1/6*u**6 + 2/5*u**5. Suppose h(z) = 0. What is z?
0, 2, 3
Suppose 6*p + 5*b - 370 = 2*p, 6 = -3*b. Factor -p*j**4 + 32*j + 536*j**3 + 368*j**2 + 98*j**5 - 150*j - 394*j - 256 - 381*j**4.
2*(j - 2)**3*(7*j + 4)**2
Suppose 4*g + 0 = 4*t - 4, -3*g + 9 = 0. Let l(n) be the first derivative of -1/2*n**t - 1/3*n**3 + 0*n**2 + 1/3*n**6 + 1/5*n**5 + 0*n - 11. Factor l(p).
p**2*(p - 1)*(p + 1)*(2*p + 1)
Let m(g) = -5*g**3 - 110*g**2 + 2285*g - 7945. Let c(j) = -2*j**3 - 56*j**2 + 1143*j - 3975. Let q(b) = -5*c(b) + 3*m(b). Factor q(k).
-5*(k - 6)**2*(k + 22)
Let d(z) be the third derivative of z**10/50400 - z**8/6720 + z**5/2 + z**3/6 + 43*z**2. Let i(a) be the third derivative of d(a). Factor i(y).
3*y**2*(y - 1)*(y + 1)
Let s(a) be the second derivative of a**4/42 + 3*a**3 + 342*a**2/7 + a - 1224. Solve s(k) = 0 for k.
-57, -6
Let c(u) be the first derivative of 45/2*u**2 + 81/4*u - 166 + 59/6*u**3 + 1/20*u**5 + 5/4*u**4. Suppose c(i) = 0. Calculate i.
-9, -1
Suppose -1/3*v**3 - 4 + 0*v**2 + 13/3*v = 0. Calculate v.
-4, 1, 3
Let d = -291571 - -291571. Let a = -3/80 - -7/16. Determine u so that -4/5*u**2 - 6/5*u**3 + 0 + d*u**4 + a*u**5 + 0*u = 0.
-1, 0, 2
Suppose 1010*p**2 + 2/9*p**3 + 772725750 + 1530150*p = 0. Calculate p.
-1515
Let g(q) be the first derivative of q**3/3 - 21*q**2 + 56*q + 236. Let x(d) = -3*d**2 + 131*d - 168. Let z(v) = -8*g(v) - 3*x(v). Suppose z(k) = 0. Calculate k.
1, 56
Let i(n) be the first derivative of n**6/2 + 12*n**5/5 - 9*n**4/2 - 16*n**3 + 87*n**2/2 - 36*n - 3923. Factor i(d).
3*(d - 1)**3*(d + 3)*(d + 4)
Let l be 66/891*792 + -54. Factor -56/3*f + 10/3*f**3 - 8 + l*f**2.
2*(f - 2)*(f + 3)*(5*f + 2)/3
Suppose 35*m = 21*m + 70. Let g(s) = s**2 + 16*s + 25. Let f(t) = -2*t**2 - 31*t - 49. Let z(y) = m*g(y) + 3*f(y). What is q in z(q) = 0?
-11, -2
Let i(k) = -k**3 + 50*k**2 + 106*k - 102. Let t be i(52). Let l(m) be the first derivative of 14/15*m**3 - 1/15*m**4 + t + 10/3*m - 4*m**2. Factor l(c).
-2*(c - 5)**2*(2*c - 1)/15
Suppose -11*r = -12*r. Suppose r = -3*c - 10 + 49. Let g(m) = 8*m**2 - 37*m + 29. Let d(z) = 4*z**2 - 18*z + 14. Let s(i) = c*d(i) - 6*g(i). Factor s(p).
4*(p - 2)*(p - 1)
Determine y, given that -10761*y**2 - 480351*y + 4232084*y + 62*y**3 - 422130*y + 6314941*y - 59*y**3 + 9655308 = 0.
-1, 1794
Suppose 0 = 3*p + 2*n - 76 - 135, 3*p - n = 214. Suppose 23 - p = -3*c. Factor 17*o**2 + 6 + c*o**2 - 35*o**2 - 4*o.
-2*(o - 1)*(o + 3)
Let a(d) be the first derivative of -15/11*d**2 + 2/33*d**3 + 72/11*d + 154. Solve a(n) = 0.
3, 12
Let x(s) be the first derivative of -s**4/3 + 244*s**3/9 - 238*s**2/3 + 236*s/3 - 2072. Factor x(c).
-4*(c - 59)*(c - 1)**2/3
Let c(v) be the first derivative of v**3 - 1137*v**2 + 430923*v - 766. Factor c(k).
3*(k - 379)**2
Let i(k) = -2*k**2 + k + 2. Let c(m) = 5*m**2 - 21*m - 126. Let z(u) = -c(u) - 2*i(u). Let g be z(24). Suppose -3/2*y + 1 + 1/2*y**g = 0. Calculate y.
1, 2
Let r be -2*(-3 + (1 - (-4 - -3))). Factor -36*l**r - 28*l**3 + 65*l**3 - 34*l**3 + 108*l.
3*l*(l - 6)**2
Factor -223132*n + 223132*n - 1420*n**2 - 12*n**4 + 225*n**3 + 119*n**3.
-4*n**2*(n - 5)*(3*n - 71)
Suppose -21*b - 20350 = 4*b. Let h be (b/(-185))/(21/(-9) + 3). Suppose 54/5 - h*j**3 - 261/5*j - 192/5*j**2 = 0. Calculate j.
-3, 2/11
Let t(p) be the second derivative of -1/35*p**5 + 0 + 132*p + 2/21*p**3 + 1/7*p**2 + 0*p**4 - 1/105*p**6. Factor t(o).
-2*(o - 1)*(o + 1)**3/7
Let q be (-280)/(-36) 