. Let t(u) be the second derivative of q(u). What is r in t(r) = 0?
1, 3
Let v(q) be the first derivative of -4*q**3/3 - 108*q**2 + 2268*q - 12245. Factor v(c).
-4*(c - 9)*(c + 63)
Find w such that 5*w**2 + 1960 + 163867*w - 164182*w + 0*w**2 = 0.
7, 56
Let p(i) be the first derivative of 7*i**5 + 555*i**4/2 - 355*i**3/3 - 555*i**2 + 320*i - 79. Determine s, given that p(s) = 0.
-32, -1, 2/7, 1
What is u in 0 + 143*u**2 - 360*u**2 + 0 - 80*u + 219*u**2 = 0?
0, 40
Let t(h) be the first derivative of h**3 - 189*h**2/2 + 540*h - 61. Factor t(m).
3*(m - 60)*(m - 3)
Let c(j) be the first derivative of 1/2*j**3 + 0*j**2 - 3/8*j**6 - 3/5*j**5 - 23 + 3/16*j**4 + 0*j. Let c(y) = 0. What is y?
-1, 0, 2/3
Let k = -842 - -1107. Let s = k + -262. Factor -2/3*h**s + 2*h + 4/3 + 0*h**2.
-2*(h - 2)*(h + 1)**2/3
Let a(i) = -100*i**4 + 10734*i**3 - 33570*i**2 + 28762*i - 7446. Let u(x) = -x**3 + x**2 + x - 3. Let g(b) = -a(b) - 14*u(b). Suppose g(d) = 0. What is d?
3/5, 2, 104
Let m = -142389 + 18510223/130. Let w = -1/390 - m. Factor -2/3*v + 2/3*v**3 - 8/3 + w*v**2.
2*(v - 1)*(v + 1)*(v + 4)/3
Let h(s) be the second derivative of -3*s**4/4 - 17*s**3/6 + s**2 + 8598*s. Let h(n) = 0. What is n?
-2, 1/9
Let d(a) be the second derivative of -a**5/130 + 89*a**4/26 - 794*a**3/39 + 528*a**2/13 + 9170*a. Solve d(c) = 0.
1, 2, 264
Let w(z) = 8*z**2 + 511*z - 907. Let o(g) = 2*g**2 + 168*g - 302. Let h(p) = 7*o(p) - 2*w(p). Factor h(i).
-2*(i - 75)*(i - 2)
Let m = 33 - 29. Let y(i) be the second derivative of -15*i + 1/3*i**m + 3/5*i**5 + 0 + 0*i**2 - 4/3*i**3. Let y(v) = 0. Calculate v.
-1, 0, 2/3
Let m be ((-10)/(-32))/((-5310)/(-624456)). Factor 0 + 21*f**3 - 3*f**2 + 0*f - m*f**4.
-3*f**2*(7*f - 2)**2/4
Factor -3/8*l**2 + 879/4*l + 0.
-3*l*(l - 586)/8
Let k(h) be the first derivative of 5/9*h**6 - 20/3*h**3 + 0*h - 35 + 20/3*h**2 + h**5 - 25/6*h**4. Let k(l) = 0. What is l?
-2, 0, 1/2, 2
Let r be ((-7560)/(-560))/((-9)/(-8)) - 10. Suppose 2/3*m**r + 0 - 1/6*m**5 - 6*m + m**4 + 9/2*m**3 = 0. What is m?
-2, 0, 1, 9
Let c(n) be the first derivative of 2/3*n**3 + 4/3*n**2 + 9*n + 1/9*n**4 + 2. Let x(l) be the first derivative of c(l). Determine p so that x(p) = 0.
-2, -1
Let x(i) be the first derivative of -63/4*i**4 - 120*i**3 - 150*i**2 + 82 - 3/5*i**5 + 0*i. Factor x(r).
-3*r*(r + 1)*(r + 10)**2
Let j(w) be the third derivative of w**5/390 + 37*w**4/78 - 63*w**2 + 6. Factor j(l).
2*l*(l + 74)/13
Let g(b) be the third derivative of -11*b**5/60 + 43*b**4/12 - 25*b**3/2 - 3*b**2 - 55. Determine r, given that g(r) = 0.
1, 75/11
Let t(w) = -w**3 + 32*w**2 - w + 35. Let x = -38 + 70. Let y be t(x). Factor -5/3*c**y - 125*c - 625/3 - 25*c**2.
-5*(c + 5)**3/3
Let i(c) be the second derivative of 1/120*c**6 + 0*c**2 - c**3 + 1/40*c**5 - 1/4*c**4 - 27*c + 0. Let d(k) be the second derivative of i(k). Factor d(z).
3*(z - 1)*(z + 2)
Let m be (2217 - 2215)*((-36)/(-8) + -3). Suppose 2/13*p**2 + 4/13*p + 0 - 6/13*p**m = 0. What is p?
-2/3, 0, 1
Suppose 0 - 42/5*b**2 + 2/5*b**4 + 36/5*b + 4/5*b**3 = 0. What is b?
-6, 0, 1, 3
Let t(f) be the third derivative of 1/18*f**4 - 1/180*f**5 + 0*f - 148*f**2 + 0 + 5/18*f**3. Factor t(u).
-(u - 5)*(u + 1)/3
Suppose 4*f**2 - 401*f - 29*f**4 + 191*f - 19*f**3 + 210*f + 0*f**2 - 6*f**5 = 0. What is f?
-4, -1, 0, 1/6
Suppose -25 = -33*c + 41. Let v be (-1)/c + (377/(-78) - -6). Let 0*a**2 - 1/3*a**3 + v + a = 0. What is a?
-1, 2
Factor -112*q**2 - 1/2 - 128*q**3 + 31/2*q.
-(q + 1)*(16*q - 1)**2/2
Let w(x) = -140*x**2 - 188*x + 1080. Let o(a) = 40*a**2 + 54*a - 308. Let i(n) = 18*o(n) + 5*w(n). Factor i(l).
4*(l - 2)*(5*l + 18)
Let q(v) be the first derivative of 0*v + 1/15*v**4 + 5/2*v**2 + 5 - 1/10*v**3 - 1/60*v**5. Let b(z) be the second derivative of q(z). What is c in b(c) = 0?
3/5, 1
Let x(b) be the first derivative of 28/9*b - 5/9*b**2 - 2/27*b**3 + 82. Factor x(o).
-2*(o - 2)*(o + 7)/9
Let f = 25369/39 - 1921/3. Let v = 1478/143 - f. Factor -1/11*j**3 + 0 - v*j**2 - 1/11*j.
-j*(j + 1)**2/11
Let r(l) be the second derivative of 99*l + 0*l**2 - 2 - 6/5*l**4 + 3/100*l**5 + 72/5*l**3. Determine b, given that r(b) = 0.
0, 12
Suppose 19*g - 44*g = -21*g. Let d(h) be the second derivative of 2*h + g + 1/48*h**4 + 5/8*h**2 + 1/4*h**3. Solve d(z) = 0.
-5, -1
Let j(s) = -6*s**2 + 6*s - 8. Let x be 6/4 + 7/(-2) + 4. Let i(m) = -8*m**2 + 5*m - 9. Let k(a) = x*i(a) - 3*j(a). Suppose k(l) = 0. What is l?
1, 3
Let x = 349 - 307. Factor 5 - x*z - 5 + 9*z + 3*z**2.
3*z*(z - 11)
Let s(z) be the third derivative of z**6/1260 - 3*z**5/35 + 65*z**4/21 - 1352*z**3/63 + 6*z**2 - 9. Let s(d) = 0. Calculate d.
2, 26
Suppose 11*o - 448 = -5*o. Factor -14*t**3 + 49*t**2 + 71*t**2 - 19*t - 5*t - o*t**2 - 4*t**2.
-2*t*(t - 6)*(7*t - 2)
Let z be (38/(76/(-6)))/(6/(-8)). Let v(h) be the second derivative of 4/3*h**z + 1/5*h**5 + 0*h**2 - 10*h + 2*h**3 + 0. Factor v(u).
4*u*(u + 1)*(u + 3)
Let k(n) = 19*n**3 - 216*n**2 + 4093*n - 17387. Let b(y) = -3*y**3 + 37*y**2 - 682*y + 2898. Let d(z) = -13*b(z) - 2*k(z). Suppose d(h) = 0. Calculate h.
10, 29
Let r(s) be the second derivative of s**5/100 - 39*s**4/10 + 3042*s**3/5 - 237276*s**2/5 - 69*s + 8. What is w in r(w) = 0?
78
Let v = 4477/3899 - 3/557. Let y be (60/42)/(-2)*3*6/(-45). Factor 0*a**2 + 0*a - y*a**5 - 8/7*a**4 - v*a**3 + 0.
-2*a**3*(a + 2)**2/7
Let t = -75867/4 + 19020. Determine i, given that 12*i**5 - 3 - 93/4*i**2 - t*i**3 + 21*i + 6*i**4 = 0.
-2, -1, 1/4, 2
Let b = -75 - -81. Let -4*y**3 + 31*y**2 - 5*y**3 + 47*y**2 + 3*y - 78 + b*y**3 = 0. What is y?
-1, 1, 26
Let z(g) be the third derivative of -1/672*g**8 + 1/10*g**5 + 0*g**3 - 1/105*g**7 + 1/120*g**6 - 3*g - 3/16*g**4 + 0 - 6*g**2. Factor z(x).
-x*(x - 1)**2*(x + 3)**2/2
Let g(x) = 451*x**2 + 492 - 226*x**2 + 63*x - 226*x**2. Let w be g(70). What is p in 1/10*p**w + 3/5*p + 0 = 0?
-6, 0
Let h(r) = r**3 - r + 1. Let q(l) = l**3 + 8*l**2 + l - 4. Let m be q(-8). Let x(g) = -8*g**3 + 48*g**2 + 96*g + 28. Let o(p) = m*h(p) - x(p). Factor o(i).
-4*(i + 1)**2*(i + 10)
Let f(l) = -35*l**2 + 115*l - 690. Let r(c) = 2*c**2 + 2. Let v(y) = f(y) + 15*r(y). Let v(o) = 0. What is o?
11, 12
Let j(r) = -4*r**3 - 72*r**2 - 95*r - 3. Let f(b) = b**3 - 9*b**2 - b + 1. Let w(c) = -9*f(c) - 3*j(c). Factor w(p).
3*p*(p + 1)*(p + 98)
Let f(k) be the first derivative of -k**6/360 - 7*k**5/60 - 2*k**4 - 160*k**3/9 + 141*k**2/2 + 173. Let l(z) be the second derivative of f(z). Factor l(h).
-(h + 5)*(h + 8)**2/3
Let p be (-1 + 4)*5/(75/80). Factor p*n**2 - 7*n**3 - 100*n**4 - 25*n**3 + 112*n**4.
4*n**2*(n - 2)*(3*n - 2)
Let s(f) be the first derivative of f**4/12 + 7*f**3/6 - 9*f**2 - 67*f + 116. Let y(v) be the first derivative of s(v). Factor y(g).
(g - 2)*(g + 9)
Factor -161*l - 662 - 4*l**2 - 423*l + 82.
-4*(l + 1)*(l + 145)
Suppose -2*y = -4*y - 5*k + 17, 3*y - 28 = -5*k. Suppose y*j - 1 = 21. Let 0*i + 4/5*i**j - 4/5*i**4 - 16/5*i**3 + 16/5*i**5 + 0 = 0. What is i?
-1, 0, 1/4, 1
Let p(u) be the second derivative of u**6/540 + 7*u**5/180 - 2*u**4/9 - u**3/2 + 3*u**2 + 3*u - 5. Let b(y) be the second derivative of p(y). Factor b(g).
2*(g - 1)*(g + 8)/3
Suppose 15 = 4*t - 5. Let y(u) = -2*u**5 - 6*u**4 + 3*u**3 + u**2 - u + 5. Let s(l) = l**5 + 3*l**4 - 2*l**3 + l - 3. Let h(g) = t*s(g) + 3*y(g). Factor h(d).
-d*(d - 1)*(d + 1)**2*(d + 2)
Let d = 19024 - 38047/2. Let u(a) be the first derivative of -16/7*a - 12/7*a**3 - 2/35*a**5 - 20/7*a**2 - d*a**4 - 6. Suppose u(l) = 0. What is l?
-2, -1
Let r(a) be the third derivative of -a**7/735 + 31*a**6/420 - a**5/7 - 22*a**2 + 14*a + 1. Factor r(i).
-2*i**2*(i - 30)*(i - 1)/7
Let o be (10/6)/((-10)/(-36)). Suppose -k + 9 = o. Let 12*g + 5 - 3 - 3*g**2 + 4 - 12*g**3 - k = 0. Calculate g.
-1, -1/4, 1
Let x = -791995/4 - -198001. Let 0*y - x*y**4 + 0 + 15/4*y**5 + 0*y**2 - 3/2*y**3 = 0. What is y?
-2/5, 0, 1
Factor -219*c**3 + 2*c - 401500*c**4 - c - 37*c**5 + 401279*c**4 - 37*c**5 - 71*c**2.
-c*(c + 1)**3*(74*c - 1)
Let a = 1209 - 1216. Let p be 16 + a + (-42)/5. Factor 0 + 6/5*d + p*d**2 - 3/5*d**3.
-3*d*(d - 2)*(d + 1)/5
Let c(q) = q**4 + 34*q**3 + 39*q**2 - 68*q - 2. Let i(b) = -b**4 - b**2 - b + 1. Let t(n) = -c(n) - 2*i(n). Factor t(z).
z*(z - 35)*(z - 1)*(z + 2)
Let h(u) be the third derivative of u**6/480 - 49*u**5/240 +