 9*a - 36*a**2 + 10 + 18*a**2. Let f be p(-9). Determine o, given that 3*o**2 + 7*o**2 + f*o - 5*o**2 = 0.
-2, 0
Suppose -12 = -4*j, 10*j + 18 = 2*x + 14*j. Let w(n) be the first derivative of -8/13*n**x + 7/26*n**4 + 11 + 3/13*n**2 + 4/13*n. Factor w(p).
2*(p - 1)**2*(7*p + 2)/13
Let m(i) be the second derivative of -i**6/540 + 7*i**5/45 + 5*i**4/3 - 82*i**3/3 - 264*i. Let a(r) be the second derivative of m(r). Solve a(f) = 0 for f.
-2, 30
Suppose -75/2*u**3 - 85/2*u**2 - 5*u + 0 = 0. What is u?
-1, -2/15, 0
Let v(f) be the first derivative of 47/2*f**2 - 200 - 30*f - f**3. Determine g, given that v(g) = 0.
2/3, 15
Let p(o) be the first derivative of -o**5/5 + 23*o**4/4 - 17*o**3/3 - 107*o**2/2 - 66*o + 3306. Determine g so that p(g) = 0.
-1, 3, 22
Let d be (-3)/36*7*(-4)/56. Let i(r) be the third derivative of 0*r**4 - d*r**6 - 1/42*r**7 + 1/6*r**5 + 0*r**3 + r**2 + 0*r + 0. Suppose i(g) = 0. What is g?
-2, 0, 1
Let l(m) be the first derivative of 1/8*m**4 - 23/8*m**2 + 5/12*m**3 + 5/2*m + 15. What is p in l(p) = 0?
-5, 1/2, 2
Let m(l) = l - 3. Let g(w) = 4*w**3 + 68*w**2 + 298*w + 402. Let b = -237 - -239. Let c(z) = b*m(z) + g(z). Determine y, given that c(y) = 0.
-11, -3
Suppose 66 = 2*j + 24. Suppose 11 = 2*w - j. Solve 16*k + 16 - 8 + 12*k - w*k**2 = 0 for k.
-1/4, 2
Let r(h) = 11*h**3 - 415*h**2 + 812*h - 408. Let n(x) = -8*x**3 + 414*x**2 - 814*x + 408. Let w(m) = -6*n(m) - 4*r(m). Let w(a) = 0. Calculate a.
1, 204
Let v(q) = 22*q**3 + 86194*q**2 + 16588895*q - 2371615. Let m(g) = 4*g**3 + 21548*g**2 + 4147224*g - 592904. Let w(a) = 15*m(a) - 4*v(a). Solve w(d) = 0.
-385, 1/7
Suppose -3*c + j + 298 = 0, -4*c = -3*j - j - 400. Factor -18*u**2 - c + 58 - 40*u + 32*u**2 - 13*u**2.
(u - 41)*(u + 1)
Let q be (51/27 - 3) + 2/(4 + (-5)/2). Find x, given that 12800/9 + q*x**2 + 320/9*x = 0.
-80
Let o(t) be the third derivative of -1 + t**4 - 7/2*t**3 + 29*t**2 + 0*t - 1/20*t**5. Factor o(n).
-3*(n - 7)*(n - 1)
Let q(v) be the first derivative of -33 + 0*v**2 + 1/3*v**3 - v. Let q(c) = 0. What is c?
-1, 1
Let y = 2445 + -1171. Let g = -1272 + y. Factor -5*f + 25/2 + 1/2*f**g.
(f - 5)**2/2
Let o(h) be the third derivative of h**8/336 - h**7/84 + h**5/12 - 5*h**4/24 + 11*h**3/6 - 6*h**2 - 7. Let p(n) be the first derivative of o(n). Solve p(y) = 0.
-1, 1
Suppose -4 = -4*x, -u + 5*x = -2*u - 11. Let g = 8 - u. Let -g*m**2 - 6*m + 10*m**2 + 15*m**2 = 0. What is m?
0, 6
Let i(p) = 17*p**2 + 416*p + 279. Let o(t) = 6*t**2 + 144*t + 93. Let y(c) = 3*i(c) - 8*o(c). Let y(u) = 0. What is u?
-31, -1
Let h(k) be the first derivative of 5*k**4/42 + k**3/7 - 2*k**2 - 40*k - 131. Let j(v) be the first derivative of h(v). Let j(i) = 0. What is i?
-2, 7/5
Suppose 0 = 8*s + 21 - 45. Suppose -q + 8 = 2*d, 4*d - 9 = -3*q + s*d. Determine n so that 15/7*n - 3/7*n**3 - 6/7 + 3/7*n**4 - 9/7*n**q = 0.
-2, 1
Suppose 5*q + p - 4*p = 16, 0 = -2*q + p + 7. Factor -11*s - 500*s**2 + q*s**5 - 2*s**4 + 31*s + 480*s**2 - 15*s**3 + 12*s**4.
5*s*(s - 1)**2*(s + 2)**2
Let u be ((-368)/(-480) - 6/10)/((-5)/((-180)/57)). Factor 242/19 - 44/19*n + u*n**2.
2*(n - 11)**2/19
Let t(j) be the first derivative of -3*j**5/25 + 169*j**4/20 - 382*j**3/15 + 108*j**2/5 - 15238. What is y in t(y) = 0?
0, 1, 4/3, 54
Determine u, given that 43/3*u - 5*u**4 - 43/3*u**3 - 2 + 7*u**2 = 0.
-3, -1, 2/15, 1
Let w be (15/260)/((-1221)/(-44)). Let n = 969/3367 - w. Let -10/7*b - 2/7*b**4 + 6/7*b**2 + n*b**3 + 4/7 = 0. What is b?
-2, 1
Let s(t) be the second derivative of 4*t**5/5 - 167*t**4/3 - 428*t**3/3 - 86*t**2 + t + 737. Factor s(i).
4*(i - 43)*(i + 1)*(4*i + 1)
Let a(h) be the second derivative of -50 + 1/60*h**6 - 1/24*h**4 - 1/40*h**5 + 2*h + 1/12*h**3 + 0*h**2. Factor a(x).
x*(x - 1)**2*(x + 1)/2
Let z = 1 + 1. Suppose 0 = 78*i - 90*i - 39*i + 153. What is s in 4/9*s**z - 2/9*s**i - 2/9*s + 0 = 0?
0, 1
Factor 17/4*n**3 + 18447/4*n - 1121/4*n**2 + 1089/4.
(n - 33)**2*(17*n + 1)/4
Solve 0 - 6*o - 1/4*o**3 - 11/4*o**2 = 0.
-8, -3, 0
Let m(x) = -x**2 + x. Let l(j) = -6*j + 1. Let t be l(0). Let v(p) = 21*p**2 - 258*p + 48. Let a(r) = t*v(r) - 12*m(r). Factor a(n).
3*(n - 8)*(11*n - 2)
Solve -3*z**3 - 133*z - 114 + 320*z + 224*z - 201*z**2 + 79 - 172 = 0.
-69, 1
Let l(t) be the first derivative of 5*t**4/4 - 70*t**3/3 - 45*t**2/2 + 630*t - 14420. Suppose l(b) = 0. What is b?
-3, 3, 14
Let h(m) be the second derivative of -m**4/8 - 4*m**3 + 27*m**2 - 5*m - 444. Factor h(o).
-3*(o - 2)*(o + 18)/2
Let v(i) be the third derivative of -i**7/945 + i**6/135 - 2*i**5/135 + 215*i**2 + 3. What is q in v(q) = 0?
0, 2
Let p(a) = 276*a**2 - 2202*a - 46. Let g be p(8). Suppose -33/8 + 9/2*d - 3/8*d**g = 0. Calculate d.
1, 11
Let k(b) = b**2 - 5*b - 1. Let j(n) = 10*n**2 - 86*n + 126. Let z(p) = j(p) - 6*k(p). Solve z(c) = 0 for c.
3, 11
Suppose 0 = -15*u - 58*u + 1168. Let m(s) be the first derivative of 4/5*s**5 + 5 - 16/3*s**3 - 2*s**4 + 0*s + u*s**2. Factor m(d).
4*d*(d - 2)**2*(d + 2)
Let m(x) be the second derivative of x**7/105 + 2*x**6/75 - 9*x**5/50 - x**4/15 + 8*x**3/15 + 900*x. Suppose m(a) = 0. What is a?
-4, -1, 0, 1, 2
Suppose 4 = d - 4*i + 2*i, 5*d + 3*i = 7. Find s, given that -3*s - 13*s + 5*s**d + 2*s**3 + 3*s**2 + 14*s - 8 = 0.
-4, -1, 1
Let l(t) be the third derivative of t**5/12 - 115*t**4/6 + 1430*t**3 + 243*t**2 - 3*t. Factor l(b).
5*(b - 66)*(b - 26)
Suppose -8*s + s = 7. Let r(t) = -2*t**5 - 7*t**4 + t**3 + 6. Let w(x) be the first derivative of -x**5/5 + x + 20. Let i(k) = s*r(k) + 6*w(k). Factor i(g).
g**3*(g + 1)*(2*g - 1)
Let u = 45/328 - 23/205. Let g(k) be the third derivative of 1/350*k**7 - 1/200*k**6 + 0*k + 1/5*k**3 + 0 + 15*k**2 + u*k**4 - 3/100*k**5. Solve g(v) = 0.
-1, 1, 2
Let v(g) be the first derivative of g**6/6 + 2*g**5 - 29*g**4/2 - 16*g**3/3 + 177*g**2/2 + 126*g - 969. Factor v(u).
(u - 3)**2*(u + 1)**2*(u + 14)
Factor 77 - 72 + 121 + 3*d**2 - 39*d.
3*(d - 7)*(d - 6)
Solve 29*h**2 - 50*h**2 + 10*h**2 + 13*h**2 - 34*h = 0 for h.
0, 17
Let w(j) = 25*j - 5*j**2 - 5 + 44*j - 84*j. Suppose 0 = 2*a + 2*a - 4. Let k(h) = -1. Let x(c) = a*w(c) + 5*k(c). Factor x(m).
-5*(m + 1)*(m + 2)
Let z(x) = 132*x + 168. Let k be z(-2). Let t be 3 + k/18 + 5. Factor 0 + 4/3*f**2 + t*f.
4*f*(f + 2)/3
Let 53*y**3 - 48*y**3 - 103*y**2 - 15*y**2 - 377*y**2 = 0. Calculate y.
0, 99
Let j(b) = b**3 - 5*b**2 + 3*b - 18. Let y be j(4). Let a be -1*(11 - (-9 - y)). Factor 23/3*d - 7/3*d**2 - a.
-(d - 3)*(7*d - 2)/3
Let r(x) = -16*x**3 + 86*x**2 + 102*x + 72. Let q(i) = -7*i**3 + 40*i**2 + 51*i + 36. Let b(c) = 9*q(c) - 4*r(c). Find h such that b(h) = 0.
-12, -3, -1
Let i(q) = -129*q + 6065. Let m be i(47). Find j such that 1/4*j**m + 225/4 - 15/2*j = 0.
15
Let l(t) be the first derivative of t**6/72 + t**5/24 - 5*t**4/12 + 11*t**3 + 8. Let g(w) be the third derivative of l(w). Determine j, given that g(j) = 0.
-2, 1
Let v(u) = 31*u**5 + u**4 - 15*u**3 + 3*u**2 + 32*u - 12. Let p(m) = -4*m**5 + m**4 - m**3 + m**2 - m - 1. Let h(k) = -24*p(k) - 3*v(k). Solve h(n) = 0 for n.
-1, 1, 2, 5
Let j(b) be the first derivative of -2*b**3/9 - 25*b**2 + 632*b/3 + 2244. Factor j(d).
-2*(d - 4)*(d + 79)/3
Let a be ((-24776)/(-95))/(-8) - -33. Solve 16/5*h - 8/5 - 2*h**3 + 2/5*h**5 - a*h**2 + 2/5*h**4 = 0 for h.
-2, 1
Let s(b) be the third derivative of b**5/6 + 1495*b**4/72 - 125*b**3/9 + 5155*b**2 - 1. Factor s(w).
5*(w + 50)*(6*w - 1)/3
Factor 10/3*m**2 - 72 + 56*m.
2*(m + 18)*(5*m - 6)/3
Let l(c) = -39*c - 543. Let r be l(30). Let s = 3435/2 + r. Let 3/2*x + 9/2*x**3 - 3/2*x**4 + 0 - s*x**2 = 0. Calculate x.
0, 1
Let n(m) be the first derivative of m**5/7 + 1777*m**4/28 + 710*m**3/21 + 8093. Factor n(l).
l**2*(l + 355)*(5*l + 2)/7
Let o(m) = m**2 - 2*m + 3. Let f be o(1). Suppose 36*b**f + 16*b**3 - 52*b**4 + 43*b**4 + 30*b**4 - 61*b**3 - 87*b**3 = 0. Calculate b.
0, 2/7, 6
Suppose 0 = -110*z + 75*z + 167020. Suppose z*k = 4773*k - 2. Factor -2/5*i**k - 24/5*i + 0.
-2*i*(i + 12)/5
Let n(s) = -5*s**2 + 83*s - 46. Let q = 1030 + -1014. Let m be n(q). Solve d**m + 1/4*d**5 - 1/2*d**4 + 1/4*d - 1/2*d**3 - 1/2 = 0.
-1, 1, 2
Let a(g) = 11*g**2 - 58*g + 6. Let c(u) = -10*u**2 + 55*u - 5. Let l(i) = -5*a(i) - 6*c(i). Factor l(s).
5*s*(s - 8)
Let m(d) be the second derivative of -d**5/10 - 25*d**4/6 - 57*d**3 - 31