277
Let w(y) be the first derivative of -77 - 2*y**4 - 2/3*y**3 + 16*y**2 + 8*y. Suppose w(l) = 0. What is l?
-2, -1/4, 2
Let s(t) = -190*t + 4. Let c be s(0). Let j(r) be the third derivative of -1/48*r**5 + 0 + 0*r**c + 0*r - 8*r**2 + 5/6*r**3. Find o such that j(o) = 0.
-2, 2
Find z, given that 566 + 6231*z + 3*z**2 - 6120*z + 130 = 0.
-29, -8
Let d(v) be the second derivative of -v**4 - 73*v**3/6 + 25*v**2/2 - 85*v. Let g(l) = 11*l**2 + 74*l - 25. Let s(r) = -4*d(r) - 3*g(r). Factor s(p).
5*(p + 5)*(3*p - 1)
Let f = -3203/3 - -32033/30. Let r(t) be the second derivative of 2*t**2 + f*t**5 + 0 - t**3 + 0*t**4 - 17*t. Let r(g) = 0. Calculate g.
-2, 1
Let q = -1/15864 + 1327/79320. Let k(x) be the second derivative of -q*x**6 + 0*x**2 + 0*x**4 + 0*x**3 + 1/40*x**5 - 34*x + 0. Factor k(i).
-i**3*(i - 1)/2
Let n be 3/9 + (-47)/(-12) + 55/(-220). Suppose 3*y + 2*x - 1 = -0*x, -2*x - 8 = 0. Factor -2/7*k**2 + 2/7*k**n + 0 + 2/7*k - 2/7*k**y.
2*k*(k - 1)**2*(k + 1)/7
Suppose -j - 192 = -195. Suppose i = 5*h - 4, 2*i = -j*h - i - 12. Factor 0 + 0*y + 2/5*y**3 + h*y**2.
2*y**3/5
Let h = -3143967/7 + 449139. Factor -3/7*c**2 - h*c + 0.
-3*c*(c + 2)/7
Let f be ((605/44)/(-11))/(75/(-216)) - (-2)/5. Let z be (-4)/(-10)*-7*-2. Suppose -z*t**3 - 16/5*t + 6/5*t**f + 8*t**2 + 0 = 0. What is t?
0, 2/3, 2
Let o = -1075 - -1081. Let b(d) be the second derivative of -28/9*d**3 - 8/3*d**2 - 19*d - 73/36*d**4 - 7/10*d**5 + 0 - 1/10*d**o. Find w such that b(w) = 0.
-4/3, -1
Factor -15 - 27/4*m**2 - 1/4*m**3 + 22*m.
-(m - 2)*(m - 1)*(m + 30)/4
Let u(p) be the second derivative of 7/45*p**5 + 0*p**3 + 0*p**2 - 1/9*p**4 - 6*p + 0 - 2/27*p**6 + 2/189*p**7. Let u(s) = 0. Calculate s.
0, 1, 3
Let n(g) = 3*g**2 - g - 5. Suppose 0*k - 40 = -8*k. Let j(q) = -4*q**2 + q + 7. Let t(i) = k*j(i) + 7*n(i). Factor t(y).
y*(y - 2)
Factor -1/5*i**3 - 1853388/5*i + 485587656/5 + 2358/5*i**2.
-(i - 786)**3/5
Let b(f) be the second derivative of f**4/144 - 7*f**3/12 + 39*f**2/8 - 221*f + 1. Factor b(x).
(x - 39)*(x - 3)/12
Let u = -147417 - -442252/3. Factor 0 - u*i + 1/3*i**2.
i*(i - 1)/3
Let c be (-13)/(((-75)/300)/(6/156)). Let 20*z - 4*z**4 + 1/3*z**5 - 56/3 + 38/3*z**c - 31/3*z**3 = 0. What is z?
-2, 1, 14
Let u be (-12 + (-1558)/(-133))*(-182)/18*(-81)/(-54). Let 1/3*m**4 - u + 10/3*m**3 + 38/3*m - 12*m**2 = 0. What is m?
-13, 1
Let i(k) = -105*k**2 + 5285*k + 10150. Let x(j) = 8*j**2 - 406*j - 781. Let v(b) = -3*i(b) - 40*x(b). Find s, given that v(s) = 0.
-2, 79
Solve -9359*z**2 - 2520 - z**4 - 60*z**3 + 870*z - 4*z**4 + 9574*z**2 = 0.
-14, -4, 3
Factor -6*r**2 - 10*r - r + 17*r**2 - 2 + 2*r.
(r - 1)*(11*r + 2)
Suppose -28*w + 135 = -117. Factor -4*x**3 + 24*x + 2*x**4 + w*x**3 + 50*x**2 + 9*x**3 + 14*x**3.
2*x*(x + 1)**2*(x + 12)
Let u(z) = -5*z**4 - 2*z + 1. Let l(o) = 9*o**4 + 134*o**3 - 265*o**2 + 136*o - 2. Let n(f) = 5*l(f) + 10*u(f). Factor n(v).
-5*v*(v - 132)*(v - 1)**2
Suppose 105*h - 25712 = 33823. Let j be (1458/h)/(3/2). Let 0*i + j*i**2 + 0 - 16/7*i**3 = 0. Calculate i.
0, 3/4
Let b(w) = 2*w - 47. Let a be b(16). Let v be a/45 - ((-66)/(-45) + -2). Factor 1/5*m**3 + 0*m - v*m**5 + 0 + 1/5*m**4 - 1/5*m**2.
-m**2*(m - 1)**2*(m + 1)/5
Let r be ((-40)/320 - (-41)/8) + -5. Let 0 - 3/5*y**3 - 3/5*y**2 + r*y = 0. What is y?
-1, 0
Let g(y) be the third derivative of -1/3*y**6 + 5/12*y**5 + 0*y**3 + 5/8*y**4 + 0 + 0*y - 30*y**2. Factor g(u).
-5*u*(u - 1)*(8*u + 3)
Suppose 0 = -l + 51 - 46. Let w(z) be the first derivative of -1/15*z**4 + 1/5*z**2 - 2/25*z**l + 4/45*z**3 + 2/15*z - 2 - 1/45*z**6. Factor w(i).
-2*(i - 1)*(i + 1)**4/15
Let r(l) be the second derivative of -l - 1/3*l**4 + 0*l**2 + 4/9*l**3 + 0*l**5 - 24 + 2/45*l**6. Suppose r(u) = 0. Calculate u.
-2, 0, 1
Let c(u) be the third derivative of -u**6/1080 - 7*u**5/54 + 71*u**4/216 - 2*u**2 - 95. Find o such that c(o) = 0.
-71, 0, 1
Let s(c) be the second derivative of 7/80*c**5 + 0 + 11/2*c**2 + 1/80*c**6 + 3/16*c**4 - 25*c + 0*c**3. Let b(l) be the first derivative of s(l). Factor b(g).
3*g*(g + 2)*(2*g + 3)/4
Let w = -7771 + 18921. Factor 4*v**5 + 44*v**4 - w*v + 140*v**3 + 100*v**2 + 11150*v.
4*v**2*(v + 1)*(v + 5)**2
Factor 4410*f**2 - 2067245 - 7445*f - 4415*f**2 + 1015*f.
-5*(f + 643)**2
Let x = -20/75563 - -151186/226689. Let 56/3*l**2 + x*l**3 - 118/3*l + 20 = 0. Calculate l.
-30, 1
Let k = 896292 - 2688875/3. Factor 5/3*g - 50/3 + k*g**2.
(g - 5)*(g + 10)/3
Factor -73*y**4 - y**5 - 974*y**3 - 208*y**2 - 1088*y**2 - 394*y**3.
-y**2*(y + 1)*(y + 36)**2
Let u(y) = y**2 - 11*y + 4. Let h(m) = 21*m**2 - 195*m + 72. Let n(z) = h(z) - 18*u(z). Suppose n(l) = 0. What is l?
-1, 0
Factor 96/17 - 16/17*x**2 - 8/17*x - 2/17*x**3.
-2*(x - 2)*(x + 4)*(x + 6)/17
Let b(z) be the third derivative of -z**5/15 + 11*z**4/2 - 484*z**3/3 + 250*z**2 + 5. Solve b(f) = 0 for f.
11, 22
Let r(a) be the second derivative of a**5/190 - 4*a**4/57 - 55*a**3/57 + 350*a**2/19 + 12679*a. Determine z so that r(z) = 0.
-7, 5, 10
Let j(m) = 2*m**3 + 7*m**2 + m. Let h(k) = 18*k**3 + 78*k**2 + 100*k. Let r(g) = -2*h(g) + 20*j(g). Factor r(a).
4*a*(a - 9)*(a + 5)
Let g be 5/(-9)*(1 + 303/(-15)). Factor -4/3*m**5 + g*m**3 + 0*m**2 + 0 + 8/3*m**4 + 0*m.
-4*m**3*(m - 4)*(m + 2)/3
Let v(w) = -43*w**2 + 16084*w - 8064113. Let x(p) = -18*p**2 + 8040*p - 4032058. Let f(c) = -2*v(c) + 5*x(c). Factor f(q).
-4*(q - 1004)**2
Let y = -241796 - -241798. Factor -4/5*i + 1/5*i**4 + 4/5*i**3 + 2/5*i**y - 3/5.
(i - 1)*(i + 1)**2*(i + 3)/5
Suppose -2*r + 2 = -0*r, -5*l - 3*r = -18. Find t such that -60*t**2 + 6*t**l - 33 - t**3 - 35 - 223*t + 91*t - t**3 = 0.
-1, 17
Let a(c) be the third derivative of -c**5/60 - 5*c**4/24 + c**3/6 - 18*c**2. Let l be a(-4). Determine q so that -2*q**3 - q**4 + 5*q**4 - 3*q**l + q**5 = 0.
0, 1
Solve -30204/11*d**2 + 6/11*d**4 - 60504/11*d - 5010/11*d**3 - 40368/11 = 0 for d.
-2, 841
Let g(t) = -5*t**2 - 144*t - 622. Let z(k) = -26*k**2 - 734*k - 3112. Let i(j) = 16*g(j) - 3*z(j). Factor i(p).
-2*(p + 7)*(p + 44)
Let r be (-2)/(-5)*(-16)/((-128)/360). Suppose -22*y + 2*m = -r*y, 5*y + 3*m = 0. Determine v, given that 0*v + v**4 + 0*v**2 + y - 1/2*v**3 + 3/2*v**5 = 0.
-1, 0, 1/3
Let b(h) be the second derivative of -2*h + 5/13*h**3 - 64 + 14/13*h**2 + 1/78*h**4. Suppose b(o) = 0. Calculate o.
-14, -1
Determine z, given that 36 - 2/9*z**2 + 14/3*z = 0.
-6, 27
Let q = 1594717 - 1594715. Determine z so that 1/2*z**5 - 1352 - 107/2*z**4 + 3019/2*z**3 - 8425/2*z**q + 4108*z = 0.
1, 52
Let l(i) = -11*i**3 - 365*i**2 - 3*i + 371. Let z(y) = 39*y**3 + 1094*y**2 + 10*y - 1115. Let a(b) = -14*l(b) - 4*z(b). Factor a(p).
-2*(p - 367)*(p - 1)*(p + 1)
Let b = -4557/83590 - -40/643. Let j(z) be the second derivative of -b*z**5 + 0 + 0*z**2 + 1/26*z**4 - 2/39*z**3 - 9*z. Factor j(w).
-2*w*(w - 2)*(w - 1)/13
Let b be -2*(-3)/(-12)*0. Let j be (b/1)/(465/(-155)). Factor j - 5*r**3 - 5/2*r**2 + 5*r + 5/2*r**4.
5*r*(r - 2)*(r - 1)*(r + 1)/2
Suppose 227 = 16*b + 163. Let k(t) be the first derivative of -1/3*t**3 + 0*t - 1/4*t**2 - 1/8*t**b - 13. Suppose k(x) = 0. What is x?
-1, 0
Let v(w) be the first derivative of -w**4/2 - 184*w**3/3 + 191*w**2 + 564*w - 6267. Factor v(n).
-2*(n - 3)*(n + 1)*(n + 94)
Solve 1152*d**2 + 40*d**5 - 3759711 - 13*d**5 - 1104*d - 312*d**3 - 60*d**4 + 3759903 = 0.
-4, 2/9, 2
Suppose 4*w = t - 289, 5*t - 2*w = 4*t + 283. Factor -5*s**3 - 221*s + 4*s**2 + s**3 + t*s - 96.
-4*(s - 3)*(s - 2)*(s + 4)
Suppose 938 + 22 = -4*c. Let a = 382 + c. Find w, given that a*w**3 - 5*w**2 - 147*w**3 - w + 11*w = 0.
-2, 0, 1
Let n = 190402 - 380803/2. Suppose -7/4*m + 1/4*m**5 + 1/2*m**4 - 2*m**2 - 1/2 - n*m**3 = 0. What is m?
-1, 2
Let j(z) = -3*z**3 - 11*z**2 - 6*z - 5. Let x be j(-4). Factor -18*g**2 + g - 16*g**2 + x*g**2.
g*(g + 1)
Let b(g) = -g**2 - g - 9. Let r(c) = 8*c**2 + 120*c + 393. Let n(a) = 35*b(a) + 5*r(a). Factor n(u).
5*(u + 3)*(u + 110)
Let k(p) be the first derivative of -3*p**4/8 + 495*p**3 - 184509*p**2 + 732108*p + 5174. Let k(m) = 0. Calculate m.
2, 494
Let c(l) be the first derivative of l**6/2 - 21*l**5/5 - 183*l**4/4 + 7*l**3 + 90*l**2 - 4487. Determine b so that c(b) = 0.
-5, -1, 0, 1, 12
Let h(i) = -i**4 - 2*i**3 - i**2 - i - 1. Let x(r) = 7*r**4 + 28*r**3 + 59*r**2 + 67*r + 29. Let c(b) = 5*h(b) + x(b). 