lculate s.
1, 2
Suppose -164*i + 10 = -1794. Find r, given that i*r + 1/2*r**2 + 121/2 = 0.
-11
Suppose 2*k = -2*n + 36 - 0, n = -3*k + 26. Determine s, given that 0 - 8/7*s + k*s**2 = 0.
0, 2/7
Let o(l) be the first derivative of -45*l**2 - 1/10*l**4 + 4*l**3 + 0*l - 161. Determine y, given that o(y) = 0.
0, 15
Let z(i) = i**3 - 31*i**2 - i + 35. Let v be z(31). Let c(t) be the first derivative of 1 + 1/10*t**v + 0*t**2 + 0*t - 2/15*t**3. Factor c(b).
2*b**2*(b - 1)/5
Let g = -133 - -142. Factor -240 - 4*h**3 - 40*h + 48*h**2 + 8*h**2 - 6*h**3 + g*h**2.
-5*(h - 4)**2*(2*h + 3)
Let l = 1946/9 + -216. Let j = 32/249 + 70/747. Factor j*i**5 - l*i**3 + 0*i - 2/9*i**2 + 2/9*i**4 + 0.
2*i**2*(i - 1)*(i + 1)**2/9
Suppose -45 = -4*r - r. Let c be 22/((-704)/(-24912))*4/18. What is q in 25*q**2 + r*q**3 - 143*q + c*q - 4*q**3 = 0?
-3, -2, 0
Let f(c) = c**3 + 25*c**2 - 53*c + 51. Let g be f(-27). Suppose 2*u = 4*q + g, -u - q + 0*q = 3. Factor -1/2*l**3 - 3/2*l**u + 1/2*l + 1/2*l**4 + 1.
(l - 2)*(l - 1)*(l + 1)**2/2
Let p(l) be the second derivative of l**4/84 - 55*l**3/42 - 57*l**2/7 + 2*l + 2551. Solve p(w) = 0 for w.
-2, 57
Let f(j) be the third derivative of 1/420*j**5 + 0 + 1/6*j**4 + 0*j - 270*j**2 - 10/7*j**3. Determine c so that f(c) = 0.
-30, 2
Let a be ((-20)/(-8) - 2)*(-1 - 11). Let t(s) = 4*s**3 - 2*s**2 - 2*s - 12. Let w(b) = -3*b**3 + 2*b**2 + b + 10. Let m(n) = a*w(n) - 5*t(n). Factor m(v).
-2*v*(v - 1)*(v + 2)
Let h(y) = -y**3 + 52*y**2 + 14*y - 211. Let c be h(52). Let u = c + -515. Solve 0 + 0*d - 1/3*d**u + 1/3*d**3 = 0 for d.
0, 1
Let v(r) be the first derivative of r**6/360 - 7*r**4/72 + r**3/3 + 101*r**2/2 + 126. Let t(m) be the second derivative of v(m). Find y such that t(y) = 0.
-3, 1, 2
Suppose -2*o = -5*j + 5 + 4, -4*o + 12 = 0. Let h = 847 - 844. Factor 8*f**j - 5*f**4 + 0*f**2 + 7*f**h - 10*f**2.
-5*f**2*(f - 2)*(f - 1)
Suppose -8*g + 27 = -5*g. Suppose 731*s**3 - 4*s**5 + 31*s**4 + g*s**4 - 767*s**3 = 0. What is s?
0, 1, 9
Suppose -15*l - 22*l + 1443 = 0. Let z = l + -36. Factor -2*j**2 - 2/3*j + 2/3*j**z + 2.
2*(j - 3)*(j - 1)*(j + 1)/3
Let r = 431948 + -431946. Let 17/3*c - 3 - 7/3*c**r - 1/3*c**3 = 0. What is c?
-9, 1
Let m be ((-636)/(-36) - 17)/(2/99). Suppose 3*y - 2*a = 18, -5*a - 10 + m = y. Factor 24/5*k**2 + 10/3 + y*k.
2*(6*k + 5)**2/15
Let j(t) be the first derivative of -t**3/9 + 31*t**2/3 - 59*t + 1635. Factor j(k).
-(k - 59)*(k - 3)/3
Let g = 1123 - 1201. Let j be (3*(-16)/28)/(g/21). Factor 0*d + 0 + 0*d**2 - 2*d**4 + j*d**5 + 8/13*d**3.
2*d**3*(d - 4)*(3*d - 1)/13
Let t(z) be the second derivative of z**5/190 + 7*z**4/38 + 134*z**3/57 + 240*z**2/19 + z - 655. Factor t(d).
2*(d + 3)*(d + 8)*(d + 10)/19
Let y(p) be the first derivative of 13*p**6/48 + 9*p**5/40 - 7*p**4/4 - 3*p**3/2 + p**2 - 1817. Let y(o) = 0. What is o?
-2, -1, 0, 4/13, 2
Solve 501/5*l - 132/5*l**3 + 81*l**2 - 36/5 = 0 for l.
-1, 3/44, 4
Let p(z) be the third derivative of 0 - z - 1/120*z**5 + 10*z**2 + 4/3*z**3 + 1/8*z**4. Suppose p(j) = 0. What is j?
-2, 8
Let g(k) be the first derivative of -k**3/24 + 915*k**2/8 - 1829*k/8 + 53. Factor g(p).
-(p - 1829)*(p - 1)/8
Let w = -6/24317 - -52160049/340438. Let v = w + -649/7. Factor 11*o - 1/2*o**2 - v.
-(o - 11)**2/2
Let x be 8*(-15 + ((-7785)/(-210) - 22)). Factor 2/7*c**4 + 6/7*c**3 + 2/7*c**2 - 6/7*c - x.
2*(c - 1)*(c + 1)**2*(c + 2)/7
Let h(i) be the first derivative of i**4/12 - 49*i**3/3 + 1825*i**2/2 - 5329*i/3 + 938. Factor h(p).
(p - 73)**2*(p - 1)/3
Let r be (-2)/11 - (-1240)/(-440). Let f be (-18)/(-4) + (6 + r - 7). Factor -4*x**2 + f*x + 0 + 25/2*x**5 + 20*x**4 + 3*x**3.
x*(x + 1)**2*(5*x - 1)**2/2
Let j = 168 - 166. Factor 92*x**2 - 11*x - 147*x**j - 167*x**3 + 35*x**4 + 192*x**3 - 130*x**2 + 166*x - 30.
5*(x - 1)**2*(x + 3)*(7*x - 2)
Let w(j) be the third derivative of -j**6/60 - 13*j**5/5 - 451*j**4/4 + 6724*j**3/3 - 1831*j**2. What is z in w(z) = 0?
-41, 4
Let n = -266 + 445. Factor 355*f + 24 - 180*f - n*f - 4*f**2.
-4*(f - 2)*(f + 3)
Solve 2/11*k**2 + 2340/11 - 186/11*k = 0.
15, 78
Let s(n) be the third derivative of -1805/6*n**3 - 95/12*n**4 + 58*n**2 - 1/12*n**5 + 0 + 0*n. Factor s(p).
-5*(p + 19)**2
Let v(u) be the first derivative of 1/24*u**6 + 0*u**2 + 95 + 5/12*u**3 - 1/16*u**4 - 1/4*u**5 + 0*u. Find k such that v(k) = 0.
-1, 0, 1, 5
Suppose 0 = -3*k + 181 + 5. Let -5*j**2 - 177*j + 10*j**2 + k*j + 90*j = 0. Calculate j.
0, 5
Let a(s) be the first derivative of -s**4/4 - 199*s**3/3 - 4900*s**2 + 10000*s - 543. Factor a(w).
-(w - 1)*(w + 100)**2
Let n(g) be the first derivative of g**7/126 - g**6/90 - g**5/20 + g**4/36 + g**3/9 + 49*g - 21. Let i(m) be the first derivative of n(m). Factor i(r).
r*(r - 2)*(r - 1)*(r + 1)**2/3
Let q(k) = 22*k**2 + k + 1. Let r(v) = 94*v**2 + 104*v + 68. Let w(t) = 4*q(t) - r(t). Suppose w(i) = 0. Calculate i.
-16, -2/3
Let i = 110 + -106. Solve -34*q**4 - 45*q**2 + 24*q**i + 8 + 36*q**3 + 11*q**2 = 0 for q.
-2/5, 1, 2
Let r(u) be the third derivative of u**5/270 + 95*u**4/108 + 92*u**3/9 + 8*u**2 + 16. Factor r(x).
2*(x + 3)*(x + 92)/9
Factor 0*f**4 + 0*f + 2/13*f**5 + 0*f**2 + 0 - 8/13*f**3.
2*f**3*(f - 2)*(f + 2)/13
Let u(v) be the second derivative of -5*v**4/12 + 4285*v**3/6 - 4275*v**2 + 6951*v. Find q, given that u(q) = 0.
2, 855
Let g(j) be the first derivative of j**6/600 + j**5/25 - 13*j**4/120 + 3*j**2/2 + 6*j + 18. Let c(t) be the second derivative of g(t). Factor c(z).
z*(z - 1)*(z + 13)/5
Suppose -3550 - 6950 = -12*p. Let z = 14877/17 - p. Let -z*h**2 - 2/17 - 4/17*h = 0. Calculate h.
-1
Let y(k) = 152*k + 14748. Let u be y(-97). Let -8/11*d**u + 34/11*d**3 - 28/11 + 74/11*d + 144/11*d**2 = 0. What is d?
-2, -1, 1/4, 7
Suppose 0 = -5*u - 10, -3*z - u + 90 = -46. Suppose 5*h - k + 3*k - z = 0, h - 12 = k. Let 2 - h*l - 3*l**3 - 2*l + 15*l - 4*l**2 + 2*l**4 = 0. Calculate l.
-1, -1/2, 1, 2
Suppose -5*h + 4915 = 4*n + 4964, 0 = 4*n - 3*h - 55. Factor 2/7*j**n + 0 + 2/7*j**3 + 16/7*j - 20/7*j**2.
2*j*(j - 2)*(j - 1)*(j + 4)/7
What is z in -111/7*z**2 - 825/7 - 933/7*z - 3/7*z**3 = 0?
-25, -11, -1
Let h(r) be the second derivative of 0*r**2 + 148*r + 5/6*r**3 + 1/24*r**4 + 0. Solve h(v) = 0 for v.
-10, 0
Let k be (-680)/(-144) + (-63)/14. Let a(c) be the first derivative of k*c**3 - 26 + 0*c**2 + 0*c - 1/4*c**4. Suppose a(b) = 0. What is b?
0, 2/3
Suppose 4*x + 630 = 11*x. Suppose -x = -k + 4*k. Let u(w) = w**4 - 3*w**3 + 9*w**2 + 5*w. Let t(f) = -f**2 - f. Let z(n) = k*t(n) - 5*u(n). Factor z(y).
-5*y*(y - 1)**3
Let d(j) be the first derivative of j**6/30 - j**5/5 - 2*j**4/3 + 11*j**2/2 - j + 5. Let y(k) be the second derivative of d(k). Factor y(l).
4*l*(l - 4)*(l + 1)
Let t = 1142 - 358. Let h = -784 + t. Factor 2/7*w + 0*w**4 - 4/7*w**3 + 2/7*w**5 + h + 0*w**2.
2*w*(w - 1)**2*(w + 1)**2/7
Let l(r) be the third derivative of -r**5/330 - 5*r**4/44 + 108*r**3/11 - 174*r**2 + 12*r. Factor l(k).
-2*(k - 12)*(k + 27)/11
Let t(g) = -g**3 - 19*g**2 + 52*g - 21. Let l be t(-22). Factor 213*s**2 + 81*s + l*s**2 + 45 + 32*s + 187*s.
5*(10*s + 3)**2
Let x(l) be the second derivative of l**5/25 + 89*l**4/20 + 197*l**3/30 - 33*l**2/5 - 55*l - 10. Let x(g) = 0. Calculate g.
-66, -1, 1/4
Let c(q) be the second derivative of -2 - 1/4*q**5 + 33*q - 1445/2*q**3 - 24565/2*q**2 - 85/4*q**4. Find b such that c(b) = 0.
-17
Let m be 1 - 1 - (-13 - -9). Let w(l) be the third derivative of -17/96*l**m + 0 - 1/480*l**6 + 28*l**2 - 1/30*l**5 - 5/12*l**3 + 0*l. Factor w(u).
-(u + 1)*(u + 2)*(u + 5)/4
Factor -3/2*p**3 + 549*p**2 + 2723772 - 66978*p.
-3*(p - 122)**3/2
Let j(v) = v**2 + 3*v - 12. Let h be j(7). Let p = 60 - h. Factor -u**2 + 5*u - 7 + 2*u**3 - 7*u**3 + 6*u**p + 2.
-5*(u - 1)**2*(u + 1)
Let i(p) be the third derivative of -3*p**7/56 + 463*p**6/80 - 667*p**5/80 - 61*p**4/8 - 57*p**2 + 12. Let i(y) = 0. Calculate y.
-4/15, 0, 1, 61
Let m(k) be the first derivative of k**3/18 - 169*k**2/2 + 1013*k/6 - 1962. Find p such that m(p) = 0.
1, 1013
Find n, given that 24/5*n**3 - 648/5*n + 1458/5 + 2/5*n**4 - 36/5*n**2 = 0.
-9, 3
Suppose -4*v - 4 = -l - 0, 5*l = -v + 20. Suppose l = -10*s + 24. Factor -6 - 21*j - 3*j**3 - 23*j**s - 3 + 8*j**2.
-3*(j + 1)**2*(j + 3)
Let g = -522775/189 - -2766. Let h = g + 572/945. Solve 3/5 + h*s**2 - 6/5*s = 0 f