2297/11. Factor -x + a*k**2 - 2/11*k**3 + 2/11*k.
-2*(k - 1)**2*(k + 1)/11
Let q = 454/6765 - 1/2255. Let b(s) be the third derivative of 16*s**2 + 1/3*s**4 + 2/3*s**3 + 0 + 0*s**5 - 2/105*s**7 - q*s**6 + 0*s. Let b(i) = 0. What is i?
-1, 1
Suppose 4*l - 44 - 62 = -2*p, -5*l - 4*p + 134 = 0. Suppose l*h = 46*h. Factor -140/3*u**3 - 88/3*u**2 - 50/3*u**4 + h - 16/3*u.
-2*u*(u + 2)*(5*u + 2)**2/3
Let r(n) be the third derivative of -n**7/30 + 611*n**6/120 - 194*n**5/15 + 43*n**4/6 - 3*n**2 - 166*n. Factor r(m).
-m*(m - 86)*(m - 1)*(7*m - 2)
Let h(k) be the second derivative of -17/36*k**3 + 0 + 13/72*k**4 - 1/60*k**5 + 175*k - k**2. Let h(a) = 0. Calculate a.
-1/2, 3, 4
What is l in -8/11*l + 2/11*l**3 + 96/11 - 24/11*l**2 = 0?
-2, 2, 12
Factor 2/11*x**2 - 336/11*x + 14112/11.
2*(x - 84)**2/11
Let 0 + 1/5*o**2 + 81/5*o = 0. What is o?
-81, 0
Let d(j) be the first derivative of 5*j**6/6 + 14*j**5 + 375*j**4/4 + 950*j**3/3 + 560*j**2 + 480*j - 6052. Let d(o) = 0. What is o?
-4, -3, -2, -1
Let l be 43/(-688)*88 - ((-1 - -3) + -8). Find u, given that -15/2*u**2 + l*u**3 + 63/2*u - 49/2 = 0.
1, 7
Let o(n) be the first derivative of -18*n + 0*n**3 - 3/4*n**4 + 79 + 21/2*n**2. Solve o(l) = 0.
-3, 1, 2
Let i(f) = 25*f + 41. Let z be i(-17). Let q = z - -387. Factor -6/7*p**5 + 4/7*p - 2*p**4 + 0 + 6/7*p**2 - 6/7*p**q.
-2*p*(p + 1)**3*(3*p - 2)/7
Let g(i) be the first derivative of 2/5*i**2 - 26/45*i**3 - 17 - 13/15*i**4 + 0*i - 14/75*i**5. Let g(j) = 0. What is j?
-3, -1, 0, 2/7
Let n(g) be the first derivative of -52 - 3*g**2 + 3/2*g**4 - 2/3*g**3 + 2*g. Factor n(h).
2*(h - 1)*(h + 1)*(3*h - 1)
Let t(l) be the first derivative of 0*l - 4*l**2 - 124 + l**4 + 4/3*l**3. Factor t(g).
4*g*(g - 1)*(g + 2)
Let r = 15892 - 15889. Let f(l) be the first derivative of -11 + 1/8*l**4 - 256*l + 48*l**2 - 4*l**r. Solve f(p) = 0 for p.
8
Solve 14/5*w + 0 - 1/5*w**2 = 0.
0, 14
Let w be ((-38)/(-399))/(4/28). Find a such that -2/3*a + w*a**2 + 0 = 0.
0, 1
Determine m, given that 414/13*m**4 + 20368/13*m**3 - 108976/13*m**2 - 89888/13 + 2/13*m**5 + 178080/13*m = 0.
-106, 1, 2
Let q(a) = -8*a + 14. Let c = 12 + -36. Let t be q(c). Find f such that t*f - 5 - 96*f + 15*f**4 - 95*f - 10*f**2 - 5*f**5 - 10*f**3 = 0.
-1, 1
Let j(i) be the second derivative of -12*i**6/5 - 951*i**5/10 + 784*i**4/3 - 260*i**3 + 112*i**2 - 4853*i. Solve j(r) = 0.
-28, 1/4, 2/3
Factor -86*n**2 - 2/5*n**3 + 23328/5 - 22896/5*n.
-2*(n - 1)*(n + 108)**2/5
Factor -2510*j - j**3 + 3*j**3 + 650 + 1199*j**2 + 61 + 53*j**2 + 545.
2*(j - 1)**2*(j + 628)
Determine j so that 410*j**3 - 196*j + 611*j**3 - 1025*j**3 - 56*j**2 = 0.
-7, 0
Let m(z) be the second derivative of -z**6/10 - 3*z**5/20 + z**4 + 2*z**3 - 3682*z. Factor m(d).
-3*d*(d - 2)*(d + 1)*(d + 2)
Let o be (-5)/20*(-30)/(-9)*-6. Suppose -38607 = -o*y + 12228. Factor -y*d + 803*d - 1944*d**2 - 144*d**3 - 2300*d - 4*d**4 - 26244.
-4*(d + 9)**4
Let b(k) = 41524*k + 290668. Let f be b(-7). Suppose -27/2*t**2 + 0 - 3/2*t**5 + f*t - 21/2*t**4 + 51/2*t**3 = 0. What is t?
-9, 0, 1
Let h = -1687/8 + 211. Let o be (-28)/12 - 186/(-72). Factor -o*x - 1/8 - h*x**2.
-(x + 1)**2/8
Let y be ((70/7 - -4) + -6)*1. Let a(q) = -q + 12. Let p be a(0). Factor 3 + y + 2*z**2 + 4 - p*z - 5.
2*(z - 5)*(z - 1)
Let g(m) be the first derivative of -2*m**5/5 - 31*m**4/4 - 27*m**3 - 77*m**2/2 - 25*m + 3499. Factor g(b).
-(b + 1)**3*(2*b + 25)
Factor -171/2 - 515/4*y - 3/4*y**2.
-(y + 171)*(3*y + 2)/4
Let q be (-136)/612 - (-110)/9. Let r(l) be the first derivative of 22 + l**3 + q*l + 15/2*l**2. Let r(x) = 0. What is x?
-4, -1
Find g such that -32*g**4 + 6*g**4 + 4*g**5 - 34*g**4 + 152*g**3 - 96*g**2 = 0.
0, 1, 2, 12
Let a(o) be the second derivative of 21*o + 0 - 8*o**2 + 1/48*o**5 + 5/24*o**4 + 0*o**3. Let u(m) be the first derivative of a(m). Solve u(c) = 0 for c.
-4, 0
Let z be (2/36)/((-46)/(-1449)). Let d be 22/33*(-3)/(-2). Determine b so that -4*b + d + z*b**2 = 0.
2/7, 2
Let s(i) = 16*i + 131. Let w be s(-8). Suppose -w*y + 24*c - 27*c - 3 = 0, -5*y + 27 = -3*c. Factor 2/11*a**y + 10/11*a**2 + 6/11*a - 18/11.
2*(a - 1)*(a + 3)**2/11
Let j(z) be the second derivative of -z**5/50 - z**4/3 + 13*z**3/5 - 561*z. Let j(t) = 0. What is t?
-13, 0, 3
Suppose 4*g + 13 - 1 = -5*a, -18 = -3*g + 3*a. Suppose -p - 4 = -2*l, 2*p - 3*l = -g - 3. What is s in -6*s**2 + 0*s**p + 4*s**2 + 4*s - 32*s = 0?
-14, 0
Suppose -3*k = 2*k + 3*d - 14, -2*d = -3*k + 16. Let -8*j**2 + 12*j**3 - 24*j**2 + 2*j**4 + k*j**2 + 14*j**3 = 0. Calculate j.
-14, 0, 1
Factor 7/4*a - 3/4*a**2 + 3/2.
-(a - 3)*(3*a + 2)/4
Find j, given that -1408/13*j - 247808/13 - 2/13*j**2 = 0.
-352
Suppose 8*u - 48 + 16 = 0. Suppose -4*c**5 - 36 + 10*c**3 - 5*c**2 - 33*c**2 - 84*c - 2*c**2 + 41*c**3 - 27*c**3 + 12*c**u = 0. What is c?
-1, 3
Let o(t) = t**3 + 11*t**2 - t - 7. Let y be o(-11). Suppose -p = 2*p + y*z - 32, 4*p + z = 21. Factor 10*d**4 - 7*d**4 - 12*d**3 - 7*d**p.
-4*d**3*(d + 3)
Let n(x) be the third derivative of x**8/1680 - 3*x**7/350 + x**6/30 - 35*x**2 - 34*x - 1. Factor n(t).
t**3*(t - 5)*(t - 4)/5
Let h(g) = 5*g**4 - 9*g**3 + 2*g**2 + 8*g. Let v(b) = 2*b**3 - b. Let o(q) = 3*h(q) + 24*v(q). Factor o(m).
3*m**2*(m + 1)*(5*m + 2)
Let j(g) be the second derivative of g**5/26 + 17*g**4/26 - 15*g**3/13 - 11*g**2/13 + 4*g + 1215. Solve j(d) = 0 for d.
-11, -1/5, 1
Find f, given that 1/3*f**2 - 12 + 3*f = 0.
-12, 3
Let u(r) be the third derivative of -3*r**5 + 0*r - 16/3*r**3 - 5 - 2*r**2 + 5/24*r**6 - 13/2*r**4. Factor u(f).
(f - 8)*(5*f + 2)**2
Let s be (733513/(-38038) - -19) + (-2)/(-7). Let t = s - -491/1482. Solve -2/3*v**3 + 2/3*v + t*v**2 - 1/3*v**4 + 0 = 0.
-2, -1, 0, 1
Let z(x) be the third derivative of 13*x**8/2352 + 32*x**7/735 - x**6/168 + 809*x**2. Suppose z(p) = 0. Calculate p.
-5, 0, 1/13
Solve -75/7*q**4 + 0 + 0*q + 3/7*q**5 - 132/7*q**2 + 204/7*q**3 = 0.
0, 1, 2, 22
Determine m, given that 25*m**3 + 435*m + 148*m**2 - 435*m + 20*m**3 + 11*m**3 = 0.
-37/14, 0
Let w(f) be the third derivative of f**7/2310 - f**6/165 - 113*f**5/660 - 10*f**4/11 + 3432*f**2. Factor w(q).
q*(q - 16)*(q + 3)*(q + 5)/11
Let u(i) be the second derivative of -30*i**3 + 15*i - 1/8*i**5 - 175/48*i**4 + 405/8*i**2 + 4. Factor u(p).
-5*(p + 9)**2*(2*p - 1)/4
Let d(h) = 566*h**2 - 567*h + 3. Let v(r) be the first derivative of -1135*r**3/3 + 1135*r**2/2 - 5*r + 158. Let m(c) = -5*d(c) - 2*v(c). Factor m(y).
-5*(y - 1)*(112*y - 1)
Suppose 152*c + 38*c - 580 = 45*c. Suppose 4/3*s - 4/9 - 4/9*s**5 + 4/3*s**c - 8/9*s**2 - 8/9*s**3 = 0. What is s?
-1, 1
Let -5*g**5 + 6904*g**2 + 160*g**4 + 2*g**3 + 3*g**3 - 7064*g**2 = 0. Calculate g.
-1, 0, 1, 32
Let c(v) be the first derivative of -v**3 + 3*v**2/2 + 270*v - 894. Factor c(w).
-3*(w - 10)*(w + 9)
Let f(r) be the first derivative of -r**4/38 + 4436*r**3/19 - 14758572*r**2/19 + 21823008464*r/19 + 10685. Factor f(t).
-2*(t - 2218)**3/19
Let p be 1/((-6)/60*5). Let o(s) = -s**4 + s**3 - s**2 + 1. Let r(z) = -5*z**2 - 4*z**2 + 12*z**3 - 12*z**4 - 5 + 16. Let x(l) = p*r(l) + 22*o(l). Factor x(c).
2*c**2*(c - 2)*(c + 1)
Let p(j) = -j**2 - 14 + 3*j + 6*j - 2*j + 9*j. Let m be p(14). Factor -10*i + m*i - i**2 - 45 + 41.
-(i - 2)**2
Let p = -2/23907 - -71729/95628. Factor -3/4*r**2 + 3*r + 3 - p*r**3.
-3*(r - 2)*(r + 1)*(r + 2)/4
Let g(z) = 27*z - 50. Let q be g(2). Factor 3*d**2 + 14*d**q + d**2 - 4*d - 12*d**4 - 6*d**4 + 4*d**3.
-4*d*(d - 1)**2*(d + 1)
Solve 16428 + 1/3*k**2 + 148*k = 0 for k.
-222
Let v(l) = -13*l**2 - 555*l - 1613. Let o(g) = 19*g**2 + 833*g + 2419. Let x(c) = -5*o(c) - 7*v(c). Factor x(k).
-4*(k + 3)*(k + 67)
Suppose -7 = -335*j + 2 - 9. Let p be ((-160)/(-140))/((-20)/(-14)). What is i in -18/5*i**2 - p*i - 4*i**3 + j = 0?
-1/2, -2/5, 0
Let y = 369 + -358. Solve y*p - 4*p - 5*p + 9 - 8*p + p**2 = 0 for p.
3
Suppose -3*h + 35266 = -93*k + 92*k, 5*h = 2*k + 58778. Factor h*c + 3*c**2 - 7*c**2 - 11250*c - 15876.
-4*(c - 63)**2
Let t(p) be the third derivative of -p**8/168 - 2*p**7/105 + 2*p**6/15 - p**5/15 - 7*p**4/12 + 4*p**3/3 + 1805*p**2 + 1. What is w in t(w) = 0?
-4, -1, 1
Factor -6203 - 589*o + 4743 + o**2 + 2048*o.
(o - 1)*(o + 1460)
Let l be (-36)/(-84) - 494/(-7). Let s = -68 + l. Factor -12*n**2 + s*n**3 + 40*n**4 - 11*n**3 - 2 - 8*n - 42*n**4.
-2*(n + 