, -1, 2/3
Find w, given that -660*w - 671 + 399 + 1592*w**2 - 3178*w**2 - 1753 + 1591*w**2 = 0.
-3, 135
Factor -9*w**3 + 3/5*w**4 - 135*w**2 - 375*w + 0.
3*w*(w - 25)*(w + 5)**2/5
Let h(b) = -b**2 - 455*b + 78206. Let q be h(133). Suppose -1 - 1/2*w**3 - 2*w**q - 5/2*w = 0. Calculate w.
-2, -1
Let o(p) be the first derivative of -p**4/20 + 26*p**3/5 + 79*p**2/10 - 3. Solve o(x) = 0 for x.
-1, 0, 79
Suppose 5*f = -3*p - 5, -3*f - 902*p + 11 = -903*p. What is l in 1/2*l**f + 1/6*l**3 + 1/3*l + 0 = 0?
-2, -1, 0
Let i be 0/((-36)/(-45)*-5 + (12 - 0)). Let h(p) be the first derivative of -64/3*p + 4/3*p**3 + i*p**2 + 4 - 1/6*p**4. Find b, given that h(b) = 0.
-2, 4
Let u(x) = -3*x**2 + 24*x + 21. Let d be u(10). Let c = 42 + d. Factor 15/4*q**c + 0*q + 5/4*q**2 + 0.
5*q**2*(3*q + 1)/4
Let a be 1 + 3/(-2) - 352/(-64). Solve a*g**2 + g - 2419 + 2*g + 2424 + 7*g = 0.
-1
Let d(q) be the third derivative of -q**7/42 - q**6/4 - q**5/4 + 25*q**4/12 + 29*q**2 - 17. Suppose d(m) = 0. What is m?
-5, -2, 0, 1
Factor -25/4*k**2 + 1/4*k**3 + 127/4*k + 153/4.
(k - 17)*(k - 9)*(k + 1)/4
Suppose -288/7 - 4/7*m**3 - 48/7*m + 40/7*m**2 = 0. What is m?
-2, 6
Let r(g) be the second derivative of -g**4/4 - 20*g**3 + 123*g**2/2 + 1076*g. Factor r(b).
-3*(b - 1)*(b + 41)
Let h(b) be the third derivative of -b**8/168 - 2*b**7/35 - b**6/15 + b**5/5 + 5*b**4/12 + 167*b**2 - 5*b. Suppose h(o) = 0. Calculate o.
-5, -1, 0, 1
Find z, given that -2/21*z**4 + 320/21*z - 52/21*z**3 + 16/21*z**2 + 2/21*z**5 + 256/21 = 0.
-4, -2, -1, 4
Let y(a) = 3*a**3 + 750*a**2 - 3054*a - 1521. Let k be y(-254). Factor -6*c - 2/7*c**k + 28 - 24/7*c**2.
-2*(c - 2)*(c + 7)**2/7
Let m = -236072/3 + 78692. Factor 0 - m*g**5 + 0*g + 16/3*g**4 - 20/3*g**3 + 8/3*g**2.
-4*g**2*(g - 2)*(g - 1)**2/3
Let r(p) be the first derivative of p**3/7 - 54*p**2/7 + 135*p - 2128. Factor r(n).
3*(n - 21)*(n - 15)/7
Let z be (1 + 0)*1112/6116. Factor 0*m**2 + 0*m + 0 - z*m**4 + 28/11*m**3.
-2*m**3*(m - 14)/11
Solve -12*m - 4*m + 3*m**2 - 288417 + m + 288345 = 0 for m.
-3, 8
Let d(q) be the second derivative of -q**4/66 - 10*q**3/33 + 96*q**2/11 - 12*q - 9. Solve d(n) = 0.
-16, 6
Let o(z) = 6*z**2 + 3*z + 2. Let d(v) = 100*v**2 + 50*v + 35. Let c(j) = -2*d(j) + 35*o(j). Let p(f) = 9*f**2 + 6*f. Let g(a) = -4*c(a) + 5*p(a). Factor g(l).
5*l*(l + 2)
Let t(o) be the third derivative of -o**5/60 - 153*o**4/2 - 6*o**2 + 8*o + 3. Factor t(h).
-h*(h + 1836)
Let y(h) be the first derivative of -4*h + 5/3*h**3 + 3/2*h**2 - 3/4*h**4 - 1/5*h**5 - 118. Factor y(w).
-(w - 1)**2*(w + 1)*(w + 4)
Let s be (-37)/(407/(-102)) + -9. Let f(b) be the first derivative of 0*b + 8 + s*b**2 - 4/33*b**3. Solve f(l) = 0.
0, 3/2
Factor 0*t + 413/5*t**4 + 0 + 0*t**2 + 1/5*t**5 + 0*t**3.
t**4*(t + 413)/5
Suppose -619*i + 616*i + 75 = 0. Factor -26 - 264*n + i + 21 - 153*n**2 - 36*n**3 - 65 - 3*n**4 - 99.
-3*(n + 1)*(n + 3)*(n + 4)**2
Let x be ((-40)/260)/((-84)/1486). Let y = -5/91 + x. Factor -y*q + 4*q**2 - 4/3.
4*(q - 1)*(3*q + 1)/3
Let c(d) be the first derivative of -2*d**3/15 + 389*d**2/20 - 97*d/10 - 1007. Determine m so that c(m) = 0.
1/4, 97
Let h be ((-122)/427)/((-1069)/7). Let n = 19228/7483 + h. Solve -36/7*g**2 - n*g**4 - 2/7*g**5 + 54/7*g + 54/7 - 52/7*g**3 = 0 for g.
-3, -1, 1
Determine m, given that 46853 - 93708 - 45*m**2 + 25*m + 46855 + 15*m**3 + 5*m**4 = 0.
-5, 0, 1
Suppose 33 = 30*a - 9 - 48. Let p(x) be the first derivative of 49/24*x**4 + 2/3*x - 2*x**2 + 25 + 7/6*x**a. Factor p(l).
(l + 1)*(7*l - 2)**2/6
Let g(b) be the third derivative of -b**6/420 + b**5/210 + 23*b**4/28 - 9*b**3 + 2*b**2 + 2*b + 2546. Factor g(i).
-2*(i - 7)*(i - 3)*(i + 9)/7
Let t be (-592)/(-300) - (-10)/375. Factor -36/5*k**t + 108/5*k + 3/5*k**3 + 0.
3*k*(k - 6)**2/5
Let v = 4/8751 + 44726/2917. Factor 2 - v*t + 32/3*t**3 + 80/3*t**2.
2*(t + 3)*(4*t - 1)**2/3
Let p = 102 - 55. Factor 50*c + 15 + 2*c**2 - 20 - p.
2*(c - 1)*(c + 26)
Let c(s) be the third derivative of 2*s**5/45 + 103*s**4/72 - 13*s**3/18 + 2*s**2 - 214. Factor c(i).
(i + 13)*(8*i - 1)/3
Let k be (23 + -31 - 3) + 15. Let m(b) be the third derivative of 0*b - 1/540*b**6 + b**3 - 1/4*b**k + 0 + 19*b**2 + 1/30*b**5. Let m(x) = 0. Calculate x.
3
Let t(k) = -17*k**3 + 37*k**2 - 128. Let c(v) = -8*v**3 + 18*v**2 - 64. Let z be ((-2)/(-4))/((261/(-108))/29). Let s(q) = z*t(q) + 13*c(q). Factor s(i).
-2*(i - 4)**2*(i + 2)
Let g(t) be the second derivative of -t**5/120 - 4*t**4/9 - 23*t**3/4 - 2*t + 1958. Solve g(b) = 0 for b.
-23, -9, 0
Let s(z) = -4*z**2 + 147*z - 1293. Let t(q) = 9052 - 1028*q - 2*q**2 + 20*q**2 + 7*q**2 + 3*q**2. Let l(a) = -20*s(a) - 3*t(a). Suppose l(r) = 0. What is r?
18
Let r(b) be the first derivative of -42*b**2 + b**4 - 28/3*b**3 + 108*b + 259. Let r(t) = 0. What is t?
-3, 1, 9
Let x(m) be the third derivative of m**6/720 - m**5/360 - m**2 - 350. Let x(k) = 0. What is k?
0, 1
Suppose 3*x = -3*k - 3, -6*x + 2*x = 3*k + 7. Let g be ((-2)/3)/(5 + 80/(-15)). Factor g*i**2 + 5 - 4*i - k - 2.
2*i*(i - 2)
Let b(s) be the first derivative of -s**4/2 - 244*s**3/3 - 237*s**2 + 720*s - 4556. Solve b(t) = 0.
-120, -3, 1
Let n = 127 + -130. Let z be (n + (-1 - -6))*(-4)/(-88). Find j, given that 0*j - z*j**4 + 0*j**3 + 0 + 1/11*j**2 = 0.
-1, 0, 1
Suppose 0 = -3*u + 1155 - 621. Determine v so that 6*v**2 + 0*v**4 - 6*v**4 + 166*v**3 + 3*v - u*v**3 + 9*v**5 = 0.
-1, -1/3, 0, 1
Determine w, given that -13/3*w**3 + 0 + 0*w + 1/6*w**5 + 1/6*w**4 + 4*w**2 = 0.
-6, 0, 1, 4
Let z(v) be the first derivative of -47 + 16*v**2 + 20/3*v**3 + 12*v. Factor z(q).
4*(q + 1)*(5*q + 3)
Let h(n) be the second derivative of n**5/130 - 5*n**4/13 + 149*n**3/39 - 120*n**2/13 - 67*n - 18. Factor h(i).
2*(i - 24)*(i - 5)*(i - 1)/13
Let j(q) = q**3 + 6*q**2 + 7*q + 4. Let h be j(-4). Suppose -3*f - 2*n = -0 - h, 3 = 3*n. Factor y**2 - 15*y - 2*y**f - 1 + 0*y**2 + 13*y.
-(y + 1)**2
Determine s, given that -3572012*s**4 + 783*s**2 - 219*s**3 + 56 + 489*s + 116*s**5 + 10 - 386*s**5 + 3571163*s**4 = 0.
-22/9, -1, -1/2, -1/5, 1
Let k(n) be the first derivative of 0*n + 1/21*n**3 - 75 - 4/7*n**2. Factor k(c).
c*(c - 8)/7
Let y(m) be the second derivative of -m**6/30 - m**5/15 + 33*m**2 - 107*m. Let t(p) be the first derivative of y(p). Factor t(h).
-4*h**2*(h + 1)
Solve 26*f**3 - 90*f + 1578*f**4 - 6*f**3 - 1583*f**4 + 15*f**2 = 0 for f.
-2, 0, 3
Let 428/9*o**3 - 20/3*o**4 - 160/3 - 4/9*o**5 + 60*o**2 - 424/9*o = 0. What is o?
-20, -1, 1, 6
Let y(d) be the third derivative of -d**5/12 + 445*d**4/6 + 1790*d**3/3 - 27*d**2 + d + 35. Solve y(a) = 0.
-2, 358
Let z(f) be the first derivative of 7/6*f**2 - 2/3*f + 76 + 4/9*f**3. Let z(q) = 0. What is q?
-2, 1/4
Let w(r) be the third derivative of -7/96*r**4 + 14*r**2 - 1/240*r**5 + 1/3*r**3 + 0*r - 1. Suppose w(a) = 0. Calculate a.
-8, 1
Let u = -51 - -29. Let b be 2/((-8)/(-2)) + (-25)/u. Let b*y + 28/11*y**3 - 12/11*y**4 + 2/11*y**5 - 32/11*y**2 - 4/11 = 0. Calculate y.
1, 2
Let v(a) be the third derivative of a**5/12 - 265*a**4/6 + 1055*a**3/6 + 13*a**2 + 28. Suppose v(z) = 0. Calculate z.
1, 211
Suppose -307*d + 303*d = -16. Let g(m) be the first derivative of -1/8*m**d + 1/2*m**3 - 14 + 0*m - 1/2*m**2. Factor g(s).
-s*(s - 2)*(s - 1)/2
Let k(c) be the first derivative of -2*c**3/21 + 39*c**2/7 + 540*c/7 - 6401. Solve k(f) = 0.
-6, 45
Let h(b) = -8*b + 31. Let l be h(4). Let y be l/(1 - (-44)/(-37)) + -5. Factor 1/7*v**3 - y - 1/7*v - 1/7*v**4 + 3/7*v**2.
-(v - 2)*(v - 1)*(v + 1)**2/7
Let f(j) be the second derivative of 2*j**7/21 - 2*j**6/3 - 21*j**5/5 + 63*j**4 - 288*j**3 + 648*j**2 - 1813*j. Factor f(z).
4*(z - 3)**3*(z - 2)*(z + 6)
Let g(v) be the second derivative of -10/3*v**3 + 100*v + 1/12*v**4 + 50*v**2 + 0. Factor g(q).
(q - 10)**2
Suppose 82*z - 56 = 4*n + 78*z, 0 = -3*n + 5*z - 70. Let 0*f**2 - 3/2*f**4 + n + 3/2*f**3 + 0*f = 0. Calculate f.
0, 1
Let v = -213 - -216. Factor 20*z**4 + 17*z**3 - 166*z**5 + 161*z**5 + 8*z**v.
-5*z**3*(z - 5)*(z + 1)
Suppose 14*r + 5*r = 76. Suppose -4*d = 3*k + 2, 1 = -r*d - 7. Let -24/7 + 20/7*t + 44/7*t**k = 0. What is t?
-1, 6/11
Let v(k) be the first derivative of -19044*k**5/5 - 27600*k**4 - 25879*k**3 - 8739*k**2/2 - 270*k - 1645. Suppose v(h) = 0. Calculate h.
-5, -2/3, -3/46
Let b be ((-3)/(-6) - 2/4)/(-117 + 1