- d + 22 = q. Factor 171 + 5*c**4 + 234 + 270*c**2 - 2*c**4 + q*c**4 - 60*c**3 - 540*c.
5*(c - 3)**4
Let r be 1/3 + (-2)/(-6)*23. Suppose -3*p + r*p - 15 = 0. What is i in 3*i + 83*i**3 - 3*i - 82*i**p = 0?
0
Suppose -29*f + 24*f = 25. Let q be f + 1 - 3*-2. Solve 16*d + 4*d**5 - 8*d + 36*d**3 - 20*d**4 - 17*d**2 - 11*d**q = 0 for d.
0, 1, 2
Let k(s) be the third derivative of s**5/150 + 3*s**4/4 + 86*s**3/15 + 2547*s**2. What is q in k(q) = 0?
-43, -2
What is l in 663*l**2 + 6040*l**3 - 411*l**2 + 4*l**4 - 5780*l**3 - 4*l**5 = 0?
-7, -1, 0, 9
Factor 8 - 11*z + 14*z - 16*z + z - 32*z**2 - 12*z**3.
-4*(z + 1)*(z + 2)*(3*z - 1)
Let t(g) be the third derivative of -g**8/84 + 4*g**7/35 + 17*g**6/30 - 2*g**5/5 - 8*g**4/3 + 649*g**2 - 4. What is a in t(a) = 0?
-2, -1, 0, 1, 8
Let b(q) = -15*q**2 - 63*q. Suppose -3*d + 4*k = d + 16, -d = -4*k + 4. Let l(t) = -7*t**2 - 31*t. Let j(i) = d*b(i) + 9*l(i). Determine p, given that j(p) = 0.
-9, 0
Let u be ((-96)/576)/((-11)/1749). Factor -38*t - 1/2*t**4 - 18 - 7*t**3 - u*t**2.
-(t + 1)*(t + 2)**2*(t + 9)/2
Suppose -5*y + 5*q = 170, 6*y - 168 = 11*y - 3*q. Let p = -29 - y. Factor -115*g**3 - 8*g + 123*g**3 + 16*g**2 - p*g**2.
4*g*(g + 2)*(2*g - 1)
Let s(w) = w**2 - 2*w - 22. Let g be s(6). Suppose 0 = -8*l + 7*l + 5, 19 = -g*v + 5*l. Factor v - 4/3*i**3 - 2/3*i**2 + 4*i + 1/3*i**4.
(i - 3)**2*(i + 1)**2/3
Let j(y) be the first derivative of 1/15*y**4 + 8/15*y + 4/15*y**2 - 69 - 14/45*y**3. What is s in j(s) = 0?
-1/2, 2
Let h(x) = -55*x**2 - 6237*x - 6221. Let o(c) = 13*c**2 + 1559*c + 1555. Let b(a) = 3*h(a) + 13*o(a). Let b(s) = 0. What is s?
-388, -1
Factor -3388/25*n + 792/25*n**2 + 2/25*n**4 + 2662/25 - 68/25*n**3.
2*(n - 11)**3*(n - 1)/25
Suppose 111*x + 196 - 65*x - x**3 + 81*x - 46*x**2 + 24*x = 0. What is x?
-49, -1, 4
Suppose -3200 + 76*w**3 + 36*w**4 - 139*w**4 + 128*w + 38*w**4 + 61*w**4 + 600*w**2 = 0. Calculate w.
-4, 2, 25
Let q(z) = z**2 - 18*z + 184. Let a be q(22). Let s = a + -272. Factor s*l - 1/3 + 1/3*l**2.
(l - 1)*(l + 1)/3
Let m(o) be the third derivative of -o**8/448 + o**7/840 + 3*o**6/160 - 3*o**5/80 + o**4/48 - 90*o**2 + 2. Suppose m(l) = 0. What is l?
-2, 0, 1/3, 1
Let t be -1 - ((1 - 2) + 0). Let q be (-4)/(2/(-4) - 366/244). Suppose 8/5*m**5 + 0 + t*m + 22/5*m**3 + 26/5*m**4 + 4/5*m**q = 0. What is m?
-2, -1, -1/4, 0
Suppose -19*f = -2*f - 884. Let s be (-55 - 1)*f/(-156). Determine k so that -16/3*k + 16/3 - s*k**3 - 76/3*k**2 - 4*k**4 = 0.
-2, -1, 1/3
Let i = -205585 - -822343/4. Factor 105/4 + 27*w + i*w**2.
3*(w + 1)*(w + 35)/4
Suppose 10 = 2*b - 5*a - 12, b = 3*a + 9. Determine v so that 15*v - 3*v**2 + b - 129 + 13*v + 6*v**2 - v = 0.
-12, 3
Let z = -78043/395 - 539/79. Let l = -204 - z. Factor l*w**3 + 6*w**2 + 50 + 30*w.
2*(w + 5)**3/5
Suppose 13*k + 1868 + 1852 = 3746. Find i such that 20/9*i**4 - 16/9*i + 0 + 16/9*i**k + 52/9*i**3 = 0.
-2, -1, 0, 2/5
Let g(w) = -110*w + 1214. Let s be g(11). Let n(b) be the third derivative of -1/108*b**s - 1/270*b**5 + 0*b**3 + 10*b**2 + 0 + 0*b. Let n(k) = 0. Calculate k.
-1, 0
Let o(z) be the first derivative of -z**5 + 735*z**4/4 - 9810*z**3 + 87850*z**2 - 147000*z + 5448. Factor o(g).
-5*(g - 70)**2*(g - 6)*(g - 1)
Let j(c) = 15*c**2 + 1315*c - 83210. Let n(h) = -11*h**2 - 1310*h + 83209. Let x(y) = -4*j(y) - 5*n(y). Factor x(s).
-5*(s - 129)**2
Factor 31*f - 1402*f**2 - 57*f - 150 - 119*f + 1407*f**2.
5*(f - 30)*(f + 1)
Suppose 223*q - 4876 = 117*q. Let h(z) = -z**3 - z**2 + 5. Let r be h(0). Let 5*a**4 + 101*a**3 - 50*a**3 - q*a**3 - 5*a - r*a**2 = 0. Calculate a.
-1, 0, 1
Determine u, given that -63/2*u**3 - 24*u**2 - 3/2*u**4 + 120 + 126*u = 0.
-20, -2, -1, 2
Let o(h) be the first derivative of h**4/20 + 41*h**3/15 + 19*h**2/5 - 16*h - 1965. Determine f so that o(f) = 0.
-40, -2, 1
What is d in 5/2*d**2 - 4*d**4 + 25/4*d**3 - 3/8*d**5 - 47/8*d + 3/2 = 0?
-12, -1, 1/3, 1
Let u = -24/2033 + 4234/14231. Suppose u*o - 16/7 + 16/7*o**2 - 2/7*o**3 = 0. Calculate o.
-1, 1, 8
Let c(k) = -k**2 - 14*k - 7. Let x(i) = 3*i. Let g = -42 + 36. Let a(b) = g*x(b) - 3*c(b). Let a(w) = 0. What is w?
-7, -1
Suppose 0 = -4*c + 24 + 12. Suppose 6 - 3 = m - 5*g, 3*m + g = c. Let -510*j + 5*j**5 + 3*j**4 - 2*j**m + 510*j = 0. Calculate j.
-1, 0, 2/5
Let x = -28 + 39. Suppose -79 - x = -10*n. Factor 31 - 4*h - 24*h + n + 4*h**2.
4*(h - 5)*(h - 2)
Let 18*n + 1/2*n**2 + 99/2 = 0. What is n?
-33, -3
Let x(d) be the second derivative of d**7/5040 - d**6/36 + 5*d**5/3 - d**4/6 - 5*d**2/2 - 45*d. Let t(p) be the third derivative of x(p). Factor t(n).
(n - 20)**2/2
Let 5067 - 5*d**3 - 1893*d**2 + 213*d**2 + 3375*d - 1618 - 3213 - 1926 = 0. Calculate d.
-338, 1
Let o(j) be the third derivative of 0*j - 2 + 40*j**2 + 19/96*j**4 + 1/240*j**5 - 5/6*j**3. Factor o(k).
(k - 1)*(k + 20)/4
Let u(w) be the second derivative of 3*w**5/100 + 151*w**4/20 + 6059*w**3/10 + 15987*w**2/2 - 1463*w. Solve u(a) = 0.
-73, -5
Suppose -43*m + 40*m + 639 = 0. Factor 2*x**2 - 4*x**2 + 191*x - m*x.
-2*x*(x + 11)
Suppose 0 = -10*p + 77 + 93. Factor 8 - p*d - 12*d - 5*d + 8*d**2.
2*(d - 4)*(4*d - 1)
Suppose 287*d + 19008 = 2522*d + 855*d + 78*d. Find l such that 0 - d*l**2 + 13/2*l - 1/2*l**3 = 0.
-13, 0, 1
Let p(h) = -24*h + 36. Let k be p(1). Suppose -s + 10 = l + l, l - 3*s = k. Let -40/17*x**2 - 36/17 + l*x - 50/17*x**3 = 0. What is x?
-2, 3/5
Suppose 3*j - 3*u = 27, j - 40 = -4*j + 4*u. Suppose j = 2*h - 0. Factor -9*a - 21*a**h + 17 - 17 + 6*a**3 + 3*a + 21*a**4.
3*a*(a - 1)*(a + 1)*(7*a + 2)
Let i be (-4337)/(-26022)*((-1)/3 - -1). Factor -1/3*d**2 - 2/9*d + 0 - i*d**3.
-d*(d + 1)*(d + 2)/9
Let q(g) = -2*g**4 + 2*g**3 + 16*g**2 - 18*g - 12. Let v(o) = o**3 - 2*o**2 - o - 1. Suppose 31*j + 1 = 30*j. Let z(t) = j*q(t) - 6*v(t). Factor z(k).
2*(k - 3)**2*(k + 1)**2
Suppose -1410*q = 209 - 3029. Factor 0*t**3 - 7/4*t**q - 3/2*t + 1/4*t**4 + 0.
t*(t - 3)*(t + 1)*(t + 2)/4
Let -6 - 413 - 927*i - 113 + 12*i**2 + 95*i - 28 = 0. What is i?
-2/3, 70
Let c(t) be the first derivative of 9/20*t**4 + 14/5*t - 9/10*t**2 - 1/25*t**5 - 13/15*t**3 - 218. Suppose c(m) = 0. What is m?
-1, 1, 2, 7
Let w be (-468)/(-27378) + ((-48)/(-27))/4. Let o(m) be the first derivative of 23 + w*m**2 + 1/26*m**4 + 10/39*m**3 + 0*m. What is g in o(g) = 0?
-3, -2, 0
Let q(u) be the first derivative of -u**4/20 + 4*u**3/5 - 18*u**2/5 + 32*u/5 + 4862. Factor q(l).
-(l - 8)*(l - 2)**2/5
Let a = 52 - 28. Let v = 27 - a. Solve 9*z + v*z**2 + 3*z**2 + 1 - 1 - 3*z**3 = 0 for z.
-1, 0, 3
Suppose 0 = -13*o + 8*o - 365. Let l = o + 1057/13. Factor -14/13*i**3 + 54/13*i + l - 18/13*i**2 - 2/13*i**4.
-2*(i - 2)*(i + 3)**3/13
Let k be (-2)/((-1)/(-1) + 40/(-24)). Solve 1 - 26*d - 21 + 0*d**2 + 3*d**2 + k*d**2 = 0 for d.
-2/3, 5
Let z(w) be the first derivative of 0*w**4 + 21/2*w**2 + 1/120*w**6 - 2/3*w**3 + 1/20*w**5 + 0*w + 16. Let t(h) be the second derivative of z(h). Factor t(m).
(m - 1)*(m + 2)**2
Let z(i) = -i**2 - 35*i + 245. Let m(r) = 2*r**2 + 66*r - 491. Let a(x) = -3*m(x) - 5*z(x). Factor a(o).
-(o - 8)*(o + 31)
Let v be (-160)/32 - (-3 - 2). Factor -18*j - 4*j**4 - 61*j**2 - 28*j**3 + 17*j**2 - 2*j + v*j.
-4*j*(j + 1)**2*(j + 5)
Let i(p) be the first derivative of -3*p**5/25 - 357*p**4/20 - 118*p**3/5 + 5062. Factor i(h).
-3*h**2*(h + 1)*(h + 118)/5
Suppose -67 = 3*p - 136. Let f be -4*3/42 - p/(-7). Factor -1031 + 35*l - l**2 - l**2 - f*l**2 + 981.
-5*(l - 5)*(l - 2)
Suppose -h + 53 = 9. Let r = 10 + h. Factor 180*a**2 + r + 56*a**5 - 58*a**5 - 26*a + 22*a**4 - 136*a - 92*a**3.
-2*(a - 3)**3*(a - 1)**2
Let r be 238/85 - (-2)/10. Let h(a) = 2*a**2 - a + 5. Let p = -7 - -11. Let k(o) = -3*o**2 + o - 6. Let q(i) = p*h(i) + r*k(i). Factor q(b).
-(b - 1)*(b + 2)
Let w be 12128/(-1516)*(1 - 33/24). Factor 176/5 + 1592/5*k + 3636/5*k**2 + 162/5*k**w.
2*(k + 22)*(9*k + 2)**2/5
Let m = -112 + 194. Let x = m - 78. Determine z, given that -x - 5*z + 3 - 1 - 3*z**2 = 0.
-1, -2/3
Let r be (-96)/(-528)*11/10. Factor -3/5*t - r*t**2 - 2/5.
-(t + 1)*(t + 2)/5
Suppose 3440/7*r - 44/7*r**4 + 612/7*r**3 + 288/7 + 3048/7*r**2 = 0. What is r?
-2, -1/11, 18
Suppose 272*b + 33 = 273*b + 2*a, -3*b - a = -94. Let t(g) be the first derivative of -b + 2*g - 2*g**2 + 2/3*g**3. Factor t(d).
2*(d - 1)**2
Let x(n) be the first derivat