, 12
Let h(w) = -15*w**2 - 540*w - 1111. Let l(o) = 10*o**2 + 360*o + 745. Let r(d) = -5*h(d) - 7*l(d). Determine k, given that r(k) = 0.
-34, -2
Let z(l) be the first derivative of -l**3 - 1347*l**2 - 604803*l - 355. Find x such that z(x) = 0.
-449
Let s(n) = -n**3 - n**2 - 3*n + 1. Let w(l) = -4*l**3 - l**2 - 46*l + 12. Let z(c) = 60*s(c) - 5*w(c). Find r such that z(r) = 0.
-2, 0, 5/8
Let n(g) be the third derivative of -8/5*g**5 - 1/21*g**8 + 0*g**4 + 6/35*g**7 + 0*g + 1 + 0*g**3 + 47/15*g**6 + 57*g**2. Suppose n(l) = 0. What is l?
-4, 0, 1/4, 6
Let l(t) be the first derivative of 10*t**6/9 - 1628*t**5/45 - 122*t**4/3 + 224*t**3/27 + 5418. Let l(q) = 0. Calculate q.
-1, 0, 2/15, 28
Factor -42/17*d + 2/17*d**2 - 44/17.
2*(d - 22)*(d + 1)/17
Suppose -9126/11 - 106/11*g**2 + 1742/11*g + 2/11*g**3 = 0. What is g?
13, 27
Factor 0*g**2 - 2/7*g**4 + 0*g**3 - 2/7*g**5 + 0*g + 0.
-2*g**4*(g + 1)/7
Factor -6*d**3 + 0*d + 0 + 0*d**2 - 1/4*d**4.
-d**3*(d + 24)/4
Let -2/9*d**3 + 130/9*d - 28 + 124/9*d**2 = 0. Calculate d.
-2, 1, 63
Suppose 2/13*p**3 + 67830*p - 884450/13 + 2658/13*p**2 = 0. What is p?
-665, 1
Let l(u) be the first derivative of u**4/36 + 2*u**3/9 - 5*u**2/6 - 43*u + 35. Let y(s) be the first derivative of l(s). Solve y(k) = 0.
-5, 1
Factor 49*q**2 - q**5 + 5*q**5 - 24764*q**3 - 12*q + 24713*q**3.
q*(q - 3)*(q + 4)*(2*q - 1)**2
Let i be 4/(-209)*(3185/(-98) - -23). Let -24/11*j - 16/11*j**2 + 2/11*j**4 + i*j**3 + 0 = 0. What is j?
-2, 0, 3
Suppose 37*r = 35*r - 4*x - 8, 2*x = 0. Let t(b) = -3*b**2 - 22*b - 23. Let p(v) = -v - 2. Let z(g) = r*p(g) + t(g). Determine a, given that z(a) = 0.
-5, -1
Let c be (-12)/9 - (-4 + (-812)/(-21)). Let n be 48/(-27) + (-72)/c. Factor -4/3*h - 16/9 - n*h**2.
-2*(h + 2)*(h + 4)/9
Solve -1040*w + 2*w**3 + 25707*w**2 - 25742*w**2 - 1900 + 3*w**3 = 0 for w.
-10, -2, 19
Let v = 178/2455 + 65573/9820. Factor v*t**3 + 3/4*t**4 + 15/2 + 75/4*t**2 + 81/4*t.
3*(t + 1)**2*(t + 2)*(t + 5)/4
Let k be -10*(2/8 + 87/(-116)). Let m(l) be the second derivative of 0*l**2 + 0 + 1/4*l**k + 1/9*l**4 - 2/9*l**3 - 17*l. Find f, given that m(f) = 0.
-2/3, 0, 2/5
Let a(d) = -d**3 + 5*d**2 - 2*d - 5. Let z be a(4). Let w be (-25)/(-50)*(-52)/(-13). Suppose -j - 1/7*j**z - 5/7*j**w - 3/7 = 0. What is j?
-3, -1
Suppose 3*p = 2*t - 1, -5*t + 70 - 10 = 4*p. Factor 4/3*w**4 + 2/9*w**p + 20/9*w**2 + 8/3*w**3 + 0 + 2/3*w.
2*w*(w + 1)**3*(w + 3)/9
Let d(l) be the second derivative of l**4/84 - 16*l**3/21 - 39*l**2/2 - 215*l - 8. Let d(x) = 0. Calculate x.
-7, 39
Let r(n) be the first derivative of -11*n**3/6 + 351*n**2/4 + 16*n + 669. What is m in r(m) = 0?
-1/11, 32
Let c(w) be the second derivative of -w**6/6 + 5*w**5/4 + 35*w**4/12 - 25*w**3/6 - 15*w**2 - 2*w + 12. Determine m, given that c(m) = 0.
-1, 1, 6
Suppose -199 = -10*d + 151. Solve -8 + 15*r**4 - 13*r**2 + d*r**3 - 2 - 35*r + 0 + 8*r**2 = 0.
-2, -1, -1/3, 1
Let u(a) = 3*a**3 + 4*a**2 - 10*a + 2. Let n be u(4). Suppose -9*s + 259 = -n. Solve -s + 26 + 27 + l**4 + 8*l**3 + 16*l**2 = 0 for l.
-4, 0
Let s be (-21)/(-12)*19/((-931)/(-49)). Factor -3/2 - 1/2*y**3 - s*y + 9/4*y**2.
-(y - 3)*(y - 2)*(2*y + 1)/4
Suppose 5*o + 1936 = 2*c - 6*c, 4*o = 3*c - 1555. Let i = o - -391. Factor 0 + 2/3*b**i + 4/3*b**2 + 2/3*b.
2*b*(b + 1)**2/3
Let u(k) = 2*k**2 + 8*k + 2. Let y be u(-4). Let g be (19 + -38 - -16) + (-63)/(-13). Factor -g*z - 2/13*z**3 + 16/13 + 12/13*z**y.
-2*(z - 2)**3/13
Let o(b) be the third derivative of -b**5/510 - 115*b**4/34 - 39675*b**3/17 + b**2 + 94*b. Factor o(f).
-2*(f + 345)**2/17
Find r, given that 96/7 - 20/7*r**4 + 184/7*r + 2/7*r**5 - 54/7*r**3 + 8*r**2 = 0.
-2, -1, 2, 12
Let b(a) be the second derivative of 222/5*a**6 + 0*a**2 + 3*a - 2 + 39*a**5 - 2*a**3 + 19/3*a**4. Factor b(p).
4*p*(3*p + 1)**2*(37*p - 3)
Let i(d) be the second derivative of -1/450*d**5 + 0 - 37/2*d**2 + 21*d + 0*d**3 + 1/180*d**4. Let a(f) be the first derivative of i(f). Factor a(c).
-2*c*(c - 1)/15
Let w(m) be the first derivative of 5/4*m**4 + 0*m - 5/3*m**3 + 0*m**2 + 121. What is d in w(d) = 0?
0, 1
Let v(c) be the first derivative of -5*c**6/3 + 31*c**5/10 + 13*c**4/8 - 35*c**3/6 + 7*c**2/4 + 2*c + 3003. Let v(r) = 0. Calculate r.
-1, -1/4, 4/5, 1
Let n(o) be the first derivative of o**4/9 - 16*o**3/9 + 14*o**2/3 + 18*o + 70. Let d(r) be the first derivative of n(r). Factor d(t).
4*(t - 7)*(t - 1)/3
Let v(f) be the first derivative of 2*f**7/105 - 7*f**6/30 + 4*f**5/5 - 287*f**2/2 - 29. Let s(x) be the second derivative of v(x). Find r such that s(r) = 0.
0, 3, 4
Factor -150 + 24*x + 1/6*x**2.
(x - 6)*(x + 150)/6
Suppose 330*j - 91*j + 164*j - 1209 = 0. Determine d so that -10/3*d**j + 0*d**2 + 0*d + 35/3*d**4 - 25/3*d**5 + 0 = 0.
0, 2/5, 1
Let h(v) = v**4 + 2*v**3 + v**2 - 1. Let i(z) = -119*z**3 + 994*z - 5*z**4 + 1317*z**2 - 10255*z + 44*z**3 + 6. Let r(g) = -6*h(g) - i(g). Factor r(f).
-f*(f - 21)**3
Let m = 156321 - 156319. Suppose -4/5*g - 3/5 - 1/5*g**m = 0. Calculate g.
-3, -1
Let g(p) = 10*p**3 - 100*p**2 + 107*p - 104. Let x(d) = -31*d**3 + 298*d**2 - 330*d + 311. Let j(y) = 17*g(y) + 6*x(y). Factor j(o).
-(o - 2)*(4*o - 7)**2
Let o(j) = -j**2 + 14*j - 12. Suppose m + 12 = 3*m. Let b be o(m). Factor -21 - b*n**4 - 25 + 8*n**3 + 28*n**5 + 46.
4*n**3*(n - 1)*(7*n - 2)
Let n be (-1 + 1)*(-1)/3. Solve n*c + 14*c + 4*c**2 + 6*c = 0 for c.
-5, 0
Let u(h) = -19*h**3 + 78*h**2 + 351*h - 425. Let q(z) = 6*z**3 + z**2 - 2*z. Let d(c) = 12*q(c) + 4*u(c). Factor d(p).
-4*(p - 85)*(p - 1)*(p + 5)
Let x(q) be the first derivative of 2*q**3/9 + 53*q**2/3 - 152*q - 9242. Suppose x(n) = 0. What is n?
-57, 4
Let m be ((-102)/12 - -10)*(4 - 0). Let l be 10/(-8) - (-8 + m). Factor 0 + 1/4*o**4 + 0*o**3 - l*o**2 + 1/2*o.
o*(o - 1)**2*(o + 2)/4
Let q(l) be the third derivative of -l**6/1620 + l**5/180 - 20*l**3/3 - 102*l**2. Let d(j) be the first derivative of q(j). Factor d(z).
-2*z*(z - 3)/9
Let w(u) = -20*u - 154. Let a be w(-11). Let x be (54/81)/(a/(-27) - -3). Factor -8/5*j**3 + 0 + x*j**2 - 1/5*j.
-j*(2*j - 1)*(4*j - 1)/5
Let y(l) = -l**3 + 221*l**2 - 1654*l - 2458. Let i be y(213). Factor 1/4*b**3 + 24*b**2 + 768*b + i.
(b + 32)**3/4
Let p(g) be the first derivative of 20*g**3/3 - 54*g**2 + 40*g - 787. Factor p(t).
4*(t - 5)*(5*t - 2)
Suppose 37*w - 30*w = 693. Let u be (-18)/w - (0 - 35/132). What is k in 0 + 1/12*k**5 - 1/12*k**4 + 1/12*k**2 - u*k**3 + 0*k = 0?
-1, 0, 1
Let a be 4 + 5481/(-1463) + (-3)/(-11). Determine n so that 10/19*n**3 - 6/19*n**2 - a*n + 8/19 - 2/19*n**4 = 0.
-1, 1, 4
Let j(z) be the first derivative of 40 - 20*z - 11*z**2 - 2/3*z**3. Factor j(c).
-2*(c + 1)*(c + 10)
Suppose 982 = -4*w + 5*f + 1020, -3*f = -3*w + 24. Let -2/7*c**5 + 2/7*c**w + 0*c + 2/7*c**3 + 0 - 2/7*c**4 = 0. What is c?
-1, 0, 1
Let o(k) be the second derivative of 13/11*k**2 - 1/66*k**4 + 30*k + 0 + 4/11*k**3. Solve o(c) = 0 for c.
-1, 13
Suppose 22*d = 17*d + 145. Suppose -d*z = -28*z - 4. Factor -z*b**3 - 578 + 578 + 40*b**2.
-4*b**2*(b - 10)
Let a(u) = -u**2 + 20*u + 15. Let g be a(19). Factor 179*r**3 - 174*r**3 - 40 - 16*r**2 - g*r**2 + 85*r.
5*(r - 8)*(r - 1)**2
Suppose -4*q = 16, 4*w + w + 3*q = -2. Let b(l) be the third derivative of -13/16*l**4 + 0*l + 0 + 3/2*l**3 - 20*l**w - 1/8*l**5. Suppose b(y) = 0. What is y?
-3, 2/5
Determine v so that 7/3*v**3 + 1 + 1/3*v - 11/3*v**2 = 0.
-3/7, 1
Let i(o) = 2*o + 1. Let k be i(1). Suppose k*h - 9 = 2*n, 3*n - 7 = 4*n - 2*h. Suppose -7*a + 3*a - n*a**2 - 32 + a**2 + 20*a = 0. Calculate a.
4
Factor -9/2*j - 1/4*j**3 - 9/4*j**2 + 0.
-j*(j + 3)*(j + 6)/4
Let y = 707 + -675. Suppose 8*o = -y + 64. Let 1/2*n**3 - 1/2*n + 0*n**2 - 1/4 + 1/4*n**o = 0. What is n?
-1, 1
Let r(c) be the first derivative of -40/3*c**3 + 5/8*c**6 - 20*c**2 + 0*c + 27 + 95/8*c**4 + 23/4*c**5. What is g in r(g) = 0?
-4, -2/3, 0, 1
Let y(k) be the first derivative of 2*k**3/9 - k**2/6 - 7994. Determine g, given that y(g) = 0.
0, 1/2
Let s be 41/((-1025)/30) + 5396/1330. Let -16/7 - 4/7*v**3 - s*v**2 - 32/7*v = 0. What is v?
-2, -1
Let t(r) = 3*r + 24. Let n be t(-9). Let x be (-20)/6*n/5. Determine i so that x*i - 29*i**4 + 3*i**3 + 28*i**4 - 5*i**2 + i**3 = 0.
0, 1, 2
Let c(r) be the second derivative of 74 - 2883/2*r**2 - 2*r + 31*r**3 - 1/4*r**4. Suppose c(k) = 0. W