- 615*r - 1275. Let f(k) = 11*i(k) - 2*j(k). Suppose f(p) = 0. Calculate p.
-5, -3, 17
Let r(j) = -57*j**2 + 1932*j. Let k(s) = -7*s**2 + 241*s. Let q(z) = -33*k(z) + 4*r(z). Factor q(h).
3*h*(h - 75)
Let w(r) be the third derivative of r**8/80640 - r**6/180 + r**5/15 + r**4/3 - 37*r**2 + r. Let v(j) be the third derivative of w(j). Let v(z) = 0. Calculate z.
-4, 4
Factor 625*t + 164 + 110*t**2 + 5*t**3 + 91 + 265.
5*(t + 1)*(t + 8)*(t + 13)
Let n(h) = 7*h**2 - 2332*h + 257643. Let y(k) = -k**2 + 31*k + 1. Let c(l) = n(l) + 2*y(l). Factor c(m).
5*(m - 227)**2
Let u(h) = 2714*h - 168264. Let m be u(62). Suppose 3/2*x**m + 0*x + 27/4*x**3 + 0 - 15/4*x**2 = 0. What is x?
-5, 0, 1/2
Let l(n) be the first derivative of -8/5*n**2 - 85 + 3/10*n**4 + 8/25*n**5 - 4/3*n**3 - 1/15*n**6 + 0*n. Solve l(j) = 0 for j.
-1, 0, 2, 4
Suppose 3*n + 0*l = -l + 21, 4*n - 5*l = 9. Find t such that 3*t**2 + 3*t**3 + n*t**2 - 8*t - 12*t**4 + 7*t**2 + 5*t**3 - 4 = 0.
-1, -1/3, 1
Let z(x) = 2*x**2 + 1. Let j be z(-5). Suppose -j*a = -46*a - 20. Solve -2 + 5*d**3 - 8*d**a + 9*d**4 + 7*d - 9*d**2 - 2*d**4 = 0 for d.
1, 2
Let q(y) be the second derivative of -11/80*y**5 + 25/6*y**3 + 1/168*y**7 + 0 + 1/20*y**6 - 5/4*y**4 + 24*y + 0*y**2. Factor q(c).
c*(c - 2)**2*(c + 5)**2/4
Let f = -39251 - -39251. Suppose 1/2*q + 0 + f*q**2 - 1/2*q**3 = 0. Calculate q.
-1, 0, 1
Let a(g) be the first derivative of 64/13*g + 6 + 160/39*g**3 - 1/39*g**6 - 80/13*g**2 - 20/13*g**4 + 4/13*g**5. Factor a(b).
-2*(b - 2)**5/13
Suppose f - 23*a + 7 = -25*a, -f + 29 = -4*a. Factor -3/2*o**3 - 1/2*o**f + 0*o - 5/2*o**4 + 0 + 9/2*o**2.
-o**2*(o - 1)*(o + 3)**2/2
Let u(t) be the third derivative of t**7/105 + 37*t**6/60 + 33*t**5/5 + 95*t**4/3 + 248*t**3/3 + t**2 - 22. Factor u(q).
2*(q + 2)**3*(q + 31)
Let u be (-362 + 376)/((-70)/(-36)). Factor -32/5*p - u + 4/5*p**2.
4*(p - 9)*(p + 1)/5
Let l(g) be the second derivative of g**6/150 + g**5/20 - 163*g**4/60 + 667*g**3/30 - 51*g**2 + 13*g + 57. Solve l(q) = 0.
-17, 1, 5, 6
Let j(r) be the first derivative of -r**4/12 - r**3/6 + r**2 + 137*r - 159. Let b(h) be the first derivative of j(h). Determine o, given that b(o) = 0.
-2, 1
Let g be (-94)/(-1) + 174/(-18) + 9. Let n = -467/6 + g. Suppose 3 + 3/2*m**4 + 23/2*m + 17/2*m**3 + n*m**2 = 0. What is m?
-3, -1, -2/3
Suppose 4495*q - 4584*q = -178. Let -52/5*r - 24/5 - 4*r**q = 0. What is r?
-2, -3/5
Find x, given that -348*x**4 - 98*x + 206*x - 456*x**3 - 20*x**5 - 128*x**2 - 108*x = 0.
-16, -1, -2/5, 0
Let j(z) = -35*z**2 - 15*z + 20. Let v be (13 - 43)*6/(-9). Let f(g) = 5*g**2 + 2*g - 3. Let m(r) = v*f(r) + 3*j(r). Factor m(p).
-5*p*(p + 1)
Let l(p) be the third derivative of 0 + 0*p + 1/21*p**4 - 108*p**2 - 1/105*p**5 + 2/7*p**3. Factor l(k).
-4*(k - 3)*(k + 1)/7
Let b be -160*79/(88480/(-64)). Suppose -36/7*i**3 + 2/7*i**5 + 12/7 + 4/7*i**4 + b*i**2 - 46/7*i = 0. Calculate i.
-6, 1
Let h(n) be the third derivative of -2*n**2 + 1/10*n**6 + 14/3*n**4 + 8*n**3 + 5 + 0*n + 17/15*n**5. Factor h(j).
4*(j + 2)*(j + 3)*(3*j + 2)
Let c = 46666 + -46666. Solve -2/9*j**5 + c - 2/3*j**4 - 2/9*j**2 - 2/3*j**3 + 0*j = 0.
-1, 0
Factor 56*f + 281/5 - 1/5*f**2.
-(f - 281)*(f + 1)/5
Let z(n) = -n - 2. Let s be z(-6). Let y be (-21 + (-8 - -13))*(-1)/2 - 6. Find v, given that s*v**2 - 3*v - y*v - v**2 + 3*v = 0.
0, 2/3
Suppose -5 = -286*v + 281*v. Determine p, given that 2*p**3 - v + 19*p**2 + 14*p - 9*p**2 + 0*p**3 + 7 = 0.
-3, -1
Suppose -6 = -4*m - 118. Let l = -21 - m. Factor -5*x + 11*x**2 + l*x - 4 - 9*x**2.
2*(x - 1)*(x + 2)
Let i be ((-21)/(945/(-18)))/((-11)/5 - -4). Factor 0 - 2/9*z + i*z**2.
2*z*(z - 1)/9
Let o = -557 - -575. Determine s, given that -o*s**2 - 17*s + 113*s + 4381*s**3 - 3*s**4 + 96 - 4402*s**3 = 0.
-4, -1, 2
Let 4040/7 - 2/7*j**2 - 288*j = 0. What is j?
-1010, 2
Let g(b) be the second derivative of -6*b + 1/8*b**4 + 93/4*b**2 - 7 + 8*b**3. Factor g(t).
3*(t + 1)*(t + 31)/2
Let o(y) be the third derivative of -y**6/840 + y**5/140 + 2*y**4/21 + 2*y**3/7 + 24*y**2 - 4*y. Factor o(v).
-(v - 6)*(v + 1)*(v + 2)/7
Solve 86/15*x + 2 - 14/15*x**2 - 2/5*x**3 = 0.
-5, -1/3, 3
Let k(r) be the second derivative of 5/2*r**3 + 3*r + 1 - 3/20*r**5 + 1/10*r**6 - 3/4*r**4 - 3*r**2. Factor k(o).
3*(o - 1)**3*(o + 2)
Suppose -787 + 138*k**2 - 74*k - 944*k - 532 + 391 - 230*k**2 - 2*k**3 = 0. What is k?
-29, -16, -1
Let p(z) = z**3 + 14*z**2 - 19*z - 27. Let i be p(-17). Let j = -501 - i. Suppose -j*a**4 - 40/3*a**2 + 0*a - 64*a**3 + 50/3*a**5 + 0 = 0. Calculate a.
-2/5, 0, 5
Let z(s) be the second derivative of 7*s**6/135 - 29*s**5/90 + 11*s**4/54 + 41*s**3/27 - 2*s**2/3 - 8698*s. Suppose z(c) = 0. Calculate c.
-1, 1/7, 2, 3
Let p = -1 - -3. Let -l**4 + 1024 + 14*l - 144*l**p - 22*l**3 - 54*l - 88*l = 0. What is l?
-8, 2
Let g(p) = -1 - 10*p + 3*p + p**2 - 3*p**3 + 3*p + 5*p. Let s be g(-1). Solve 3*k + 6*k**2 - 8 - 2*k**3 - s*k - k = 0 for k.
-1, 2
Let j(v) be the first derivative of -44/15*v**3 + 12/5*v**4 + 36 + 7/5*v**2 - 4/5*v**5 + 1/15*v**6 + 0*v. Determine k, given that j(k) = 0.
0, 1, 7
Solve -2000 + 13/2*m**5 + 2372*m**3 - 10760*m**2 + 14600*m - 209*m**4 = 0 for m.
2/13, 2, 10
Let l be (1 - 4/8)/((-2)/24). Let j be l/(6 - 3)*-1. Solve 0 + 2/3*o - 1/6*o**j = 0 for o.
0, 4
Let l = 75933 + -75933. Solve 1/2*w**3 + 2 + l*w - 3/2*w**2 = 0 for w.
-1, 2
Let s = 4611/91820 + -1/4591. Let r(v) be the first derivative of -1/25*v**5 + 0*v - 10 - s*v**4 + 4/15*v**3 + 2/5*v**2. Factor r(z).
-z*(z - 2)*(z + 1)*(z + 2)/5
Determine s, given that -35*s**4 - 14666*s**5 + 14662*s**5 + 352*s**2 - 17*s**4 + 960 - 96*s**3 + 1216*s = 0.
-10, -2, 3
Let i = 8257 + -8255. Let t(d) be the second derivative of -1/2*d**4 - 22*d - 9/2*d**i + 0 + 7/2*d**3. Factor t(b).
-3*(b - 3)*(2*b - 1)
Let n(r) = -r**4 - r**3 + r**2. Let v(i) = 8*i**4 - 2*i**3 - 153*i**2 + 160*i + 800. Let d(u) = -3*n(u) - v(u). Factor d(w).
-5*(w - 4)**2*(w + 2)*(w + 5)
Let s be 32/(960/1410) - -74. Factor -s - 55/3*k - 1/3*k**3 + 19/3*k**2.
-(k - 11)**2*(k + 3)/3
Let z be 4671645/(-1373675) + (-4*1)/(-1). Let m = 2/2389 + z. Suppose 0 + 0*x**4 + 3/5*x**3 - m*x**5 + 0*x + 0*x**2 = 0. Calculate x.
-1, 0, 1
Let j be (-1722)/4 + (-3 - (-12)/2). Let z = 430 + j. Suppose -z*n**2 - 1/6*n**4 + 0 - 7/6*n**3 - 3/2*n = 0. Calculate n.
-3, -1, 0
Let s(j) be the first derivative of j**4/10 + 526*j**3/15 + 3267*j**2 - 51030*j + 13174. Determine l so that s(l) = 0.
-135, 7
Let s be -9 + ((30 - 6)/(-12) - -16). Factor 0 - 3*f**2 - 13/4*f**4 + 1/4*f**s + 23/2*f**3 - 18*f.
f*(f - 6)**2*(f - 2)*(f + 1)/4
Let m(i) be the first derivative of i**5/30 - 4*i**4/3 - 11*i**3/6 - 4293. Factor m(l).
l**2*(l - 33)*(l + 1)/6
Let r = -131 + 137. Find q such that 14*q**5 + 13*q**5 - 29*q**5 + r*q**3 + 4*q**4 = 0.
-1, 0, 3
Let z = -9127 + 45647/5. Suppose 12/5 - 9/5*g**2 - 3/5*g**4 - z*g**3 + 12/5*g = 0. What is g?
-2, -1, 1
Let l(w) be the first derivative of w**4 - 14728*w**3 + 81342744*w**2 - 199669322272*w - 2759. Let l(o) = 0. What is o?
3682
Let k(z) be the first derivative of -z**4/28 - 211*z**3/21 + 106*z**2/7 - 662. Factor k(w).
-w*(w - 1)*(w + 212)/7
Let s be (-5)/(-8)*(-646)/(-1615). Suppose -z - 8 = -3*z. What is x in -5/4*x**3 - s + x**z - 3/4*x**2 + 5/4*x = 0?
-1, 1/4, 1
Let z(q) be the first derivative of -116 - 16*q**2 + 80*q - 4/3*q**3. Factor z(h).
-4*(h - 2)*(h + 10)
Let d = -35258783/186 + 189564. Let b = 1/62 + d. Factor -2*t + 4/3 + b*t**2.
2*(t - 2)*(t - 1)/3
Let r(t) be the third derivative of -t**7/630 - t**6/40 - 11*t**5/180 + 7*t**4/24 + 344*t**2 + 2. Factor r(d).
-d*(d - 1)*(d + 3)*(d + 7)/3
Let u(k) be the first derivative of k**4/26 - 742*k**3/39 + 739*k**2/13 - 738*k/13 - 2336. Suppose u(t) = 0. Calculate t.
1, 369
Let t(a) = -a**3 - 6*a**2 - a - 7. Let n be t(-6). Let k be (-6)/(-9)*(5 - n). Factor -4*g**2 - 18*g**4 + 2*g**3 + 33*g**4 - 9*g**k.
2*g**2*(g + 1)*(3*g - 2)
Let u(b) be the first derivative of -2*b**3/9 - 19*b**2 - 108*b - 10909. Find s such that u(s) = 0.
-54, -3
Let x = 30679/2 - 14906. Let y = 438 - x. Factor 3/2*u**2 - y*u + 3.
3*(u - 2)*(u - 1)/2
Let c(w) = -5*w**2 + 5 - 12*w + 5 - 2 - 3*w**2. Let y(f) = -9*f**2 - 11*f + 8. Let q(r) = 5*c(r) - 6*y(r). Determine m so that q(m) = 0.
-1, 4/7
Let g(i) be the first derivative of -5*i**6/6 + 63*i