5*o + 1)/2
Factor 0 + 5*f**4 + 0*f + 48*f**3 + 1/6*f**5 + 144*f**2.
f**2*(f + 6)*(f + 12)**2/6
Let t(i) be the second derivative of i**5/130 + 53*i**4/78 + 56*i**3/3 + 52*i**2 - 2349*i. Suppose t(z) = 0. Calculate z.
-26, -1
Let r(z) = -35 - 2*z**2 + 145*z - 259*z - z**2 + 140*z. Let h(j) = 12*j**2 - 105*j + 141. Let x(u) = -5*h(u) - 21*r(u). Determine g so that x(g) = 0.
2, 5
Let y(o) be the second derivative of 1/27*o**4 - 2 - 1/90*o**5 + 0*o**2 + 2*o + 1/9*o**3. Determine b so that y(b) = 0.
-1, 0, 3
Let x(z) be the second derivative of 164*z + 7/2*z**2 + 0 - 4/3*z**3 + 1/12*z**4. Suppose x(k) = 0. Calculate k.
1, 7
Let z(g) = -30*g**2 - 111*g + 16. Suppose 14*j - 50 = 4*j. Let u(w) = -45*w**2 - 167*w + 24. Let a(t) = j*u(t) - 7*z(t). Factor a(d).
-(d + 4)*(15*d - 2)
Let a(y) = -27*y + 1386. Let n be a(51). Let q(g) be the second derivative of 11/3*g**3 + 0 - 2/3*g**4 - n*g + 3*g**2. Factor q(t).
-2*(t - 3)*(4*t + 1)
Let d be (-2 - -1)*(-51)/((-2142)/(-28)). Factor 2/3*s**2 - 4/3*s + d.
2*(s - 1)**2/3
Suppose -2/5*v**2 + 144/5*v - 2304/5 = 0. Calculate v.
24, 48
Let r(g) = -158*g - 626. Suppose -24 = 3*i - 4*s, -4*i = 9*s - 6*s + 7. Let b be r(i). Let 3/2*o**5 + 12*o**2 - 3*o**4 + 0*o + 0 - b*o**3 = 0. What is o?
-2, 0, 2
Let i(w) = w**2 + 246*w + 15131. Let m be i(-123). Factor 4*d + 1/5*d**m - 21/5.
(d - 1)*(d + 21)/5
Factor -20*j - 104/3 - 1/6*j**3 - 7/2*j**2.
-(j + 4)**2*(j + 13)/6
Let z(t) be the first derivative of -2*t**6/135 - t**5/9 + t**4/27 + 10*t**3/27 - 39*t - 17. Let j(a) be the first derivative of z(a). Factor j(f).
-4*f*(f - 1)*(f + 1)*(f + 5)/9
Factor -549*i**2 + 606*i**3 - 602*i**3 - 7*i**2.
4*i**2*(i - 139)
Let h(s) = -s**4 - 4*s**3 + 3*s**2 + 63*s + 3. Let x(c) = 6*c**4 + 25*c**3 - 20*c**2 - 378*c - 17. Let o(n) = -34*h(n) - 6*x(n). Factor o(a).
-2*a*(a - 3)*(a + 3)*(a + 7)
Let o = -209738/9 - -69916/3. Determine p so that 0 - 4*p + 2/9*p**5 + 2/9*p**3 + 14/3*p**2 - o*p**4 = 0.
-2, 0, 1, 3
Let v = -370 + 373. Let 112*j**3 - 20 + 136*j**2 - 60 + 5*j**4 - 235*j - 177*j**v - 361*j**2 = 0. Calculate j.
-1, 16
Let a(z) be the second derivative of -5*z**4/36 + 2083*z**3/18 + 139*z**2 + 542*z + 3. Solve a(d) = 0 for d.
-2/5, 417
Let m(k) be the third derivative of -1/210*k**5 + 8*k**2 - 4/7*k**3 + 5*k - 13/84*k**4 + 0. Find z, given that m(z) = 0.
-12, -1
Let c(a) be the third derivative of 7/3*a**3 - 11*a**2 + 0*a + 0 - 3/8*a**4 + 1/60*a**5. Solve c(w) = 0 for w.
2, 7
Let t(y) be the first derivative of -12*y**3 + 28*y**2 - 27 - 1/5*y**5 + 5/2*y**4 - 32*y. Find p, given that t(p) = 0.
2, 4
Let q(j) = -50*j**2 + 10. Let y = -1353 + 1367. Let b(h) be the second derivative of -25*h**4/2 + 31*h**2/2 - h. Let c(f) = y*q(f) - 4*b(f). Factor c(t).
-4*(5*t - 2)*(5*t + 2)
Suppose 6 - 22 = -8*q. Suppose 5*m**4 + q*m + 5 - 5 + 2*m**5 - 8*m**2 + 34*m**3 + 4 - 38*m**3 - m**4 = 0. Calculate m.
-2, -1, 1
Let d(j) = -3*j**2 - 3*j - 146. Let y(o) = 26*o**2 + 23*o + 1166. Let q(n) = 17*d(n) + 2*y(n). Factor q(m).
(m - 15)*(m + 10)
Let z(w) be the second derivative of w**9/1008 - w**8/140 + w**7/70 - 2*w**3 + 35*w. Let g(m) be the second derivative of z(m). Determine r so that g(r) = 0.
0, 2
Factor 1/4*n**5 + 0*n**2 - 114*n**3 - 113/2*n**4 + 0*n + 0.
n**3*(n - 228)*(n + 2)/4
Find y such that -129/5*y**3 - 168/5*y + 48/5 + 219/5*y**2 - 3/5*y**5 + 33/5*y**4 = 0.
1, 4
Let s(z) be the third derivative of z**5/30 - 263*z**4/12 + 262*z**3/3 - 799*z**2. Factor s(g).
2*(g - 262)*(g - 1)
Let b(u) be the second derivative of 3*u**5/20 + 151*u**4/4 + 591*u**3/2 + 1323*u**2/2 - 2*u - 106. Factor b(k).
3*(k + 1)*(k + 3)*(k + 147)
Let j be 1/4*-3*(24 + -36). Factor -5*v**3 - j*v**2 + v**3 + v**2.
-4*v**2*(v + 2)
Let g = -460367/36 - -51167/4. Factor 4 + g*b - 2/9*b**2.
-2*(b - 18)*(b + 1)/9
What is o in -2731 - 895 + 11*o**2 + 1486*o + 674 - 6*o - 13*o**2 = 0?
2, 738
Let -222*i**2 + 1112/3*i - 2/3*i**4 + 76/3*i**3 - 520/3 = 0. What is i?
1, 10, 26
Let l(d) = -d**5 + 14*d**4 + 4*d**3 + 6*d**2 - 5*d + 11. Let y(k) = -3*k**4 - k**3 - k**2 + k - 2. Suppose -5 = r + 6. Let m(z) = r*y(z) - 2*l(z). Factor m(i).
i*(i + 1)**3*(2*i - 1)
Let r(g) = g - 19. Let c be r(23). Factor 25*j**4 - 53*j**4 + 2*j**5 - j**5 + 29*j**c.
j**4*(j + 1)
Let z = -64 - -66. Suppose 0 = -3*s + 2*x - 3*x + 4, -z*x + 5 = 5*s. Factor 26*l**2 - l**5 - 12*l**3 - 18*l**2 - 18*l**2 - s*l - 6*l**4.
-l*(l + 1)**3*(l + 3)
Let p be -3 + 3/(9/(-6))*182/(-84). Let r(v) be the first derivative of -10/9*v**3 + 17 + 8/9*v - 2/9*v**4 - p*v**2. Factor r(d).
-2*(d + 2)**2*(4*d - 1)/9
Suppose -2 = 3*r + 2*b - 0*b, 0 = 5*r - 4*b - 4. Let p = 9320/189 - 1316/27. Determine f so that 6/7*f**3 + 1/7*f + r + p*f**4 + 4/7*f**2 + 1/7*f**5 = 0.
-1, 0
Let q be 64 - (-6)/(-4)*2. Let i = -59 + q. Solve 4*h + 27 - 18 - 3*h**2 + 0*h**2 + i*h = 0.
-1, 3
Let k = 50462/220465 - 2/6299. Let v(a) be the first derivative of 5/14*a**4 + 1/21*a**6 + 16 - k*a**5 + 0*a - 4/21*a**3 + 0*a**2. Suppose v(i) = 0. What is i?
0, 1, 2
Let m(v) be the second derivative of 1/16*v**3 - 1/96*v**4 + 0 - 3/160*v**5 - 89*v + 1/16*v**2. Factor m(z).
-(z - 1)*(z + 1)*(3*z + 1)/8
Let r(k) be the first derivative of -12/7*k - 1/14*k**4 - 4/7*k**3 - 11/7*k**2 + 17. Factor r(i).
-2*(i + 1)*(i + 2)*(i + 3)/7
Let g(l) = 13*l**2 + 281*l + 268. Let v(u) = -28*u**2 - 597*u - 536. Let x(t) = 13*g(t) + 6*v(t). Factor x(j).
(j + 4)*(j + 67)
Let f(y) = 5*y - 147. Let b be f(33). Let r be (9/6)/(b/28). Factor 0 + 5/3*z**3 + r*z**2 + z + 1/3*z**4.
z*(z + 1)**2*(z + 3)/3
Let h(q) be the third derivative of -5*q**8/112 - 19*q**7/70 + 9*q**6/40 + 19*q**5/20 - q**4/2 + 154*q**2 - 2*q + 6. Determine u, given that h(u) = 0.
-4, -1, 0, 1/5, 1
Let z(j) be the third derivative of -1/2*j**5 + 0 - 143*j**2 - 1/42*j**7 + 0*j**3 - 5/24*j**6 + 0*j + 0*j**4. Let z(y) = 0. Calculate y.
-3, -2, 0
Let g(j) be the second derivative of -j**6/6 + 18*j**5 - 540*j**4 - 1307*j. Find k such that g(k) = 0.
0, 36
Let r = -41/644 - -101/322. Factor r*d + 0*d**2 + 0 - 1/4*d**3.
-d*(d - 1)*(d + 1)/4
Let c = -66 + 71. Factor -1 + 16*w**2 + c*w - 9*w**2 - 10*w - w.
(w - 1)*(7*w + 1)
Let a = -8 - -3. Suppose 3*f = 3*s, -4*f - s - 12 = -2*s. Let g(d) = -d**2 + 4*d. Let z(b) = b**2 - 3*b. Let u(k) = a*z(k) + f*g(k). Factor u(p).
-p*(p + 1)
Suppose -720/11 - 6*t**2 - 516/11*t = 0. Calculate t.
-6, -20/11
Suppose -4*g - 117 = -13*g. Factor -2*j**4 - 3 + 30*j**3 + 106*j**5 + 15*j - g*j**4 - 103*j**5 - 30*j**2.
3*(j - 1)**5
Let 2 + 2/9*a**2 + 4/3*a = 0. Calculate a.
-3
Let k(n) be the first derivative of 35*n**4/4 + 710*n**3/3 + 1570*n**2 + 840*n - 4976. Factor k(i).
5*(i + 6)*(i + 14)*(7*i + 2)
What is m in -21/5*m**3 + 69/5*m**2 + 0 - 54/5*m = 0?
0, 9/7, 2
Let -648/7*q + 328/7*q**3 - 316/7*q**2 + 0 - 4/7*q**4 = 0. What is q?
-1, 0, 2, 81
Let z(y) = -9*y**3 + 37521*y**2 - 17671980*y - 17709598. Let v(d) = 2*d**3 - 7506*d**2 + 3534396*d + 3541920. Let t(j) = -11*v(j) - 2*z(j). Factor t(m).
-4*(m - 941)**2*(m + 1)
Let r = -1778 - -1781. Let k(x) be the second derivative of 3/10*x**5 - 1/2*x**r - 1/14*x**7 + 0*x**2 + 7*x + 0*x**4 + 0*x**6 + 0. Factor k(f).
-3*f*(f - 1)**2*(f + 1)**2
Let a(o) be the second derivative of -o**5/120 + 13*o**4/24 + 265*o**3/36 + 75*o**2/4 + 8063*o. Solve a(k) = 0.
-5, -1, 45
Let f be 48/(-108) + (-5)/9. Let j be (f/1)/(80/(-48)). Solve 6/5*c - 3/5*c**2 + 0 - j*c**3 = 0 for c.
-2, 0, 1
Suppose -767*h + 1010 = 396 - 920. Find x, given that -1/3*x**h - 841/3 + 58/3*x = 0.
29
Let w = 41 - 33. Suppose w*s - 10 - 6 = 0. Find c such that -3*c**2 + 10*c**2 - 2 - 5*c**s = 0.
-1, 1
Let z(j) be the second derivative of 0*j**3 - 1/21*j**7 + 0 + 2/15*j**6 + 58*j + 2/5*j**5 + 0*j**2 - 4/3*j**4. Determine r so that z(r) = 0.
-2, 0, 2
Let k(q) be the first derivative of q**4/6 - 5*q**3 + 14*q**2 + 81*q + 80. Let p(i) be the first derivative of k(i). Factor p(s).
2*(s - 14)*(s - 1)
Let b(a) be the first derivative of 3*a**2 + 1/3*a**3 + 8*a - 115. Find v, given that b(v) = 0.
-4, -2
Suppose 0 = 8*k - 63 + 55. Let o(i) = 6*i**2 + 3*i - 31. Let a(h) = h**2 - 2*h - 1. Let f(q) = k*o(q) - a(q). Suppose f(b) = 0. What is b?
-3, 2
Let u(s) be the third derivative of s**7/2940 - s**6/105 - s**5/420 + s**4/7 + 19*s**3/3 - 37*s**2. Let b(k) be the first derivative of u(k). Factor b(p).
2*(p - 12)*