r).
4*(r - 2)*(r + 10)
Factor -42/5*w**4 + 36*w**3 + 48/5*w - 216/5*w**2 + 0.
-6*w*(w - 2)**2*(7*w - 2)/5
Let f(d) be the third derivative of d**8/1848 + 19*d**7/1155 + 26*d**6/165 + 8*d**5/15 - 2*d**2 - 76*d. Determine n, given that f(n) = 0.
-11, -4, 0
Let g = 24923/20 + -1246. Let z(u) be the third derivative of 11/8*u**4 - g*u**5 - 9*u**2 + 0*u + 0 - 3*u**3. Solve z(t) = 0.
2/3, 3
Let a(w) = -142*w**2 - 853*w - 6. Let m be a(-6). Factor 4/9*h**4 - 4*h + 20/3*h**2 + m - 28/9*h**3.
4*h*(h - 3)**2*(h - 1)/9
Let q = 511 + -507. Let b(n) be the third derivative of 1/1260*n**7 + n**2 + 0 + 0*n**3 + 0*n**6 + 0*n**5 + 0*n**q + 0*n. Suppose b(k) = 0. Calculate k.
0
Let i(l) be the first derivative of -l**3/3 + 3*l**2/2 + 441. Let i(s) = 0. Calculate s.
0, 3
Factor -2*q**3 + q**4 + 24*q**3 + 3*q**4 - 36*q + 60*q**2 - 50*q**3.
4*q*(q - 3)**2*(q - 1)
Let g(h) be the first derivative of -h**4/10 - 2*h**3 - 12*h**2/5 + 56*h/5 - 420. Let g(m) = 0. What is m?
-14, -2, 1
Let p(j) = -14*j + 86. Let v be p(6). Suppose 11*w = -v*w + 52. Solve 0 + 25/4*t**3 + 5*t - 5/4*t**w - 10*t**2 = 0 for t.
0, 1, 2
Suppose 0 = 4*v + 3*m - 5, -v + 3*m - 84 = -104. Suppose -21*j**3 - 24*j**2 - 9*j**4 - 3 - 3/2*j**v - 27/2*j = 0. Calculate j.
-2, -1
Let j(w) = 2*w + 2. Let m be j(0). Suppose -8*c**2 + 4 + 8*c - 3*c**m + 6*c**3 - 3*c**3 = 0. Calculate c.
-1/3, 2
Suppose j = -15 - 3. Let n(o) = -8*o**5 + 3*o**4 + 10*o**3 - 3*o**2 + 7*o. Let m(i) = -i**5 + i**3 + i. Let f(v) = j*m(v) + 2*n(v). Factor f(g).
2*g*(g - 1)*(g + 1)**2*(g + 2)
Let r = -9548/15 - -1910/3. Suppose -8/15*x - 2/5 - r*x**2 = 0. What is x?
-3, -1
Suppose 275*c**2 + c**3 + 171*c + 5670 - 16575 - 8139 + 18597*c = 0. Calculate c.
-138, 1
Let b(r) be the first derivative of 3*r**4/32 + 17*r**3/8 + 21*r**2/8 - 12*r - 272. Factor b(z).
3*(z - 1)*(z + 2)*(z + 16)/8
Let x(q) = 6*q - q - 39 + 5*q**3 + 10*q**2 + 9. Let i(c) = -1. Let u(p) = 30*i(p) - x(p). Factor u(t).
-5*t*(t + 1)**2
Let w(o) = o**3 + 4*o**2 - 11*o + 11. Let m(d) = -d**3 - 5*d**2 + 13*d - 11. Let s(n) = 5*m(n) + 4*w(n). Factor s(k).
-(k - 1)**2*(k + 11)
Let a(o) be the third derivative of 1/42*o**3 + 10*o**2 + 0 + 1/42*o**5 + 1/294*o**7 + 0*o - 1/84*o**6 - 1/2352*o**8 - 5/168*o**4. Determine u so that a(u) = 0.
1
Let u(g) = 18*g**2 - 17*g - 28. Let y(v) = -10*v**2 + 8*v + 14. Let s(j) = 4*u(j) + 7*y(j). Factor s(a).
2*(a - 7)*(a + 1)
Solve -141*c**5 + 5*c**3 - 5*c**3 + 140*c**5 + c**4 = 0.
0, 1
Let v be (-8)/2*3/(-6). Solve -15 - 16*t + 14*t**2 + 5*t**3 + t**v + 11*t = 0.
-3, -1, 1
Let t(w) be the third derivative of -w**9/20160 - w**8/11200 + w**7/700 - w**6/300 + w**5/12 + 3*w**2. Let s(r) be the third derivative of t(r). Solve s(m) = 0.
-2, 2/5, 1
Let h be -1 + (-13)/(-15) + (-846)/(-270). Let j(c) be the first derivative of -9 + 0*c + 1/5*c**5 - 1/2*c**2 + 1/4*c**4 - 1/3*c**h. Let j(y) = 0. What is y?
-1, 0, 1
Let q(t) be the third derivative of t**6/600 - 11*t**5/300 + 7*t**4/24 - 5*t**3/6 - 173*t**2. Factor q(j).
(j - 5)**2*(j - 1)/5
Let n(w) = -9*w**3 - 45*w**2 + 18*w. Let t(f) = -f**3 - 3*f**2 + f. Let x(k) = -n(k) + 12*t(k). Determine o, given that x(o) = 0.
0, 1, 2
Let d(s) be the second derivative of -1/84*s**7 + 0*s**2 + 0 + 0*s**3 - 1/12*s**6 - 9*s - 1/6*s**4 - 1/5*s**5. Factor d(v).
-v**2*(v + 1)*(v + 2)**2/2
Let m be 28/30 - 1644/2740. Factor -1/3*n**3 - n**2 - m - n.
-(n + 1)**3/3
Let k(h) be the second derivative of 0 + 24*h + 1/3*h**3 + 1/14*h**5 - 1/105*h**6 - 2/7*h**2 - 3/14*h**4. Factor k(g).
-2*(g - 2)*(g - 1)**3/7
Let u be (-14)/(-7) - 1/(3/4). Let a(d) be the second derivative of -2/3*d**6 - 4/3*d**4 - 3*d + 0*d**3 + 0*d**2 - u*d**7 + 16/5*d**5 + 0. Solve a(g) = 0.
-2, 0, 2/7, 1
Let n(f) = -36*f**2 - 66*f - 20. Let j(i) = -3*i - 24. Let a be j(-7). Let x(d) = 7*d**2 + 13*d + 4. Let l(z) = a*n(z) - 16*x(z). Factor l(u).
-2*(u + 2)*(2*u + 1)
Let t(n) be the first derivative of 9*n**5/20 - 15*n**4/16 - 5*n**3/2 + 15*n**2/2 - 6*n - 36. Solve t(i) = 0 for i.
-2, 2/3, 1, 2
Factor 1084*r - 81*r**3 - 3*r**4 + 0*r**4 - 504*r**2 - 496*r.
-3*r*(r - 1)*(r + 14)**2
Let q(m) be the second derivative of -m**5/240 + m**4/16 - 3*m**3/8 - 5*m**2 - 12*m. Let a(i) be the first derivative of q(i). Factor a(z).
-(z - 3)**2/4
Let k(o) be the second derivative of o**7/336 + o**6/240 - 41*o**5/160 - o**4/96 + 55*o**3/6 - 25*o**2 - 209*o. Suppose k(v) = 0. What is v?
-5, 1, 4
Suppose -8/7 - 94/7*i**2 - 83/7*i**3 - 25/7*i**5 + 102/7*i**4 + 108/7*i = 0. Calculate i.
-1, 2/25, 1, 2
Let n(p) be the second derivative of -p**4/84 + 25*p**3/42 + 108*p. Factor n(u).
-u*(u - 25)/7
Suppose -i + 5*g = 3*i - 8, -2*i - 3*g = 18. Let k be 6*1/(i - -24). What is m in 0 + k*m**2 + 2/7*m**4 - 4/7*m**3 + 0*m = 0?
0, 1
Suppose 300 = -4*d + 4*k + k, 2*d = 3*k - 150. Let i = -149/2 - d. Determine g, given that 6*g**3 - 15/4*g**2 + i*g + 0 - 11/4*g**4 = 0.
0, 2/11, 1
Factor -4*t + 0*t**3 - 2/3*t**4 + 14/3*t**2 + 0.
-2*t*(t - 2)*(t - 1)*(t + 3)/3
Let u(v) be the third derivative of -v**8/168 - 23*v**7/105 - 7*v**6/10 + v**5/15 + 43*v**4/12 + 7*v**3 - 3*v**2 + 29*v. Determine o, given that u(o) = 0.
-21, -1, 1
Let -15*s - 169*s**2 + 331*s**2 - 167*s**2 + 140 = 0. What is s?
-7, 4
Let f be (288/(-56))/(4/(-14)). Solve 16*g**2 + 2*g**3 + 20*g + f - 10 + 2*g**3 = 0.
-2, -1
Suppose 11*f + 101 = -9. Let q be 34/f - -3 - 4/(-10). Find a, given that -1/3 + 1/3*a**2 + q*a = 0.
-1, 1
Let t(y) be the second derivative of -2*y + 1/13*y**3 + 0 - 2/13*y**2 - 1/78*y**4. Factor t(z).
-2*(z - 2)*(z - 1)/13
Let p(h) be the first derivative of -2*h**7/147 - 8*h**6/105 - 4*h**5/35 + 10*h - 5. Let y(w) be the first derivative of p(w). Factor y(n).
-4*n**3*(n + 2)**2/7
Determine j, given that 194*j**3 - 408*j**3 - 8*j**4 - 2*j**2 + 204*j**3 = 0.
-1, -1/4, 0
Let z(h) be the second derivative of -h**5/8 - 55*h**4/8 + 15*h**3 + 85*h**2 - 246*h. What is p in z(p) = 0?
-34, -1, 2
Let i be (-40)/(-56) + 60/14. Suppose 3*t**4 - 6/5*t + 0 - 27/5*t**3 + 21/5*t**2 - 3/5*t**i = 0. Calculate t.
0, 1, 2
Let r be (-20)/4 + 3 - (-7 - -4 - 1). Factor -2/3 - 2/9*b**r - 8/9*b.
-2*(b + 1)*(b + 3)/9
Suppose -5*p - 1 = 12*r - 16*r, 4 = r. Let d(j) be the first derivative of 5*j**3 + 3*j**4 + 5 + p*j**2 + 3/5*j**5 + 0*j. Factor d(n).
3*n*(n + 1)**2*(n + 2)
Let u(i) = 2*i**2. Let c(z) = 9*z - 7. Let q be c(6). Let l = 69 - q. Let v(p) = -p**3 + 19*p**2. Let a(d) = l*u(d) - 2*v(d). Factor a(b).
2*b**2*(b + 3)
Let p(v) be the third derivative of v**10/151200 - v**9/30240 + v**8/20160 + 11*v**5/30 + 31*v**2. Let f(z) be the third derivative of p(z). Factor f(l).
l**2*(l - 1)**2
Let k(g) be the second derivative of 1/4*g**2 - 1/24*g**4 + 19*g + 0*g**3 + 0. Find u, given that k(u) = 0.
-1, 1
Let z(y) be the second derivative of y**4/48 - y**3/2 + 9*y**2/2 - y - 23. Factor z(h).
(h - 6)**2/4
Let o be (-172)/(-24) + (-154)/22. Let -1/3*l + 0 + 1/6*l**2 - 1/2*l**5 - o*l**4 + 5/6*l**3 = 0. Calculate l.
-1, 0, 2/3, 1
Let l be -11 - -8 - (309/(-66) + 1). Let r(m) be the first derivative of 0*m - 4/33*m**6 - 1/11*m**2 - l*m**4 + 26/55*m**5 - 4 + 14/33*m**3. Factor r(w).
-2*w*(w - 1)**3*(4*w - 1)/11
Factor -17*g**2 + 125*g + 34*g**2 + 630 - 5*g**2 - 7*g**2.
5*(g + 7)*(g + 18)
Let o(n) be the third derivative of n**5/210 - 13*n**4/84 + n**2 + 38*n. Solve o(k) = 0 for k.
0, 13
Solve 19/3*q - 40 + 1/3*q**2 = 0 for q.
-24, 5
Let z = -1570/697 + 102/41. Determine c so that 2/17*c**3 + 0*c**2 + 0 - z*c**4 + 2/17*c**5 + 0*c = 0.
0, 1
Let y(h) be the first derivative of -h**6/2 + 19*h**5/5 - 31*h**4/4 + 3*h**3 + 7*h**2 - 8*h - 127. Solve y(d) = 0.
-2/3, 1, 4
Let d(i) be the second derivative of 8/3*i**3 + 0 - 19*i + 6*i**2 + 1/3*i**4. Factor d(a).
4*(a + 1)*(a + 3)
Let w = 13144 + -13139. Let -64/3*z**4 - 2000/3 + 4600/3*z - 3260/3*z**2 + 2/3*z**w + 722/3*z**3 = 0. What is z?
1, 10
Let c be (-8)/((-2)/(-1)) - (-231)/11. Factor c + 8*z**2 + 144*z + 6*z**2 + 23 + 0*z**2.
2*(z + 10)*(7*z + 2)
Let g(j) be the third derivative of -19/240*j**5 - 26*j**2 + 0 + 33/32*j**4 + 0*j + 1/480*j**6 - 27/8*j**3. Solve g(k) = 0 for k.
1, 9
Factor 0 + 1/4*j**2 + 6*j.
j*(j + 24)/4
Let d(c) = -10*c**2 - 11*c - 17. Let q be d(-7). Let y be q/(-225) - 3/27. Factor 0*v**4 + 0 + 3/5*v**2 + y*v**3 + 0*v - 12/5*v**5.
-3*v**2*(v - 1)*(2*v + 1)**2/5
Let s(y) be t