- 36*f**5 + 55*f**3 + 17*f**3 = 0.
-2, 0, 1/4, 1
Let l(w) be the third derivative of -w**5/60 + 53*w**4/24 - 26*w**3/3 + 5*w**2 + w. Factor l(y).
-(y - 52)*(y - 1)
Let c(x) be the third derivative of -x**7/70 + 11*x**6/10 - 338*x**2. Determine u, given that c(u) = 0.
0, 44
Find v such that 0 + 4/5*v - 2/5*v**3 + 2/5*v**2 = 0.
-1, 0, 2
Suppose 50 = 5*l + 30. Suppose 4*d - v - v = 4, -l = 3*d + 2*v. Factor 2/17*w + d + 2/17*w**2.
2*w*(w + 1)/17
Let r(f) be the second derivative of -f**4/24 - 61*f**3/6 - 3721*f**2/4 - 267*f. Factor r(k).
-(k + 61)**2/2
Let d = -868 + 870. Factor 8/3*c**d - 1/3*c**3 + 0 - 16/3*c.
-c*(c - 4)**2/3
Factor j**4 - 4*j + 0*j**5 + 3*j - 6*j**3 + j**2 + 3*j + 2*j**5.
j*(j - 1)**2*(j + 2)*(2*j + 1)
Suppose -5*m = 4*k - 23, -3 = 5*k + 3*m - 35. Let n be (-2)/7 + 23/k. Find u such that -6*u + 0*u**4 + 3*u**2 + 3*u**n + 7*u + u**4 = 0.
-1, 0
Let c(z) be the third derivative of 11*z**7/1050 - 47*z**6/300 + 93*z**5/100 - 27*z**4/10 + 18*z**3/5 + 237*z**2. Find v, given that c(v) = 0.
6/11, 2, 3
Suppose -3*n + 17*h = 20*h - 6, 2*h = 4*n - 8. Let s = 1/87 + 169/435. Solve 4/5*c - 2/5*c**4 + s*c**n - 4/5*c**3 + 0 = 0 for c.
-2, -1, 0, 1
Let s(z) be the first derivative of z**4/60 - z**3/5 + z**2/2 + 31*z - 26. Let w(i) be the first derivative of s(i). Determine h, given that w(h) = 0.
1, 5
Suppose 23*p + 104 - 124 = 49. Suppose 0*d = 2*d. Find l, given that 4/11*l**2 - 6/11*l**p + 2/11*l**4 + d*l + 0 = 0.
0, 1, 2
Let u = 192 - 121. Let v = 73 - u. Factor -1/3*o**v - 1/6*o**3 + 0 - 1/6*o.
-o*(o + 1)**2/6
Suppose 5*n - 15 = 2*n. Let 6*f**4 + n*f**5 - 2*f**4 - 25*f**2 - 6*f**3 - 10*f + f**4 - 9*f**3 = 0. Calculate f.
-1, 0, 2
Let d(w) be the first derivative of -2*w**5/5 - 38*w**4 - 1444*w**3 - 27436*w**2 - 260642*w - 93. Let d(h) = 0. Calculate h.
-19
Let u be ((-30)/(-75) - (-20)/(-75))*12. Factor 2/5*q**2 + u + 8/5*q.
2*(q + 2)**2/5
Let j(h) be the first derivative of -3*h**2/2 - 17*h - 9. Let m be j(-7). Suppose -6/11*x**2 - 6/11*x**3 - 2/11*x - 2/11*x**m + 0 = 0. What is x?
-1, 0
Let w(g) be the first derivative of -10/3*g**3 - 2*g**4 - 12 - 2*g**2 - 2/5*g**5 + 0*g. Factor w(a).
-2*a*(a + 1)**2*(a + 2)
Let o = 3095713/10378500 - -16/78625. Let v = -7/60 + o. Factor v*q + 2/11*q**3 + 0 + 4/11*q**2.
2*q*(q + 1)**2/11
Let p = 36 + -23. Let v be 0/((-2)/p + 15/13). What is h in v - 2/5*h**3 + 4/5*h + 2/5*h**2 = 0?
-1, 0, 2
Let t(l) be the second derivative of 0 + 29*l + 3/4*l**3 - 15/8*l**2 - 1/16*l**4. What is z in t(z) = 0?
1, 5
Factor -1250/9 - 100/9*x - 2/9*x**2.
-2*(x + 25)**2/9
Factor -4/5*r**3 - 8160*r + 8000 + 804/5*r**2.
-4*(r - 100)**2*(r - 1)/5
Find l, given that -2/13*l**3 + 0*l + 0 + 8/13*l**2 = 0.
0, 4
Let d(x) be the third derivative of -13*x**2 - 1/60*x**5 + 1/6*x**4 - 1/2*x**3 + 0 + 0*x. Factor d(w).
-(w - 3)*(w - 1)
Suppose 4*i = 20 + 16. Let j(q) = 3*q**2 + 2*q + 1. Let a be j(-1). Factor f**2 - 4*f - i*f**a - 2*f**3 - 4*f.
-2*f*(f + 2)**2
Let c(x) be the third derivative of -x**8/4032 - x**7/504 + x**5/12 - 9*x**2. Let a(n) be the third derivative of c(n). Factor a(w).
-5*w*(w + 2)
Determine k, given that -144*k + 1828 - 100 + 3*k**2 + 0*k**2 = 0.
24
Let r(a) = a**2 + 12*a - 1330. Let p be r(-43). Suppose -2/3*c + 5/3*c**2 + 0 - 4/3*c**p + 1/3*c**4 = 0. What is c?
0, 1, 2
Let k = 817/8 + -159311/1560. Let s(n) be the third derivative of 10*n**2 + 0 + 1/78*n**4 + k*n**5 + 0*n + 1/39*n**3. Determine g so that s(g) = 0.
-1
Let j = 83/1169 + 12/167. Factor -2/7 + 3/7*z**2 + 1/7*z**3 - j*z**4 - 1/7*z.
-(z - 2)*(z - 1)*(z + 1)**2/7
Let y be (5/10)/(4/16). Let z(l) = -l**2 - l + 2. Let d be z(0). Factor 4*x**4 - 2*x**y - 9 - 6*x**d + 13.
4*(x - 1)**2*(x + 1)**2
Suppose 0 = 2*r + 5*k - 4 - 7, 0 = -r + 2*k + 1. Let i(t) be the first derivative of 0*t**2 + 8/9*t - 2/9*t**3 + r - 1/18*t**4. Factor i(f).
-2*(f - 1)*(f + 2)**2/9
Let f(i) be the first derivative of i**6/3 - 6*i**5/5 - 93*i**4/2 + 1174*i**3/3 - 888*i**2 + 792*i - 438. Solve f(h) = 0.
-11, 1, 6
Factor -1 + u**2 + 3*u**3 + 4/3*u**4 - 5/3*u.
(u + 1)**3*(4*u - 3)/3
What is s in 4*s - 4*s**2 + 148*s**4 - 72*s**4 - 72*s**4 - 4*s**3 = 0?
-1, 0, 1
Let l(u) be the first derivative of -u**8/560 + u**7/70 - u**6/24 + u**5/20 + 9*u**3 - 8. Let y(a) be the third derivative of l(a). Factor y(c).
-3*c*(c - 2)*(c - 1)**2
Let y(z) be the third derivative of -z**7/42 + z**6/6 + 5*z**5/12 - 62*z**2. Let y(k) = 0. What is k?
-1, 0, 5
Let u be 3 - 2/8*4. Suppose 2*g - u = 2. Solve -8*a**3 + 1 - 3*a - 2*a**5 - g*a**5 - a**2 + 15*a**3 = 0.
-1, 1/2, 1
Let l(w) be the second derivative of w**4/42 + 110*w**3/21 + 3025*w**2/7 + 263*w. Factor l(u).
2*(u + 55)**2/7
Suppose 40 - 35/2*t**2 + 15*t = 0. Calculate t.
-8/7, 2
Let c(d) = -2*d**2 - 49*d - 144. Let f be c(-21). Let m(g) be the first derivative of 7/9*g**2 - 2/45*g**5 - 4/9*g - f - 2/3*g**3 + 5/18*g**4. Factor m(y).
-2*(y - 2)*(y - 1)**3/9
Suppose 4*g - 38 = -3*v, 0 = 5*v + 14*g - 15*g - 25. Suppose -28 + v = -11*j. Factor -1/4*b**3 - 1/2*b**2 + b + j.
-(b - 2)*(b + 2)**2/4
Let p(k) = -19*k**2 + 24*k + 59. Let z(f) = -16*f**2 + 24*f + 60. Let t(u) = -4*p(u) + 5*z(u). Let t(o) = 0. Calculate o.
-2, 8
Factor 32/3*n**2 + 0*n + 0 + 8*n**4 - 4/3*n**5 - 16*n**3.
-4*n**2*(n - 2)**3/3
Let z(p) be the first derivative of -p**4/24 - p**3/6 + 2*p**2 + 40*p/3 - 129. Factor z(l).
-(l - 5)*(l + 4)**2/6
Let k(s) = 6*s**4 + 7*s**3 - s**2 + 3*s. Let p(r) = -r**4 - r**3 - r. Let n(f) = -3*k(f) - 15*p(f). Solve n(c) = 0.
-2, -1, 0, 1
Let w = -611 + 613. Let l(y) be the second derivative of -8*y**4 + 6*y - w*y**2 + 6*y**3 + 0 + 16/5*y**5. Factor l(m).
4*(m - 1)*(4*m - 1)**2
Let q(x) be the second derivative of -x**5/150 - 2*x**4/15 - 41*x**3/45 - 2*x**2 - 6*x - 1. Find c such that q(c) = 0.
-6, -5, -1
Factor 0*m + 0 - 24*m**2 - 1/2*m**3.
-m**2*(m + 48)/2
Let r(h) be the first derivative of -3*h**5/5 - 15*h**4/2 - 33*h**3 - 54*h**2 + 8. Suppose r(j) = 0. What is j?
-4, -3, 0
Let i = -189 - -1703/9. Suppose 2*z + 23 = 5*c, 4 = 5*c + 5*z + 9. What is l in i*l + 0 - 2/9*l**c + 0*l**2 = 0?
-1, 0, 1
Let s be (20/(-16))/((-5)/80). Factor -3*d + 3*d**2 - 11*d + s*d + 3.
3*(d + 1)**2
Let d(o) be the second derivative of 0*o**2 - 2/9*o**4 + 16*o + 4/15*o**5 + 0 + 1/15*o**6 + 0*o**3 - 1/7*o**7. What is i in d(i) = 0?
-1, 0, 2/3
Let -44 - 7/2*f**3 - 69*f**2 + 174*f = 0. What is f?
-22, 2/7, 2
Suppose 0 = 3*m + 2*l - 19, 2 + 2 = 2*l. Let x(t) be the first derivative of -1/3*t**4 + 0*t**3 + 1/3*t**2 + 0*t**5 + 0*t + m + 1/9*t**6. Factor x(u).
2*u*(u - 1)**2*(u + 1)**2/3
Let a(o) be the third derivative of -o**8/10080 - o**7/840 - 13*o**5/30 + 35*o**2. Let f(j) be the third derivative of a(j). Factor f(t).
-2*t*(t + 3)
Let k = -7690/3 - -2564. Find z, given that k*z + 1 - 1/3*z**2 = 0.
-1, 3
Let z(q) = -q**3 + 17*q**2 + 13*q - 5. Let r(u) = -2*u**3 - 7 + 3*u**2 - 6 + 32*u + 1 + 39*u**2. Let d(h) = 5*r(h) - 12*z(h). Factor d(a).
2*a*(a + 1)*(a + 2)
Let c = -73 + 35. Let q = -34 - c. Find n such that -11/4*n**3 + 0 + n + 9/4*n**5 + 3/2*n**q - n**2 = 0.
-1, 0, 2/3
Let b(v) be the second derivative of -17/12*v**5 - 5/6*v**7 + 0*v**2 + 0 + 5/9*v**3 + 25/36*v**4 + 7*v - 41/18*v**6. Solve b(y) = 0.
-1, -2/7, 0, 1/3
Find y, given that 3 - 6*y**2 + 3*y - 6*y**3 + 3*y**4 + 0*y + 27*y**5 - 24*y**5 = 0.
-1, 1
Determine n, given that 254/19*n**2 - 174/19*n - 6*n**3 + 18/19 + 16/19*n**4 = 0.
1/8, 1, 3
Let c = 2110 + -2107. Solve 1/4*k**c + 9/4*k + 3/2*k**2 + 0 = 0.
-3, 0
Let t(z) be the third derivative of -z**8/588 + 2*z**7/735 + z**6/210 - z**5/105 - 6*z**2 + 8. Determine p so that t(p) = 0.
-1, 0, 1
Factor 0 + 0*k - 33/7*k**3 - 3*k**5 + 48/7*k**4 + 6/7*k**2.
-3*k**2*(k - 1)**2*(7*k - 2)/7
Let q(h) = h**5 - h**3 - h**2 - h. Let y = 33 + -31. Let j(r) = -4*r**4 - 6*r**3 - 3*r**2 - r. Let f(t) = y*j(t) - 2*q(t). Let f(s) = 0. Calculate s.
-2, -1, 0
Let f(q) be the second derivative of 3*q**5/20 - 33*q**4/4 + 255*q**3/2 + 867*q**2/2 - 92*q. Factor f(n).
3*(n - 17)**2*(n + 1)
Let g(t) be the second derivative of -9*t**2 - 1/6*t**4 + 0 - 8*t + 2*t**3. Suppose g(a) = 0. Calculate a.
3
Suppose 0*i = -17*i + 51. Factor -18*t + 14*t + 2*t + t**i - t**2.
t*(t - 2)*(t + 1)
Suppose -s + 3*i = -4, 0 = 2*s + 3*s + 4*i - 39. Suppose 9*h - s*h = 4. Determine m, given that -3*m - 5 - m**h +