- d*m**7. Factor v(w).
-2*w*(w - 2)*(w - 1)**2/3
Let t = -4/2119 - -12742/14833. Find f, given that -5/7*f - 1/7*f**2 + t = 0.
-6, 1
Factor -54 - 13*f**2 + 44*f**2 - 17*f**2 - 13*f**2 + 25*f.
(f - 2)*(f + 27)
Factor 0*y - 33*y - 2*y**2 + 8*y - 24 + 0*y**2 + y**2.
-(y + 1)*(y + 24)
Factor -48/11*z - 16/11*z**3 + 4*z**2 + 18/11 + 2/11*z**4.
2*(z - 3)**2*(z - 1)**2/11
Let a(m) be the second derivative of m**8/1680 - m**7/315 - m**6/60 - 4*m**4/3 + 14*m. Let u(b) be the third derivative of a(b). Suppose u(c) = 0. What is c?
-1, 0, 3
Let w(d) be the second derivative of -3*d**2 + 5/6*d**3 - 1/10*d**5 - 28*d + 2 + 1/4*d**4. Factor w(r).
-(r - 2)*(r - 1)*(2*r + 3)
Let p(o) = 5*o**4 + o**3 - 3*o**2 - 3*o. Let a(x) = x + 7. Let s = 12 + -21. Let c be a(s). Let m(w) = -w**4 + w**3. Let z(v) = c*m(v) - p(v). Factor z(t).
-3*t*(t - 1)*(t + 1)**2
Let i(o) be the third derivative of -o**8/7560 + o**7/504 + o**6/270 - 7*o**5/15 + 7*o**2. Let t(f) be the third derivative of i(f). Find u such that t(u) = 0.
-1/4, 4
Let n(k) be the first derivative of -20 - 1/6*k**2 - 1/30*k**5 + 1/6*k + 1/12*k**4 + 0*k**3. Factor n(v).
-(v - 1)**3*(v + 1)/6
Let j be -3 + 372/30 + -9. Find g, given that 0 - 1/5*g**4 + j*g**3 + 0*g**2 - 3/5*g**5 + 0*g = 0.
-1, 0, 2/3
Let t(k) be the second derivative of -k**4/60 - k**3/10 + 2*k**2/5 - 48*k. Factor t(u).
-(u - 1)*(u + 4)/5
Let x(o) be the third derivative of -o**7/5880 - o**6/1260 - o**5/840 - 7*o**4/24 + 6*o**2. Let c(v) be the second derivative of x(v). Let c(l) = 0. What is l?
-1, -1/3
Let x be 214/7 - (-32)/(-56). Factor 3*h**2 - 27 + 23 - x*h + 46 + 33.
3*(h - 5)**2
Let d(a) = 3*a - 4. Let x be d(2). Let m(v) be the first derivative of 2*v**x - 16*v**3 - v**2 + 9 + 13*v**3 - 3. Factor m(l).
-l*(9*l - 2)
Let 0 - 2/3*x - 14/9*x**2 - 4/9*x**3 = 0. Calculate x.
-3, -1/2, 0
Let q be 5/(-17 - 8)*(2 + -2). Factor q + 3*g**3 - 9/2*g**4 + 3/2*g**5 + 0*g + 0*g**2.
3*g**3*(g - 2)*(g - 1)/2
Let i(g) be the second derivative of g**4/3 - 80*g**3 + 7200*g**2 + 152*g. Factor i(o).
4*(o - 60)**2
Factor 22/5*v**2 + 28*v + 1/5*v**3 + 40.
(v + 2)*(v + 10)**2/5
Solve -27*y**2 + 197*y**2 + 56 - 44*y - 102*y - 42*y**3 - 28*y - 10*y**4 = 0 for y.
-7, 4/5, 1
Let z = -352/15 + 358/15. Factor z*n**5 + 2/5*n**4 - 4/5*n**2 + 2/5 + 2/5*n - 4/5*n**3.
2*(n - 1)**2*(n + 1)**3/5
Let b(c) be the second derivative of c**4/4 - 12*c**3 - 75*c**2/2 - 3*c - 1. Factor b(y).
3*(y - 25)*(y + 1)
Let l(x) be the first derivative of -x**4/32 - 23*x**3/24 - 15*x**2/2 + 18*x - 129. Suppose l(z) = 0. Calculate z.
-12, 1
Suppose -x = -1 - 4. Factor x*d**2 - 5*d - 3*d**2 - 15*d - 7*d**2.
-5*d*(d + 4)
Let 0*z - 2/7*z**3 + 0*z**2 + 0 - 1/7*z**4 = 0. What is z?
-2, 0
Suppose -26 + 69 = 3*y + 2*t, 3*t = -5*y + 72. Let m = y - 11. Let m + 0*w**2 + 2*w**2 + 3 - 4*w - 5 = 0. What is w?
1
Let n(a) = a**2 - 4*a - 27. Let x be n(8). Suppose 3*g = x*y - 7, -4*y - 5*g + 6 = -7*g. Factor -1/2*l**2 - y - 2*l.
-(l + 2)**2/2
Let b = 2177 + -2169. Let j(t) be the second derivative of 0 + 1/12*t**4 - 1/5*t**5 - 1/30*t**6 + 2/21*t**7 + 0*t**2 + 0*t**3 - b*t. Factor j(h).
h**2*(h - 1)*(h + 1)*(4*h - 1)
Let -2/5*j**5 + 26/5*j**3 + 0 + 0*j + 2*j**4 + 14/5*j**2 = 0. What is j?
-1, 0, 7
Factor -196/9 - 1/9*w**3 - 224/9*w - 29/9*w**2.
-(w + 1)*(w + 14)**2/9
Let i be 39/63 - (-18)/(-90) - (-2)/(-7). Solve -i + 2/5*t**3 + 2/15*t**2 - 2/5*t = 0.
-1, -1/3, 1
Let c(z) = z - 14. Let j be c(8). Let i be 4/(-2 + j)*-6. Find l, given that 2/5*l**i - 4/5*l - 2/5*l**2 + 0 = 0.
-1, 0, 2
Suppose -31 = -12*k + 17. Let c(b) be the second derivative of -1/5*b**5 + 0*b**3 + 0 + 1/7*b**7 + 0*b**2 + 0*b**k + 1/15*b**6 - 10*b. Factor c(i).
2*i**3*(i + 1)*(3*i - 2)
Let m(q) be the third derivative of q**5/45 - 107*q**4/18 + 212*q**3/9 + 366*q**2. Factor m(k).
4*(k - 106)*(k - 1)/3
Let p(c) = 2*c - 6. Let a(y) = -y + 13. Let s be a(7). Let r be p(s). Factor 5*g**2 + 4*g - 2*g - 2*g**3 - 13*g**2 + 2*g**4 + r*g.
2*g*(g - 2)*(g - 1)*(g + 2)
Let r = 3481143/58 - 60017. Let o = r - 6/29. Find b such that -1 + o*b**2 - 3/2*b**4 - 1/2*b**3 + 1/2*b = 0.
-1, 2/3, 1
Suppose -103/5*w**3 - 8/5 - 22*w**2 - 52/5*w - 44/5*w**4 - 7/5*w**5 = 0. Calculate w.
-2, -1, -2/7
Suppose 23*q = 29*q. Let n(x) be the third derivative of 3*x**2 - 1/6*x**3 + q + 0*x - 1/480*x**6 + 1/24*x**4 + 1/240*x**5. Factor n(v).
-(v - 2)*(v - 1)*(v + 2)/4
Let k(r) be the third derivative of r**7/1050 - 17*r**6/600 + 21*r**5/100 + 27*r**4/40 + 45*r**2. Factor k(z).
z*(z - 9)**2*(z + 1)/5
Let w(u) = -u**2 + 11*u - 10. Let i be w(9). Find s, given that 4*s + 7 - 1 - 13*s + 5*s**2 - i*s = 0.
2/5, 3
Suppose -2*y = -26 + 30. Let v be (42/(-110))/(-1) - y/(-11). Find s such that 1/5*s**4 - 2/5*s**2 + 2/5*s**3 - 1/5*s + v - 1/5*s**5 = 0.
-1, 1
Let l(j) be the third derivative of j**8/144 + j**7/70 - j**6/72 - j**5/20 - j**4/36 + 25*j**2. Determine m so that l(m) = 0.
-1, -2/7, 0, 1
Find x, given that -132 - 9*x**2 - 21*x**3 - 14*x**4 - 3*x**5 - x**4 + 132 = 0.
-3, -1, 0
Suppose -3*t + 0*s = -2*s + 4, -2*t - 4*s = -24. Factor 5*w**t + 6*w + 2*w + 0*w - 3*w.
5*w*(w + 1)
Let v(o) = -2*o**2 - 28*o + 5. Let j be v(-14). Let r(x) be the first derivative of -1/5*x**j + 0*x**2 + 0*x + 9 + 1/4*x**4 + 2/3*x**3. Factor r(p).
-p**2*(p - 2)*(p + 1)
Factor 4/3*g**2 + 0*g - 64/9 - 2/9*g**3.
-2*(g - 4)**2*(g + 2)/9
Let y = 147193/1637700 + 2/16377. Let n(m) be the second derivative of -y*m**5 - 6*m + 6/5*m**2 - 11/20*m**4 - 4/5*m**3 + 0. Suppose n(d) = 0. What is d?
-2, 1/3
Factor -74/7*b - 1/7*b**2 + 75/7.
-(b - 1)*(b + 75)/7
Suppose -79*y = 146*y - 900. Factor 0 - 4/3*i**3 + 2*i**2 + 8/3*i**5 - 10/3*i**y + 0*i.
2*i**2*(i - 1)**2*(4*i + 3)/3
Let x(t) be the first derivative of -3*t**5/35 - 3*t**4/14 + 217. Find p, given that x(p) = 0.
-2, 0
Let o be 0 + 728/42 + -16. Determine q so that 2*q**2 + 1/3*q**3 + 3*q + o = 0.
-4, -1
Let h(f) = -f**5. Let s(q) = 3*q**5 + 3*q**4 + 6*q**3 - 6*q**2 - 3*q + 3. Suppose 0 = y + 4*y - 30. Let v(k) = y*h(k) + s(k). Let v(d) = 0. What is d?
-1, 1
Determine l so that 23/3*l + 0 - 1/3*l**2 = 0.
0, 23
Let m(q) = -32*q**3 - 20*q**2 + 42*q + 65. Let o(n) = 27*n**3 + 21*n**2 - 42*n - 66. Let u(t) = -6*m(t) - 7*o(t). Suppose u(x) = 0. Calculate x.
-1, 4, 6
Let j be -1 - ((-3)/(-4))/(3/12). Let b be (6/j)/(72/(-114)). Find k such that 1/2 + 15/8*k**4 - b*k**2 - 1/2*k**3 + 1/2*k = 0.
-1, -2/5, 2/3, 1
Let p be (-9 + -20)*(-1 - 0). Suppose -4*t - p = -41. Factor 0 + 3/2*c**2 - c - 1/2*c**t.
-c*(c - 2)*(c - 1)/2
Let w(j) be the third derivative of -j**7/42 + j**6/4 - j**5/12 - 5*j**4 - 40*j**3/3 - 2*j**2 - 3*j. Solve w(z) = 0 for z.
-1, 4
Let i(g) be the first derivative of 5*g**6/6 + 8*g**5 + 5*g**4 - 130*g**3/3 - 185*g**2/2 - 70*g - 401. Find h such that i(h) = 0.
-7, -1, 2
Let o(d) = 12*d**4 + 3*d**3 + 3*d**2 - 18*d - 18. Let j(s) = s**3 - s - 1. Let g(l) = 18*j(l) - o(l). Let g(x) = 0. Calculate x.
0, 1/4, 1
Suppose 5*y + 0*y - 80 = -4*r, -2*r = 5*y - 90. Let s = -15 + y. Factor -3 + 3*t**4 + 6*t - s*t**3 - 5*t**3 + 4*t**3.
3*(t - 1)**3*(t + 1)
Let p(b) be the second derivative of b**5/30 + 5*b**4/18 - 4*b**3/9 - 20*b**2/3 - 11*b + 5. Solve p(f) = 0 for f.
-5, -2, 2
Let -2/9*h**2 - 20/9 + 14/9*h = 0. What is h?
2, 5
Let g(r) = -4*r**3 + 208*r**2 - 28*r - 14. Let u(i) = -i**3 + 69*i**2 - 8*i - 4. Let t(s) = -4*g(s) + 14*u(s). Let t(f) = 0. What is f?
-67, 0
Suppose -5*s**2 - 6/5*s + 9/5*s**4 + 1/5*s**5 + s**3 + 16/5 = 0. What is s?
-8, -2, -1, 1
Let c(b) be the third derivative of -b**6/30 - b**5/15 + b**4/6 + 2*b**3/3 - 180*b**2. Factor c(o).
-4*(o - 1)*(o + 1)**2
Let z(t) be the third derivative of -t**8/672 + 17*t**7/420 - t**6/8 - 86*t**5/15 + 152*t**4/3 + 256*t**3 + 327*t**2. Factor z(a).
-(a - 8)**3*(a + 1)*(a + 6)/2
Let k(n) be the third derivative of -n**6/300 - n**5/150 + n**4/60 + n**3/15 + 4*n**2. What is h in k(h) = 0?
-1, 1
Let v(h) be the second derivative of -h**8/2940 + 2*h**7/735 - h**6/210 - 9*h**3/2 + 8*h. Let c(s) be the second derivative of v(s). Factor c(k).
-4*k**2*(k - 3)*(k - 1)/7
Let p be 0/(-1 + 4 - 5). Let h(g) be the first derivative of -3*g**5 + 2 + p*g - 39/16*g**4 - 1/2*g**3 + 0*g**2. Factor h(b).
-3*b**2*(4*b + 1)*(5*b + 2)/4
Let r be (-11 - (5 + 468/(-28)))/((-10)/(-8)). Suppose 24/7*a + 13/7*a**2 - r = 0. Calculate a.
-2