- 380. Factor u(i).
3*i*(i - 1)*(2*i - 1)/2
Let m = 39196/3 + -13065. Factor 0*y + 5/3*y**2 + 7/3*y**4 + 0 + 11/3*y**3 + m*y**5.
y**2*(y + 1)**2*(y + 5)/3
Let q(v) be the third derivative of -v**7/3780 + 2*v**6/405 - v**5/108 - 25*v**4/54 - v**3 - 3*v**2 + 1. Let b(k) be the first derivative of q(k). Factor b(i).
-2*(i - 5)**2*(i + 2)/9
Let s = -3 + -3. Let c(l) = -2*l**2 - 2*l - 6. Let d(f) = f**2 - f - 1. Let k(v) = s*d(v) - c(v). Factor k(o).
-4*(o - 3)*(o + 1)
Let 6*v**2 + 4*v - 8*v + v + v**3 + 11*v = 0. Calculate v.
-4, -2, 0
Let d = 465664/33 - 14110. Let k = 15/11 - d. Factor -1/6*n**5 + k*n**2 + 0*n**3 - 1/3*n**4 + 1/6*n + 0.
-n*(n - 1)*(n + 1)**3/6
Let s(t) be the first derivative of 13 + 10*t + 5/2*t**4 - 5/2*t**2 - 5/6*t**6 + 2*t**5 - 20/3*t**3. Determine r so that s(r) = 0.
-1, 1, 2
Let j be 24/4*(66/(-12) - -6). Let l(m) be the second derivative of -2/15*m**j - 1/30*m**4 - 1/5*m**2 + 0 - 4*m. Find i, given that l(i) = 0.
-1
Find f, given that 64/3*f**3 + 1792/3*f - 2/3*f**4 - 1568/3 - 208*f**2 = 0.
2, 14
Let w(o) = -8*o**3 - 63*o**2 + 26*o - 3. Let z(t) = -42*t**3 - 316*t**2 + 128*t - 14. Let x(v) = -14*w(v) + 3*z(v). What is m in x(m) = 0?
-5, 0, 2/7
Let k = 103 + -103. Let c(y) be the first derivative of -2 + k*y - 2/15*y**3 - 1/5*y**2. Factor c(s).
-2*s*(s + 1)/5
Let n be 2*-9*(-6)/4. Factor -32*z - 10*z**3 - 13*z - n - 36*z**2 - z**4 - 9*z.
-(z + 1)*(z + 3)**3
Suppose -16*j + 71*j = 110. Factor 4/5*s**3 + 28/5*s**j + 36/5 + 12*s.
4*(s + 1)*(s + 3)**2/5
Let x(g) = g**3 - 8*g**2 - 11*g + 20. Let y be x(9). Factor -28*t - 12 - y*t**3 + 5 - 9 + t**2 - 15*t**2.
-2*(t + 1)*(t + 2)*(t + 4)
Suppose 2 = -2*m - 2*f, m + 1 = 5*f - 0. Let n(u) = -3*u**3 + u**2 + 2*u + 1. Let g be n(m). Factor -1/6*i**5 - 1/3*i**4 + 1/3*i**2 + 0*i**g + 1/6*i + 0.
-i*(i - 1)*(i + 1)**3/6
Let s be (-1662)/54 - 4/18. Let y = -29 - s. Determine t so that 75*t**3 - 14*t - 85*t**y + 20*t - 4 + 21*t + 5*t = 0.
1/3, 2/5
Let q(p) be the second derivative of -p**7/63 - 2*p**6/15 + p**5/15 + 2*p**4/3 - p**3/9 - 2*p**2 + 4*p + 2. Let q(y) = 0. Calculate y.
-6, -1, 1
Determine i, given that -9*i**5 + 3*i**5 + 120*i + 220*i**2 + i**5 + 110*i**3 + 0*i**5 + 5*i**4 = 0.
-2, -1, 0, 6
Solve -1095*p**4 - 5824*p - 27*p**5 + 49921/3*p**2 - 30847/3*p**3 + 588 = 0 for p.
-21, 2/9, 1
Suppose 4*d - 2*b = 28, -4 = -b + 2*b. Factor 4*z**3 + 9*z**5 + 0*z**3 + d*z**5 + 11*z**4 + 7*z**4.
2*z**3*(z + 1)*(7*z + 2)
Let q(x) be the third derivative of x**5/690 + 17*x**4/138 - 35*x**3/69 + x**2 + 53. Suppose q(d) = 0. What is d?
-35, 1
Let c(g) be the second derivative of g**7/5040 - g**6/720 + g**5/240 + 4*g**4/3 - 8*g. Let j(t) be the third derivative of c(t). Suppose j(y) = 0. Calculate y.
1
Let w(f) be the second derivative of f**4/12 - 6*f**3 + 162*f**2 - f - 34. Factor w(i).
(i - 18)**2
Let j(l) be the first derivative of 3*l**5/20 - 17*l**4/16 + 11*l**3/4 - 27*l**2/8 + 2*l - 98. Factor j(x).
(x - 1)**3*(3*x - 8)/4
Factor 4/5*x - 3/5*x**2 + 4/5.
-(x - 2)*(3*x + 2)/5
Let q(j) be the second derivative of -j**5/60 - j**4/8 - j**3/3 - 6*j**2 - 7*j. Let n(z) be the first derivative of q(z). Factor n(u).
-(u + 1)*(u + 2)
Let i(z) be the first derivative of -35*z**3/3 + 55*z**2/2 + 30*z + 137. Determine y, given that i(y) = 0.
-3/7, 2
Let k be 12*3/(36/3). Let y be (-2)/k*(-18)/4. Factor 3*g**3 - 8*g**y + 2*g**2 + 3*g**2.
-5*g**2*(g - 1)
Factor 1/8*a**2 + 6 - 19/8*a.
(a - 16)*(a - 3)/8
Factor 0*i - 3/2*i**3 + 9/2*i**2 + 0.
-3*i**2*(i - 3)/2
Let w = 17 + -10. Factor -5 + 8*o**4 + 7*o**3 + 1 + w*o**3 - 2*o**3 - 4*o**2 - 12*o.
4*(o - 1)*(o + 1)**2*(2*o + 1)
Suppose 6*w - 21 = 3. Let w*g**3 + g**3 - g**2 - 4*g**3 = 0. Calculate g.
0, 1
Let n(h) = 8*h**5 - 7*h**4 - 10*h**3 - 9*h**2 - 9. Let r(s) = -s**5 + s**4 + s**3 + s**2 + 1. Let u(p) = -2*n(p) - 18*r(p). Factor u(j).
2*j**3*(j - 1)**2
Suppose 5 = c, 6*c + 45 = 5*u + 2*c. Factor -5*f**2 + f**3 - u*f**2 + 19*f**2 - 5*f - 1 + 4*f**3.
(f - 1)*(f + 1)*(5*f + 1)
Let y(d) = -11*d**3 + 10*d**2 + 15*d + 3. Let s(m) = -30*m**3 + 30*m**2 + 44*m + 8. Let f(q) = -3*s(q) + 8*y(q). Factor f(a).
2*a*(a - 6)*(a + 1)
Let c(h) be the second derivative of -3*h**5/100 - 3*h**4/2 + 63*h**3/10 - 48*h**2/5 + 81*h. Determine y so that c(y) = 0.
-32, 1
Let b be ((-3)/6 - -2)/((-7)/(-14)). Suppose -9*x**b - 9*x + 6*x**2 + 4 - x**2 + 8*x**3 + x = 0. What is x?
1, 2
Let g(w) be the first derivative of 3/8*w**4 + 0*w + 3/20*w**5 + 3 - 1/4*w**3 - 3/4*w**2. Factor g(c).
3*c*(c - 1)*(c + 1)*(c + 2)/4
Let a(i) = 12*i**4 + 31*i**3 - 93*i**2 + 127*i - 63. Let u(z) = 7*z**4 + 16*z**3 - 47*z**2 + 64*z - 32. Let t(l) = 4*a(l) - 7*u(l). Find o such that t(o) = 0.
1, 2, 7
Let j(n) = 9*n**3 + 224*n**2 + 2621*n + 4418. Let k(r) = 26*r**3 + 671*r**2 + 7864*r + 13252. Let p(d) = -11*j(d) + 4*k(d). Factor p(u).
5*(u + 2)*(u + 21)**2
Let v = 1093/24960 + -5/384. Let w(s) be the first derivative of 0*s**4 - 2/13*s**2 + v*s**5 - 12 - 2/13*s**3 + 0*s. Factor w(f).
2*f*(f - 2)*(f + 1)**2/13
Let y(v) = v**2 - 7*v - 6. Let l be (-3)/(9/(-30)) + -2. Let d be y(l). Factor 4*b - 5*b**d + 3*b**3 + 8*b**2 - 3*b**4 - 7*b.
-3*b*(b - 1)**2*(b + 1)
Let c be (342/2964)/((-3)/(-4)). Factor 18/13 - 6/13*j - c*j**3 - 10/13*j**2.
-2*(j - 1)*(j + 3)**2/13
Let i = -17 + 29. Suppose i*g + 7*g = 16*g. Suppose 0*d**3 - 1/2 + d**2 + g*d - 1/2*d**4 = 0. What is d?
-1, 1
Suppose 3*g + 5*k - 33 = 0, 4*g - 2*k + k = 21. Let 7*x**2 - 4*x - 28*x**3 + 11*x**2 - g + 14*x**2 + 6*x**4 = 0. Calculate x.
-1/3, 1, 3
Let l be (-1224)/1088*4/18*-3. Solve 9/2*t - l*t**2 - 6 = 0.
2, 4
Let r(g) be the second derivative of -g**5/30 - g**4/9 + g**3/9 + 2*g**2/3 - 11*g - 4. Let r(o) = 0. What is o?
-2, -1, 1
Let w = -1332/5 + 282. Let f = w - 307/20. Find d, given that -1/4*d - 1/2 + f*d**2 = 0.
-1, 2
Determine g, given that -185/2*g**2 + 0 - 5/4*g**4 + 135/4*g**3 + 60*g = 0.
0, 1, 2, 24
Let m(q) be the second derivative of -q**4/32 - 3*q**3/16 - 3*q**2/8 + 298*q. Factor m(c).
-3*(c + 1)*(c + 2)/8
Factor 1116/11*g**3 + 2/11*g**5 - 76/11*g**4 + 24786/11*g - 26244/11 - 7776/11*g**2.
2*(g - 9)**4*(g - 2)/11
Let y be ((-36)/(-84))/(2/14). Determine t so that -t**y + 14*t**2 + 17*t**2 - 3*t + 1 - 28*t**2 = 0.
1
Let c(i) = i**3 - i**2 + 2*i - 16. Let y be c(0). Let d = 18 + y. Factor -2*j**4 - 10*j**2 + 4*j**2 + 2*j**3 + d*j**2 + 4*j**4.
2*j**2*(j - 1)*(j + 2)
Factor 2*w**4 + 8*w**3 + 14*w**3 - 25*w**3 - w**4 + 2*w**2.
w**2*(w - 2)*(w - 1)
Suppose -71/5 + 1/5*c**3 + 143/5*c - 73/5*c**2 = 0. Calculate c.
1, 71
Factor -2*g**3 + 0 + 2/7*g**4 + 0*g + 12/7*g**2.
2*g**2*(g - 6)*(g - 1)/7
Let u be (-2)/(-8) + (-28)/(-16). Let a = -101/4 - -715/28. Factor 2/7*m**u - 4/7*m**3 + 4/7*m - a*m**4 + 0.
-2*m*(m - 1)*(m + 1)*(m + 2)/7
Let t(z) = 5*z**4 - 12*z**3 + 5*z**2 - 6*z - 2. Let u(r) = -11*r**4 + 24*r**3 - 8*r**2 + 15*r + 5. Let c(q) = -5*t(q) - 2*u(q). Find o, given that c(o) = 0.
0, 1, 3
Let t(x) be the second derivative of 0*x**2 - 1/147*x**7 + 47*x + 0 + 1/21*x**4 - 2/105*x**6 + 1/21*x**3 + 0*x**5. Let t(k) = 0. Calculate k.
-1, 0, 1
Let p(z) be the second derivative of -z**5/70 - 5*z**4/42 + z**3/21 + 5*z**2/7 + 3*z + 3. Factor p(r).
-2*(r - 1)*(r + 1)*(r + 5)/7
Let m(w) be the second derivative of -w**6/90 + 2*w**5/15 + w**3/2 - 13*w. Let d(c) be the second derivative of m(c). Factor d(t).
-4*t*(t - 4)
Let v(n) be the first derivative of n**6/42 - 3*n**5/35 - n**4/28 + 11*n**3/21 - 6*n**2/7 + 4*n/7 + 263. Suppose v(j) = 0. Calculate j.
-2, 1, 2
Let b(a) = -121*a**2 + 3*a + 5. Let c be b(-1). Let j = c - -358/3. Factor 1/3*h**3 - j - 1/3*h + 1/3*h**2.
(h - 1)*(h + 1)**2/3
Let z(g) = -g**3 + 7*g**2 + 15*g - 15. Let f be z(7). Let k be (-12)/f + 4/30. Factor 4/7*r - 4/7*r**3 - 2/7*r**4 + 2/7 + k*r**2.
-2*(r - 1)*(r + 1)**3/7
Let r = -18311/7 - -2616. Factor 0*x + 1/7*x**5 + 1/7*x**4 - 1/7*x**2 - r*x**3 + 0.
x**2*(x - 1)*(x + 1)**2/7
Let h(a) be the third derivative of a**7/630 - 7*a**6/45 + 9*a**5/10 - 20*a**4/9 + 53*a**3/18 - 218*a**2. What is f in h(f) = 0?
1, 53
Let y(n) = -n**2 + 18*n - 5. Let f be y(13). Find c, given that 4*c**4 + 12*c**2 - 7*c**3 - 60 + f - 9*c**3 = 0.
0, 1, 3
Let r(a) be the second derivative of a**5/100 - a**4/20 + a**3/10 - a**2/10 - a - 31. Determine b so that r(b) = 0.
1
Suppose -20*w + 75 = -5*w. Factor -5/4*k**