d**6. Factor h(p).
-3*(p + 1)**3/7
Suppose 3*t + 1 = k - 5, 2*t + 4 = -3*k. Let g = 4 + t. Let 3*u**3 + g*u**4 + 0*u**3 - u**3 + 3*u**2 - 5*u**2 - 2*u**5 = 0. Calculate u.
-1, 0, 1
Let n be 3/(-9)*(-151 + 4). Let f = 49 - n. Factor 2/7*m**5 + 12/7*m**3 - 8/7*m**2 - 8/7*m**4 + f + 2/7*m.
2*m*(m - 1)**4/7
Suppose v + m + 2 = 2*m, 0 = -3*m. Let o be (-2*(-16)/(-40))/(v/5). Factor 4/3*x - 2/3*x**o + 0.
-2*x*(x - 2)/3
Factor -2/3*i**2 - 4 + 10/3*i.
-2*(i - 3)*(i - 2)/3
Let v(p) be the first derivative of p**5/20 - 19*p**4/16 + 3*p**3/2 - 199. Factor v(m).
m**2*(m - 18)*(m - 1)/4
Let y(c) be the third derivative of -c**6/3240 - c**5/108 - 25*c**4/216 - 11*c**3/6 + 5*c**2. Let g(m) be the first derivative of y(m). What is o in g(o) = 0?
-5
Let g be (-1)/(-4) - 138/(-24). Factor -14 + 4 - 12*s**2 + g - 12 - 2*s**3 - 24*s.
-2*(s + 2)**3
Let h(w) be the third derivative of w**5/3 + 1075*w**4/24 - 45*w**3 - 218*w**2. Suppose h(k) = 0. Calculate k.
-54, 1/4
Let w be (-21573)/(-611) + -26 + -9 + (0 - 0). Factor w + 2/13*m**2 + 6/13*m.
2*(m + 1)*(m + 2)/13
Factor 5*r**4 - 5*r**3 - 3*r**2 - 70145*r**5 - 2*r**2 + 70150*r**5.
5*r**2*(r - 1)*(r + 1)**2
Let b be (-2)/((-8)/12) + 2. Suppose 15 = 5*m + b. Factor -20*y**2 - 2*y**3 - 2*y + 4*y + 18*y**m + 2*y**4.
2*y*(y - 1)**2*(y + 1)
Let k = -1/17 - -19/34. Let g be (4/8)/((-7)/((-42)/12)). Factor 7/4*i + 9/4*i**2 + 5/4*i**3 + k + g*i**4.
(i + 1)**3*(i + 2)/4
Let g(r) be the first derivative of 0*r + 0*r**2 + r**4 + 9 - 8/3*r**3. Factor g(j).
4*j**2*(j - 2)
Let a(f) be the second derivative of -f**7/189 + 17*f**6/135 + 19*f**5/30 + 59*f**4/54 + 20*f**3/27 - 241*f. Factor a(j).
-2*j*(j - 20)*(j + 1)**3/9
Let p be 3*(-1 + 53/3). Suppose -p = 5*h - 10*h. Suppose -10*r**3 + 9*r**2 + h*r**5 - 9*r**2 + 4*r**2 - 4*r**4 = 0. Calculate r.
-1, 0, 2/5, 1
Let k(z) be the third derivative of z**8/28 - 26*z**7/15 + 14*z**6/15 + 4*z**5 + 347*z**2. Find s, given that k(s) = 0.
-2/3, 0, 1, 30
What is j in 7369*j**4 - 7468*j**4 + 285*j**3 + 73*j - 302*j**2 + 67*j - 24 = 0?
6/11, 2/3, 1
Suppose 1953*j - 1961*j = -24. Let p(a) be the first derivative of 2*a**5 + 5/2*a**2 - j - 1/2*a**6 + 0*a**3 - 2*a - 5/2*a**4. Determine n so that p(n) = 0.
-2/3, 1
Suppose -5*a - 5 + 0 = 0. Let b(s) = -s**5 - s + 1. Let x(l) = l**5 + 2*l**4 + 6*l**3 - 2*l**2 - l - 3. Let h(w) = a*x(w) - 3*b(w). Factor h(f).
2*f*(f - 2)*(f - 1)*(f + 1)**2
Suppose -5*d = -w + 13 + 7, 0 = -4*d - 12. Let a be (w/(-20))/((-3)/(216/10)). Factor 0 + 0*g + 9/5*g**3 + 3/5*g**5 - a*g**4 - 3/5*g**2.
3*g**2*(g - 1)**3/5
Solve 260*k**3 - 16*k**4 + 30 + 30 - 48*k**2 - 260*k + 4 = 0 for k.
-1, 1/4, 1, 16
Factor -1058/15 - 2/15*y**2 + 92/15*y.
-2*(y - 23)**2/15
Solve 2/7*m**2 + 2/7*m + 0 = 0 for m.
-1, 0
Factor -2*w**3 + 18*w**2 + 6*w**2 - 6*w**2 - 35 + 17 + 2*w.
-2*(w - 9)*(w - 1)*(w + 1)
Let l = 80617/5 - 16121. Find n, given that 3*n**2 + l*n**3 + 3/5*n**4 + 6/5*n + 0 = 0.
-2, -1, 0
Let a(t) = -2*t**2 - t + 5. Let n(q) = 3*q**2 - q + 5. Let b(w) = 2*w**2 - w + 4. Let s(m) = -4*b(m) + 3*n(m). Let v(j) = 5*a(j) + 5*s(j). Factor v(d).
-5*(d - 2)*(d + 2)
Let m = 5 - 40. Let a be (-18)/(-63) - 4/m. Solve a*l**2 + 0 + 1/5*l**3 - 1/5*l**4 + 0*l = 0 for l.
-1, 0, 2
Let r(x) be the first derivative of -x**4 + 100*x**3/3 + 2*x**2 - 100*x - 257. Factor r(f).
-4*(f - 25)*(f - 1)*(f + 1)
Let m(h) be the third derivative of -h**8/364 + 5*h**7/273 - 2*h**6/39 + h**5/13 - 5*h**4/78 + h**3/39 - 85*h**2. Factor m(s).
-2*(s - 1)**4*(6*s - 1)/13
Let a(s) be the first derivative of 1/4*s**2 - 1/6*s**3 + 5 - s + 1/24*s**4. Let v(m) be the first derivative of a(m). Find q, given that v(q) = 0.
1
Let g be -1*(-2 - -5)*-1. Let m = -84 + 90. Suppose -m*a - 7*a + 5*a**2 + 3*a**g + 15*a = 0. What is a?
-1, -2/3, 0
Suppose -18*u - 360 = -10*u. Let i be 5/(-4)*9/u. Let -1/4*p + 0 - i*p**2 = 0. Calculate p.
-1, 0
Let u = -596/3 + 200. Let g(c) be the first derivative of -u*c**2 - 8/3*c + 3 - 2/9*c**3. What is n in g(n) = 0?
-2
Let q = 7/1143 - -9053/14859. Let u be ((-3)/(-78))/(1/4). Factor 8/13 + u*n**2 + q*n.
2*(n + 2)**2/13
Let i(l) be the third derivative of -l**6/900 - 2*l**5/75 - 4*l**4/15 + 2*l**3/3 - 12*l**2. Let c(o) be the first derivative of i(o). Factor c(b).
-2*(b + 4)**2/5
Let i(b) be the third derivative of 5/24*b**4 - 13*b**2 - 5/6*b**3 + 0 - 1/42*b**7 + 1/6*b**5 - 1/12*b**6 + 5/336*b**8 + 0*b. Determine n, given that i(n) = 0.
-1, 1
Let u(w) = 3*w + 8. Let x be u(-6). Let q be ((-2)/(-5))/((-1)/x). Factor -11*z**4 + 13*z**4 + 0*z**3 - 2*z**3 + 4*z**3 - q*z**2.
2*z**2*(z - 1)*(z + 2)
Let i = -910 - -914. Let r = -59 - -127/2. Factor -r*b**3 + 3/4*b**i + 9*b**2 + 0 - 6*b.
3*b*(b - 2)**3/4
Let d(t) = -141*t - 4933. Let r be d(-35). Factor 5/2*w + 1/2*w**3 + 1 + 2*w**r.
(w + 1)**2*(w + 2)/2
Factor 6*n**2 - 52/5*n - 2/5*n**3 + 0.
-2*n*(n - 13)*(n - 2)/5
Let y(x) be the first derivative of -12*x + 55 + 1/2*x**3 - 21/4*x**2. Factor y(i).
3*(i - 8)*(i + 1)/2
Let y = -5073/5 - -1019. Let p be 2 - 4 - 28/(-10). Suppose 0 - 2/5*x**2 - 6/5*x**5 + p*x - y*x**4 - 22/5*x**3 = 0. What is x?
-2, -1, 0, 1/3
Suppose 0 = 8*i + i - 9. Let w be (4 - i) + -3*7/21. Let -1/2*n**w + n - 1/2 = 0. What is n?
1
Solve -3/5*k**4 - 24/5*k**2 + 21/5*k**3 - 48/5*k + 0 = 0 for k.
-1, 0, 4
Let f(k) = -12*k**2 - 52*k + 136. Let g(m) = 2*m**2 - m + 1. Let j(i) = -f(i) - 8*g(i). Factor j(u).
-4*(u - 12)*(u - 3)
Let c be -3*(84/6)/(-7). Suppose c*k + 11 = 35. Determine j, given that 9*j**2 + 10*j + 1/2*j**4 + 7/2*j**3 + k = 0.
-2, -1
Factor 0*z**4 - 1 - 1/2*z**5 - 3/2*z + z**2 + 2*z**3.
-(z - 2)*(z - 1)*(z + 1)**3/2
Let b(o) = -5*o**4 + 20*o**3 + 105*o**2 - 120*o - 360. Let y(x) = 3*x**4 - 10*x**3 - 53*x**2 + 60*x + 180. Let v(c) = 2*b(c) + 5*y(c). Factor v(n).
5*(n - 3)**2*(n + 2)**2
Factor -12*d + 30*d + 12*d**2 - 2*d - d**3 + 12*d.
-d*(d - 14)*(d + 2)
Suppose 0 - 42*i + 31/2*i**2 - 1/2*i**3 = 0. Calculate i.
0, 3, 28
Let f(j) = -49*j + 10. Let d be f(2). Let c = 88 + d. Determine q so that 12/5*q**2 + 9/5*q**3 + c + 3/5*q = 0.
-1, -1/3, 0
Solve -65*z - 2*z**5 + 288*z**2 - 92*z**3 - 10*z**4 - 32*z - 19*z**4 - 65*z - 3*z**4 = 0.
-9, 0, 1
Suppose 2*s - 2 = -0. Suppose -d + s + 4 = 0. Suppose -m - 3*m + 6 + 3*m**2 - d*m**2 = 0. What is m?
-3, 1
Suppose 3*d + 4 = q, -10*d = -4*q - 6*d + 16. What is n in 2/15*n**q + 2/15*n - 2/15*n**2 + 0 - 2/15*n**3 = 0?
-1, 0, 1
Let f(m) be the second derivative of m**4/3 - 92*m**3 + 9522*m**2 - 294*m. Let f(u) = 0. What is u?
69
Let n = 20 + -18. Suppose -3*t = -5*p, 2*t + 0*t + n*p = 0. Factor 0*a**2 + t*a + 0 + 2/9*a**3 + 2/9*a**4.
2*a**3*(a + 1)/9
Let c = -4925 - -34479/7. Factor -c*i - 2/7*i**2 + 0.
-2*i*(i + 2)/7
Let 4 - 4/9*x**3 - 4*x**2 + 4/9*x = 0. What is x?
-9, -1, 1
Solve 2/5*a**4 - 44/5*a + 44/5*a**3 + 46/5 - 48/5*a**2 = 0.
-23, -1, 1
Factor 0*b + 0 + 129/4*b**4 - 3/8*b**5 + 0*b**2 - 5547/8*b**3.
-3*b**3*(b - 43)**2/8
Let b(o) be the first derivative of -o**7/3360 - o**6/1440 + o**5/96 - o**4/32 + 14*o**3/3 + 8. Let l(s) be the third derivative of b(s). Factor l(g).
-(g - 1)**2*(g + 3)/4
Let j(d) be the second derivative of -d**4/84 + d**3/14 + 5*d**2/7 + 79*d. Factor j(a).
-(a - 5)*(a + 2)/7
Let z(g) = -5*g**2 - 46*g - 72. Let p(m) = -30*m**2 - 275*m - 430. Let j(k) = 6*p(k) - 35*z(k). Factor j(h).
-5*(h + 2)*(h + 6)
What is g in 93/8 + 135/4*g**2 - 3/8*g**4 - 69/2*g - 21/2*g**3 = 0?
-31, 1
Find p, given that -60*p + 1988*p**2 - 12*p - 1985*p**2 + 69 = 0.
1, 23
Let b = -240 - -3601/15. Let a(v) be the second derivative of b*v**6 - 1/10*v**5 + 1/3*v**3 + 0*v**2 + 0 - 1/6*v**4 + 3*v. Find i such that a(i) = 0.
-1, 0, 1
Let w be 0/(0 + (-2 - -4)) - (-16)/112. Find g such that 3/7*g - 4/7 + w*g**2 = 0.
-4, 1
Let a(z) be the third derivative of z**4/4 + 54*z**2. Let u be a(0). Factor -6*q**2 + 3/2*q + 9*q**3 - 6*q**4 + 3/2*q**5 + u.
3*q*(q - 1)**4/2
Factor 9*b**3 - 14*b**3 + 24*b - 4*b + 15*b**2.
-5*b*(b - 4)*(b + 1)
Let y be 2378/4305 + 1/21. Solve -1/5*x**2 - 2/5 + y*x = 0.
1, 2
Let w = -193 - -253. Let v be 8/(-6) - 13/((-234)/w). Suppose -25/3*p**3 + 19/3*p**v + 1/3 + 16/3*p**4 - 4/3*p**5 - 7/3*p = 0. Calculate p.
1/2, 1
Suppose 2*z - b = 98, 3*z - 108 = -b + 34. Let n be 2 + 0 - 0 - (-120)/z. Factor n*u - 3 - 3/2*u**2.
-3*(u - 2)*(u - 1)/2
Let i = 43 + -13. Factor 10 + i*o**2 + 1