/20. Factor 0*c + 0 - 3/4*c**2 - u*c**3.
-3*c**2*(c + 1)/4
Factor 2/9*f**2 + 20/9 + 22/9*f.
2*(f + 1)*(f + 10)/9
Solve -21/4*p**2 + 3/4*p**4 + 3/2*p**5 + 0 - 9/2*p**3 - 3/2*p = 0 for p.
-1, -1/2, 0, 2
Let l(y) = 1 + y - 9*y**2 + y**4 + y**3 + 25*y**2 - 16*y**2. Let q(x) = -x**5 - 7*x**4 - 11*x**3 - 7*x**2 - 4*x - 2. Let m(t) = -2*l(t) - q(t). Factor m(a).
a*(a + 1)**3*(a + 2)
Suppose 3*w + 16 = 7*w. Suppose 0 = n - 6 + w. Factor -g**3 + 2/3 - 1/3*g**4 - 1/3*g**n + g.
-(g - 1)*(g + 1)**2*(g + 2)/3
Let i(x) be the first derivative of -x**3/9 + 98*x**2/3 - 9604*x/3 + 251. What is y in i(y) = 0?
98
Let b(x) = x + 8. Let i be b(-6). Suppose y = -2*k - i*k + 11, -2*k = -4. Factor -4*m + 3*m**3 - m**2 + 9*m**2 - 7*m**y.
-4*m*(m - 1)**2
Let s(q) = -2*q**3 - 10*q**2 + 5*q - 5. Let g be s(-7). Let o be (3/4)/(g/32). Suppose -o + 2/13*b**3 - 6/13*b**2 + 6/13*b = 0. What is b?
1
Let w(m) = 4*m**5 - 9*m**4 + 8*m**3 - 3*m**2 + 3*m. Let v(t) = -12*t**5 + 28*t**4 - 24*t**3 + 8*t**2 - 8*t. Let i(n) = 3*v(n) + 8*w(n). Solve i(q) = 0 for q.
0, 1, 2
Let p(t) be the first derivative of 3/7*t**2 - 12 + 3/7*t**4 + 0*t - 5/7*t**3 - 3/35*t**5. Factor p(j).
-3*j*(j - 2)*(j - 1)**2/7
Let w be 11640/(-1320) - (-5 - 4). Let v be ((-4)/(-55))/(2/5). Factor w*j**2 + 0 + v*j.
2*j*(j + 1)/11
Factor -4/7*l**3 + 0*l + 22/7*l**5 + 0*l**2 + 18/7*l**4 + 0.
2*l**3*(l + 1)*(11*l - 2)/7
Let k(h) be the second derivative of -h**7/105 - 4*h**6/75 + h**5/10 + 17*h. Factor k(d).
-2*d**3*(d - 1)*(d + 5)/5
Suppose 0 = -7*d - 0*d - 308. Let a = d - -91/2. Factor 1/2*o**3 + a*o - 1/2 - 3/2*o**2.
(o - 1)**3/2
Suppose -3*v - 4*s - 4 = -18, 0 = -4*v - 3*s + 14. Let h(x) be the third derivative of 0*x + 0*x**4 + 0 - 1/21*x**3 + 1/210*x**5 - 5*x**v. Factor h(y).
2*(y - 1)*(y + 1)/7
Let r be 3/9*(-3 - -3)/6. Let i(q) be the third derivative of 1/24*q**4 - 1/60*q**5 - 1/120*q**6 + 0*q - 8*q**2 + r*q**3 + 1/210*q**7 + 0. Factor i(z).
z*(z - 1)**2*(z + 1)
Let b(w) = -w**3 - 7*w**2. Let g be b(-7). Find n, given that n**4 - 2*n**2 + 10*n**3 + g*n**2 - 9*n**3 = 0.
-2, 0, 1
Let z(s) be the second derivative of -s**7/2520 - s**6/144 - s**5/30 + 17*s**4/6 - 32*s. Let r(m) be the third derivative of z(m). Factor r(x).
-(x + 1)*(x + 4)
Let s be 46/253 - 40/(-22). Factor -375*f**s - 57*f**4 + 12*f**4 + 225*f**3 + 18*f**5 - 15*f**5.
3*f**2*(f - 5)**3
Let w = 126721/5 - 25343. Find p, given that w*p**2 - 4/5*p - 2/5*p**3 + 0 = 0.
0, 1, 2
Let y(v) be the first derivative of -3/2*v**2 - 1/3*v**3 + 12 - 2*v. Factor y(q).
-(q + 1)*(q + 2)
Let l(y) be the first derivative of y**3/3 + 47*y**2 + 2209*y - 160. Factor l(x).
(x + 47)**2
Factor 75 - 3167*l**2 - 147*l + 1634*l**2 + 3*l**3 + 1602*l**2.
3*(l - 1)**2*(l + 25)
Let j(i) be the second derivative of 1/60*i**5 - 1/12*i**4 - 2/9*i**3 + 0*i**2 + 0 + 27*i. Factor j(h).
h*(h - 4)*(h + 1)/3
Let s(i) be the third derivative of -i**7/105 - 5*i**6/12 - 57*i**5/10 - 153*i**4/4 - 144*i**3 - i**2 - 130. Solve s(k) = 0 for k.
-16, -3
Let m be 8/5*5 - 4/1. Suppose c = 2*y - 3 - 4, -y + 8 = -2*c. Suppose 12 - 2*b + 9*b + m*b + b + 3*b**y = 0. Calculate b.
-2
Let y be (-3 - (0 + -4))*2. Factor 8*r**3 + 11*r**2 - 6*r**y - r**2 + 4*r**4.
4*r**2*(r + 1)**2
Factor 86/3*p - 2/3*p**3 + 44/3 + 40/3*p**2.
-2*(p - 22)*(p + 1)**2/3
Let v(r) be the first derivative of 0*r + 0*r**3 + 3/2*r**2 - 1/420*r**6 + 1/105*r**5 - 1/84*r**4 - 1. Let w(a) be the second derivative of v(a). Factor w(i).
-2*i*(i - 1)**2/7
Suppose -21/2*v - 3/2*v**4 + 9/2*v**3 - 9 + 9/2*v**2 = 0. Calculate v.
-1, 2, 3
Let z be (-14)/(-15) + (-29)/87. Factor 1/5*j**3 + 9/5 + z*j - j**2.
(j - 3)**2*(j + 1)/5
Suppose 6 = 5*h - 4. Factor 4 - 3*x - 4 + x + 2*x**h.
2*x*(x - 1)
Let u(z) be the first derivative of 7*z**5/10 - z**4/8 + 38. Find i such that u(i) = 0.
0, 1/7
Factor -5/4*i + 7/2 - 1/4*i**2.
-(i - 2)*(i + 7)/4
Factor 0 + 1/4*o**3 - 7/4*o + 3/2*o**2.
o*(o - 1)*(o + 7)/4
Let g be 96/18 + 8/(-6). Let -g*l**3 - 23*l + 22*l + 3*l**3 - 2*l**2 = 0. Calculate l.
-1, 0
Let u(x) be the second derivative of 1/60*x**4 + 0*x**2 + 0*x**3 + 1/150*x**6 + 1/50*x**5 + 0 - 5*x. Suppose u(d) = 0. Calculate d.
-1, 0
Let v(f) be the second derivative of -f**5/10 + 5*f**4/6 + 2*f**3 - 2*f - 108. Factor v(r).
-2*r*(r - 6)*(r + 1)
Find p, given that -77/2*p**2 + 1521/2 + 1/2*p**3 + 1443/2*p = 0.
-1, 39
Factor 11*x**2 + x - 6 + 80*x**3 - 65*x - 10 - 25*x**4 - 35*x**2.
-(x - 2)**2*(5*x + 2)**2
Let w(n) be the first derivative of 230/3*n**3 + 0*n - 20 + 20*n**2 + 14*n**5 + 335/4*n**4. Find z, given that w(z) = 0.
-4, -1/2, -2/7, 0
Factor 3/5*u**2 - 6/5 - 3/5*u.
3*(u - 2)*(u + 1)/5
Suppose -193*h - 375 = -198*h. Suppose 6*l = 21*l - h. Let 16/5*b - 14/5*b**2 + 6/5*b**4 + 8/5 - 34/5*b**3 + 18/5*b**l = 0. What is b?
-1, -2/3, 1
Let y be ((-2)/(-10))/(44/8690). Let n = y - 35. Solve -27/2*t + n*t**2 - 1/2*t**3 + 27/2 = 0.
3
Let u be (-139 - -1)/(-23) + -2 + (-2 - 0). Factor -8/5 - 10*n - 2*n**3 - 52/5*n**u.
-2*(n + 1)*(n + 4)*(5*n + 1)/5
Suppose 4/3*p**4 + 16/3*p**3 - 24*p + 0 - 4*p**2 = 0. What is p?
-3, 0, 2
Let j be (2 + -2)*5*8/(-120). Let g(t) be the second derivative of -1/18*t**4 + 0 + 4*t + j*t**3 + 1/3*t**2. Factor g(d).
-2*(d - 1)*(d + 1)/3
Let 194 + 384*w - 824*w**2 + 196 + 122 + 324*w**4 - 396*w**3 = 0. Calculate w.
-8/9, 1, 2
Suppose 3 + 15 = -3*c. Let h be -2 - (29/c - -2). Find q, given that 1/6*q**5 - 2/3 - 1/6*q**2 + 4/3*q - h*q**3 + 1/6*q**4 = 0.
-2, 1
Let x be ((-12)/3 - -4)/(-2). Let x*t**4 - 4*t**4 - 2*t**4 - 6*t**3 - 2*t**2 - 2*t**5 = 0. Calculate t.
-1, 0
Let c(r) be the first derivative of 1/8*r**4 + 0*r + 9/20*r**5 + 0*r**2 - 14 + 7/24*r**6 + 0*r**3. Determine m so that c(m) = 0.
-1, -2/7, 0
Let l(b) = -5*b**2 + 192*b - 1807. Let q(u) = 5*u**2 - 193*u + 1808. Let z(j) = 3*l(j) + 2*q(j). Factor z(d).
-5*(d - 19)**2
Let v(u) be the first derivative of 11*u**3 - 9*u**2/2 + 111. Factor v(h).
3*h*(11*h - 3)
Let r(h) = -3*h - 29. Let q be r(-13). Factor 8 - 7*n**2 + 147*n**2 + 2 - q*n - 65*n**3 - 75*n.
-5*(n - 1)**2*(13*n - 2)
Let h(c) be the second derivative of c**4/114 - 8*c**3/57 + 16*c**2/19 - 30*c. What is w in h(w) = 0?
4
Let b = -1844 + 1844. Let a(q) be the second derivative of b - 2/3*q**4 + 0*q**2 - 1/3*q**3 - q. Suppose a(p) = 0. What is p?
-1/4, 0
Find s, given that -7*s - 17*s - 12 - 36*s**2 + 41*s**2 - 20*s**2 - 3*s**3 = 0.
-2, -1
Let z = -17 - -22. Suppose -32*p**4 + 22*p**3 + 14*p**z - 4*p**2 - 8 + 8 = 0. What is p?
0, 2/7, 1
Let m(u) be the second derivative of 3*u**5/20 + u**4 + 3*u**3/2 - 105*u. Find k such that m(k) = 0.
-3, -1, 0
Suppose -g = -6 + 2. Factor -14*s - 8*s + 16 + 6*s + g*s**2.
4*(s - 2)**2
Let d(y) = 3*y**2 - 30*y - 225. Let h be d(15). Suppose 0*x**2 - 6/5*x**3 + 2/5*x**5 + 0*x - 4/5*x**4 + h = 0. Calculate x.
-1, 0, 3
Factor -2/3*w**3 + 16/3*w**2 + 8*w + 0 - 2/3*w**4.
-2*w*(w - 3)*(w + 2)**2/3
Factor 1/3*o**5 + 0*o + 0*o**2 + 0 - 14/3*o**3 - 13/3*o**4.
o**3*(o - 14)*(o + 1)/3
Let 392/9 - 56/9*u + 2/9*u**2 = 0. What is u?
14
Let c(a) be the second derivative of 3*a**5/20 + 31*a**4/4 + 15*a**3 + 100*a. Factor c(v).
3*v*(v + 1)*(v + 30)
Let r = -6/563 - -1804/63619. Let q = r + 107/339. Factor 0*h**2 - 1/3*h + q*h**3 + 0.
h*(h - 1)*(h + 1)/3
Let k(r) be the first derivative of 2*r**3/21 + 82*r**2/7 + 3362*r/7 + 155. Factor k(n).
2*(n + 41)**2/7
Let d be 2/(-2)*-3 - 7/(-1). Find f such that 31*f**5 + 33*f**5 - 69*f**5 - 5*f**3 - d*f**4 = 0.
-1, 0
Let u(q) = -q**2 - 4 - 13*q - 2 + q - 2. Let t be u(-9). Let p**2 + 2 - 3*p - t + 3 + 10 = 0. What is p?
-1, 4
Suppose 64 = 17*n - n. Let w(f) be the third derivative of -1/300*f**5 + 0*f**3 + 0 + 0*f - f**2 - 1/120*f**n. Factor w(r).
-r*(r + 1)/5
Let i = -7207 - -7209. Suppose -2*j + 1/2*j**3 + i*j**2 + 0 - 1/2*j**4 = 0. What is j?
-2, 0, 1, 2
Suppose -21*i + i + 85*i - 32 + 4 - 27 - 10*i**2 = 0. What is i?
1, 11/2
Let j(i) be the third derivative of 0 - 1/60*i**4 + 12*i**2 + 1/1680*i**8 + 0*i**3 + 0*i - 1/60*i**5 - 1/200*i**6 + 1/1050*i**7. Factor j(p).
p*(p - 2)*(p + 1)**3/5
Suppose -4/15*j**4 - 14/15*j**5 - 14/15*j + 28/15*j**3 + 8/15*j**2 - 4/15 = 0. Calculate j.
-1, -2/7, 1
Let k be ((-80)/840)/((4/(-6))/(12/1)). Determine u so that -k - 2/7*u + 2/7*u**2 = 0.
-2, 3
Let k = 304/29 + 7673/145. Let t = k - 63. Let 2/5 - t*a**2 + 0*a = 0. What is a?