*4 - 1/8*t**2 + 0 + 3*t. Factor a(r).
(r - 1)*(r + 1)/4
Suppose -4*d = -4*l + 212, l - 2 - 56 = 2*d. Let j be 2/3*-2*(-8)/l. Factor 0 - j*h - 8/9*h**2 - 2/3*h**3.
-2*h*(h + 1)*(3*h + 1)/9
Suppose 4*g - 14 = -2*w - 0*w, 4*w = 5*g + 15. Suppose n**3 + 7*n - w*n**3 - n - 28 - 20*n**2 + 46*n = 0. What is n?
-7, 1
Solve -10/9*b**4 + 8/9*b**3 - 2/9 - 8/9*b + 4/3*b**2 = 0.
-1, -1/5, 1
Suppose s = 17 - 8. Let h(t) be the first derivative of 1/12*t**3 - 1/8*t**2 - 1/4*t + 1/16*t**4 - s. Let h(g) = 0. What is g?
-1, 1
Let i(f) be the third derivative of -f**5/15 + 8*f**4 - 94*f**3/3 - 19*f**2. Factor i(l).
-4*(l - 47)*(l - 1)
Let v(q) be the third derivative of -q**9/7560 + q**7/1260 - 7*q**4/24 + q**2. Let u(l) be the second derivative of v(l). Factor u(b).
-2*b**2*(b - 1)*(b + 1)
Let z be ((-55)/(-4))/((-38)/(-76)). What is w in -5 - z*w**3 + 55/2*w + 5*w**2 = 0?
-1, 2/11, 1
Let k = 9991355/217 + -46043. Let u = 1/31 + k. Factor -u*l + 1/7*l**2 + 0 - 1/7*l**4 + 1/7*l**3.
-l*(l - 1)**2*(l + 1)/7
Let u(q) be the first derivative of -q**4/28 - q**3/7 + 4*q/7 - 64. Factor u(n).
-(n - 1)*(n + 2)**2/7
Let w = -108/25 + 977/225. Let h(y) be the third derivative of 0*y - 1/6*y**4 + 3*y**2 + 0*y**3 + w*y**5 + 0. Factor h(u).
4*u*(u - 3)/3
Let j(c) = -2*c**2 + 2*c**2 - c**3 - 8*c - c**2 + 13*c + 2. Let b be j(2). Determine l so that -2/13*l + b + 2/13*l**2 = 0.
0, 1
Let l(g) be the second derivative of 3*g + 0 - 1/80*g**5 + 1/2*g**3 - 7/480*g**6 + 0*g**2 + 0*g**4. Let x(y) be the second derivative of l(y). Factor x(d).
-3*d*(7*d + 2)/4
Let p(a) = a**5 + a**4 - 2*a**2 - a - 1. Let i(m) = -3*m**5 + 25*m**4 + 172*m**3 + 478*m**2 + 599*m + 275. Let t(v) = 2*i(v) + 10*p(v). Factor t(u).
4*(u + 1)*(u + 3)**3*(u + 5)
Suppose 8*a = 12*a + 8. Let f be a/(-6) + (-17 - -18). Factor 0 + 4*w**2 + 4/3*w**4 - 4*w**3 - f*w.
4*w*(w - 1)**3/3
Let m(k) be the second derivative of 1 + 1/3*k**2 + 43*k - 1/6*k**3 - 1/36*k**4 - 1/90*k**6 + 1/20*k**5. Determine s, given that m(s) = 0.
-1, 1, 2
Let d be ((-450)/(-80) - 6)*(-4)/3. Let c(g) be the second derivative of 1/24*g**4 + d*g**2 + 1/4*g**3 + 7*g + 0. Determine m so that c(m) = 0.
-2, -1
Let m(c) be the third derivative of 5*c**8/1008 + c**7/126 - c**6/36 - c**5/18 + 5*c**4/72 + 5*c**3/18 - 86*c**2. Factor m(q).
5*(q - 1)**2*(q + 1)**3/3
Let f(y) = -4 - 10*y**2 + 3*y + 46 + 19*y**2 - 17*y**2. Let r(a) = 15*a**2 - 5*a - 85. Let q(k) = -5*f(k) - 3*r(k). Factor q(j).
-5*(j - 3)*(j + 3)
Let n(v) = v**2 + 117*v + 1265. Let a be n(-12). Factor 1/9*c**a + c**3 + 0 + 2/9*c + 7/9*c**2 + 5/9*c**4.
c*(c + 1)**3*(c + 2)/9
Suppose -5*q - 2*m = -2*q - 12, -5*m + 21 = 3*q. Find k such that k**q - 2*k + 2*k + 0*k + 4 + 4*k = 0.
-2
Suppose 5*v - 7 = 23. Factor -3 - 5 - v + 2 + 2*x**2 - 2*x.
2*(x - 3)*(x + 2)
Suppose -3*m - i = -0*i - 2, 5*i + 10 = -5*m. Let k = -1/2 + m. Factor 0 - 3/2*a**2 + k*a.
-3*a*(a - 1)/2
Let s(c) be the first derivative of 1/24*c**4 - 3 - 1/12*c**2 + 1/18*c**3 + 0*c - 1/30*c**5. Factor s(x).
-x*(x - 1)**2*(x + 1)/6
Let a(w) be the first derivative of -2*w**3/39 + 30*w**2/13 + 150. Factor a(i).
-2*i*(i - 30)/13
Let a(c) = 2*c**2 + 14*c - 193. Let r be a(-14). Solve 8/3*i**r + 2/3*i**4 + 0 + 10/3*i**2 + 4/3*i = 0.
-2, -1, 0
Let a(o) be the second derivative of o**5/30 - 7*o**4/27 + 20*o**3/27 - 8*o**2/9 + 20*o. Factor a(y).
2*(y - 2)**2*(3*y - 2)/9
Determine k, given that 4*k - 2/3*k**2 - 8/3 + 1/3*k**4 - k**3 = 0.
-2, 1, 2
Let n = 1785 + -5411/3. Let b = -18 - n. Factor -b*i**4 + 2/3*i + 2/3*i**2 - 2/3*i**3 + 0.
-2*i*(i - 1)*(i + 1)**2/3
Factor 5*s + 0 + 1/2*s**2.
s*(s + 10)/2
Let x(s) be the first derivative of -s**4/24 + 19*s**3/6 - 263. Suppose x(b) = 0. What is b?
0, 57
Let s(m) = -4*m**2 + 4*m - 7*m + 2 + 2. Let h(n) = n**2. Let x(l) = -3*h(l) - s(l). Factor x(t).
(t - 1)*(t + 4)
Factor 8/5 - 17/5*i + 4/5*i**4 - 5*i**3 - 54/5*i**2.
(i - 8)*(i + 1)**2*(4*i - 1)/5
Let g(p) = 2*p**3 - p - 1. Let k be g(0). Let u be k/((5 + 4)/(-3)). Solve -1/3 + 0*r + u*r**2 = 0.
-1, 1
Suppose 0 = 3*z - 3*y - 30, -4*y = -z - 0*y + 28. Determine t so that 3*t**z - 3*t**3 - 3 + 3/2*t**5 - 21/2*t - 12*t**2 = 0.
-1, 2
Let l(f) = -7*f**3 + 8*f**2 + 9*f - 10. Let v(p) = -22*p**3 + 24*p**2 + 26*p - 28. Let z(a) = -16*l(a) + 5*v(a). Factor z(i).
2*(i - 5)*(i - 1)*(i + 2)
Factor 2*f + 4*f**2 - 2*f**3 - 11 - 9 + 16*f**2.
-2*(f - 10)*(f - 1)*(f + 1)
Let i = 8 - 6. Suppose -j + 2*v = 5, 2 = i*j + v - 2*v. Let 6*m**j + 2*m**4 - m + 6*m**2 + 4*m - m = 0. Calculate m.
-1, 0
Let g(b) = -21*b**2 - 35*b - 72. Let n(z) = -5*z**2 - 9*z - 18. Let v be (52*(0 + 1))/2. Let x(k) = v*n(k) - 6*g(k). Factor x(q).
-4*(q + 3)**2
Let o = -20617/15 - -4133/3. Suppose -2/5*r**3 - 24/5*r + o + 12/5*r**2 = 0. What is r?
2
Let -2/3*h**2 - 37538/3 + 548/3*h = 0. Calculate h.
137
Suppose 5*a + 5*n = -15, -5*n - 15 = 137*a - 141*a. Find q such that -2/9*q**4 + a*q**2 + 8/9*q + 0 - 2/3*q**3 = 0.
-2, 0, 1
Let f be ((-2)/5)/1 - ((-308)/(-105) + -4). Factor 0*g + 0 + 2/9*g**2 - 4/9*g**3 - f*g**4.
-2*g**2*(g + 1)*(3*g - 1)/9
Suppose 2*t - 5*j = -3*j + 12, -4*j = 4*t - 16. Let k = t - 2. Solve -8*c**2 + 26*c - 218*c**4 + 4*c**5 - 6*c + 214*c**4 + 12 - 24*c**k = 0.
-1, 1, 3
Suppose y = -2*y - 2*d + 17, 4*d + 22 = 2*y. Let l(u) = -2*u**2 + 15*u - 1. Let h be l(y). Determine s, given that -9 - s**2 - 2*s**2 + 7*s**2 - s**2 - h*s = 0.
-1, 3
Let i(f) be the third derivative of -f**8/896 + f**7/280 + 9*f**6/320 - f**5/80 - f**4/8 - 609*f**2. Find c, given that i(c) = 0.
-2, -1, 0, 1, 4
Let m(i) = -i**4 - 3. Let g(z) = -z**2 + z. Let v(r) = -6*r**2 + 5*r - 1. Let n(p) = -5*g(p) + v(p). Let u(y) = -m(y) + 2*n(y). Factor u(l).
(l - 1)**2*(l + 1)**2
Let w(p) be the second derivative of -5/42*p**7 + 18*p - 1/6*p**6 + 3/4*p**5 + 0*p**2 + 5/12*p**4 + 0 - 5/3*p**3. Determine s, given that w(s) = 0.
-2, -1, 0, 1
Factor -166*h + 41*h + 5*h + 5*h**2 - h**2 + 0*h**2.
4*h*(h - 30)
Let c(s) be the first derivative of 5*s - 1/15*s**3 + 1/50*s**5 + 0*s**4 + 0*s**2 + 8. Let m(q) be the first derivative of c(q). Find g such that m(g) = 0.
-1, 0, 1
Let o(w) = 14*w**2 + 7*w + 7. Let s be o(-2). Suppose 51*t - s*t - 60 = 0. Suppose -50 - 6*x**2 - 2/5*x**3 - t*x = 0. Calculate x.
-5
Factor 40/3*f**2 - 2*f**3 + 0 - 8/3*f**4 - 1/3*f**5 - 25/3*f.
-f*(f - 1)**2*(f + 5)**2/3
Let 32/7 + 24/7*z + 0*z**2 - 2/7*z**3 = 0. What is z?
-2, 4
Let h be ((-512)/(-896))/(2/7). Let b(c) be the third derivative of 1/6*c**4 + 0*c**3 + 0*c + 1/10*c**6 - 2*c**h + 0 + 1/5*c**5 + 2/105*c**7. Factor b(l).
4*l*(l + 1)**3
Let n(u) be the first derivative of 2*u**5/5 + 2*u**4 - 2*u**3/3 - 4*u**2 - 55. Solve n(i) = 0.
-4, -1, 0, 1
Let t(f) be the second derivative of f**6/360 + f**5/48 - f**4/144 - 5*f**3/72 + 8*f + 1. Factor t(s).
s*(s - 1)*(s + 1)*(s + 5)/12
Let f(o) = 5*o - 3. Let k be f(1). Determine d, given that -k*d - 42*d**2 + 39*d**2 + d + 6 + 4*d = 0.
-1, 2
Let s(r) be the first derivative of 75/2*r - 15 + 3/8*r**4 + 105/4*r**2 + 11/2*r**3. Determine p so that s(p) = 0.
-5, -1
Let v(y) be the second derivative of -y**7/980 + y**6/1260 - 5*y**3/3 + 7*y. Let d(p) be the second derivative of v(p). Suppose d(a) = 0. Calculate a.
0, 1/3
Let d(h) be the third derivative of 1215/4*h**4 - 1/84*h**7 + 0 + 3/4*h**6 + 0*h - 81/4*h**5 - 10935/4*h**3 + 21*h**2. Factor d(w).
-5*(w - 9)**4/2
Let w(q) be the second derivative of -q**7/21 + 17*q**6/75 + 59*q**5/50 - 101*q**4/30 + 2*q**3 + 80*q. Determine d so that w(d) = 0.
-3, 0, 2/5, 1, 5
Let n = -14119/20 + 706. Let s(o) be the third derivative of -1/2*o**3 + 0*o**4 + 0 + 0*o + n*o**5 - 11*o**2. Factor s(d).
3*(d - 1)*(d + 1)
Let w(n) be the first derivative of n**6/150 - n**5/50 - n**4/20 + 2*n**3/15 + 2*n**2/5 + n + 11. Let u(m) be the first derivative of w(m). Factor u(h).
(h - 2)**2*(h + 1)**2/5
Suppose -6 + 17*m + 8*m**4 - 4*m - 11*m**3 + 3*m**4 - 2*m**4 - 2*m**5 - 3*m**2 = 0. Calculate m.
-1, 1, 3/2, 2
Let g(o) = -o**3 + 8*o**2 + o - 8. Let q be g(8). Suppose 2*n + 0*n = 4*y - 8, q = -3*y - n + 6. Determine x so that 0*x**2 - 4/3 + y*x - 2/3*x**3 = 0.
-2, 1
Let x(c) be the second derivative of -c**7/350 + c**6/200 + c**5/100 - c**4/40 + 5*c**2/2 + 2*c. Let k(j) be the first derivative of x(j). Solve k(r) = 0.
-1, 0, 1
Let p be (-4)/(-64) - 553/(-112). Let f(c) be the third derivat