 + 3/4*d**5 = 0 for d.
-2, 0, 1
Let w(f) be the third derivative of f**6/120 + f**5/30 - f**4/6 - f**3 - 9*f**2. Let n be w(-2). Let 2/3*g**3 + 0*g**n + 0*g + 7/3*g**4 + 0 = 0. What is g?
-2/7, 0
Let l(i) be the first derivative of 4 + 0*i**2 + 5/12*i**3 - 5/4*i. Factor l(r).
5*(r - 1)*(r + 1)/4
Let s = 14890/3 - 4963. Factor -2*v**3 + 0 + s*v**4 + 3*v**2 + 0*v.
v**2*(v - 3)**2/3
Factor 5/3*p**2 + 4/3*p**3 - p**4 - 2/3*p + 0.
-p*(p - 2)*(p + 1)*(3*p - 1)/3
Let c = 5 - 1. Suppose -28 = -5*s + 5*f + 12, 2*f + 6 = 0. Let -q**4 - 8*q**4 - 7*q**3 + s*q**c + 4*q + q**4 = 0. Calculate q.
-2, -1, 0, 2/3
Let s(j) = j**4 + j - 2. Let v(c) = 3*c**5 - 14*c**4 + 24*c**3 + 6*c**2 - 23*c + 4. Let q(b) = -4*s(b) + v(b). Factor q(m).
3*(m - 4)*(m - 1)**3*(m + 1)
Let l be (-178)/14 + (-10)/35. Let j be (-2)/8 + l/(-4). What is s in -85*s + s**j - s**2 + 85*s = 0?
0, 1
Let j(i) be the second derivative of i**5/5 - 8*i**4/3 - 46*i**3/3 + 60*i**2 + 157*i. Factor j(x).
4*(x - 10)*(x - 1)*(x + 3)
Let q(x) be the second derivative of -x**4/12 - 3*x**3 - 17*x**2/2 - 78*x. Factor q(d).
-(d + 1)*(d + 17)
Let p(u) = 90*u**3 - 32*u**2 - 40*u + 8. Let n(i) = 60*i**3 - 21*i**2 - 26*i + 5. Let s(o) = -8*n(o) + 5*p(o). Factor s(m).
-2*m*(3*m - 2)*(5*m + 2)
Suppose -a - 3 = -7. Let c be 3 - (a/1)/4. Factor 2*z**3 + 6/5*z - 2/5 + 18/5*z**c.
2*(z + 1)**2*(5*z - 1)/5
Let i(k) be the second derivative of k**8/2520 - k**7/630 + k**6/540 - 23*k**3/6 + k. Let z(t) be the second derivative of i(t). Let z(j) = 0. Calculate j.
0, 1
Let k be (168 - 176)*1/(-2). Let -4/11*g**3 + 6/11*g**2 - 6/11*g**k + 4/11*g + 0 = 0. Calculate g.
-1, -2/3, 0, 1
Factor 49/3 + 1/3*x**2 + 50/3*x.
(x + 1)*(x + 49)/3
Let y(f) be the first derivative of -f**6/3 + 6*f**5/5 - f**4 - 175. Factor y(o).
-2*o**3*(o - 2)*(o - 1)
Let v be (8/(-20))/(1/(-10)). Let 18*w**2 - 10*w**3 + v*w**3 - 27*w + 3*w**3 = 0. What is w?
0, 3
Suppose 58 - 22 = -2*a + 20*a. Factor 0 + 4/9*w - 4/9*w**a.
-4*w*(w - 1)/9
Let y(u) be the second derivative of 0*u**4 + u**2 - 5*u + 0*u**3 + 0 + 1/300*u**5. Let q(x) be the first derivative of y(x). Factor q(b).
b**2/5
Let b = -20 - -12. Let s be (-20)/b*12/15. Suppose 0 - 4*o - 2 - o**s - 2*o + 3*o = 0. What is o?
-2, -1
Solve -4/9*o**2 + 52/9*o - 160/9 = 0.
5, 8
Suppose 12*w - 108 = 6*w. Let -2*k**5 - 4*k**3 - 6*k**4 + 4 - 2 + 7*k**2 + 24*k - w*k - 3*k**2 = 0. Calculate k.
-1, 1
Factor -1/4*h**2 + 0 + 0*h + 3/4*h**3.
h**2*(3*h - 1)/4
Let -8*a**4 + 248*a**2 - 4*a**4 - 456*a**3 - 284*a**3 = 0. Calculate a.
-62, 0, 1/3
Factor -4905*f**4 + 4906*f**4 - 9*f**3 + 18*f + 31*f - 4*f**3 + 35*f**2.
f*(f - 7)**2*(f + 1)
Let c(p) be the third derivative of -p**6/360 + 7*p**5/180 + 49*p**2. Factor c(d).
-d**2*(d - 7)/3
Suppose -5 - 4*i**4 + 40*i**3 - 8*i - 20*i**2 + 5 - 34*i**3 - 22*i**3 = 0. What is i?
-2, -1, 0
Find r such that 0 + 9*r - 3/2*r**2 = 0.
0, 6
Let u be (-940)/(-5922)*(0 + (-9)/(-15)). Find h such that -8/21*h - u*h**3 - 10/21*h**2 + 0 = 0.
-4, -1, 0
Let y be (3 + 1)/((-4)/(-2)) - -1. Solve -k**3 + 4 + 12*k - 5*k**3 - 2*k**y + 8*k**2 + 0*k - 4*k**5 - 12*k**4 = 0 for k.
-1, 1
Let x(k) be the third derivative of -k**5/36 - 35*k**4/72 + 65*k**3/3 + 467*k**2. Let x(s) = 0. Calculate s.
-13, 6
Factor 152/7*j - 6/7*j**2 + 104/7.
-2*(j - 26)*(3*j + 2)/7
Let u(w) = -10*w**2 + 490*w - 2*w**3 + 0*w**3 - 474*w. Let f(d) = 6*d**3 + 29*d**2 - 49*d. Let b(g) = 4*f(g) + 11*u(g). Factor b(l).
2*l*(l - 2)*(l + 5)
Suppose 112*b + 174*b**4 - 34*b**4 + 3*b**5 + 464*b**2 - 96 + 32 + 13*b**5 + 412*b**3 = 0. What is b?
-4, -2, -1, 1/4
Let d be (3*2/14)/(11 + (-1125)/105). Factor 3 + 0*g**2 + 9/2*g - d*g**3.
-3*(g - 2)*(g + 1)**2/2
Let g(n) = -n + 18. Let c be g(15). Factor -8*w**2 - 3*w**4 - c*w**4 + 7*w**4 + 16.
(w - 2)**2*(w + 2)**2
Let z(w) be the second derivative of -w**6/75 + 4*w**5/25 + w**4/30 - 8*w**3/15 - 239*w. Factor z(x).
-2*x*(x - 8)*(x - 1)*(x + 1)/5
Determine g so that 208/3*g + 50*g**2 - 70/3*g**4 - 328/3*g**3 + 40/3 = 0.
-5, -2/5, -2/7, 1
Let h be 1 - -7 - 19584/2496. Factor 2/13*u**3 - h*u**2 - 2/13*u + 0 + 2/13*u**4.
2*u*(u - 1)*(u + 1)**2/13
Let y(g) = g + 6. Let i be y(-6). Let d(r) be the first derivative of -6*r**2 - 4*r**3 + i*r - 3/4*r**4 + 2. Factor d(s).
-3*s*(s + 2)**2
Let o be ((-6)/210)/(3/(-5)). Let r(d) be the second derivative of 0*d**3 - o*d**4 + d + 0 - 1/105*d**6 + 3/70*d**5 + 0*d**2. Factor r(b).
-2*b**2*(b - 2)*(b - 1)/7
Let o(b) be the first derivative of -5*b**3/3 + 110*b**2 - 2420*b + 170. Factor o(p).
-5*(p - 22)**2
Let z = 1106/33 - 7643/231. What is f in -6/7*f - 9/7*f**2 + 0 - z*f**3 = 0?
-2, -1, 0
Let h be 2/(3/72*3). Factor 23*t + h*t**2 - 11*t**2 - 13*t.
5*t*(t + 2)
Let p(k) be the first derivative of -1/18*k**6 + 0*k - 1/4*k**4 + 0*k**2 + 4 - 1/9*k**3 - 1/5*k**5. Factor p(b).
-b**2*(b + 1)**3/3
Let h be (4/(-16))/(-4*15/400). Factor 1/3*g**2 - 1/3*g**4 + h*g**3 - 1/3*g**5 + 4/3 - 8/3*g.
-(g - 1)**3*(g + 2)**2/3
Let n(l) = -1. Let d(g) = 3*g**3 + 27*g**2 + 72*g + 50. Let c(j) = -d(j) - 2*n(j). Let c(y) = 0. What is y?
-4, -1
Let m(x) = -12*x**3 + 10*x**2 + 16*x - 14. Let j(o) = o**3 - o**2 - o + 1. Let d(w) = 28*j(w) + 2*m(w). What is c in d(c) = 0?
0, 1
Let y(p) = -36*p**2 + 700*p + 692. Let s(x) = 7*x**2 - 140*x - 139. Let n(g) = 11*s(g) + 2*y(g). Solve n(a) = 0.
-1, 29
Let v = -22 + 31. Determine c, given that -3*c + 5*c + 17*c - 49*c**2 + v*c - 4 = 0.
2/7
Let n(u) = -u**5 + u**4 + u**3 + u**2 - u - 1. Let d(c) = -37*c**5 + 208*c**4 - 329*c**3 + 58*c**2 - 4*c - 4. Let q(m) = -d(m) + 4*n(m). Factor q(b).
3*b**2*(b - 3)**2*(11*b - 2)
Let r(x) be the third derivative of 1/15*x**5 + 0*x + 1/120*x**6 - x**2 + 1 + 5/24*x**4 + 1/3*x**3. Let r(u) = 0. What is u?
-2, -1
Let w(n) = -42*n + 1769. Let a be w(42). Factor -3*k**2 + 0 - 6/7*k - 3/7*k**a - 27/7*k**3 - 15/7*k**4.
-3*k*(k + 1)**3*(k + 2)/7
Let u(r) be the third derivative of -r**5/30 + 17*r**4/2 - 867*r**3 - 42*r**2. Factor u(d).
-2*(d - 51)**2
Let s(u) = 8*u + 8 - 9*u + 2. Let c be s(7). Let 3/2 + 0*y**2 + c*y - 3/2*y**4 - 3*y**3 = 0. Calculate y.
-1, 1
Let g(c) be the third derivative of c**9/241920 + c**8/40320 + c**7/20160 - 11*c**5/60 - 2*c**2. Let n(w) be the third derivative of g(w). Factor n(s).
s*(s + 1)**2/4
Suppose 0*z - 3*z - 16 = l, 4 = z + 5*l. Let o be -3*1/(-8) - z/(-16). Factor -2/3*s**2 + o*s + 0 + 2/3*s**3.
2*s**2*(s - 1)/3
Determine h so that 349 - 69 + 127 + 60*h + 2*h**2 + 43 = 0.
-15
Suppose 12*s**4 - 33*s**2 - 5*s**2 + 4*s**5 + 0*s**3 - 8*s**3 - 22*s**2 - 32*s + 12*s**2 = 0. What is s?
-2, -1, 0, 2
Let f(r) = r**2 + 2*r + 3. Let w = 143 - 143. Let h be f(w). Find x, given that 8/5*x + 44/5*x**2 - 4/5 - 48/5*x**h = 0.
-1/3, 1/4, 1
Let j(t) be the first derivative of t**4/4 - 5*t**3/3 - t**2/2 + 5*t + 276. Factor j(o).
(o - 5)*(o - 1)*(o + 1)
Let k = -393 - -393. Factor 0*a**2 - 2/7*a**3 + k + 2/7*a.
-2*a*(a - 1)*(a + 1)/7
Suppose -7*d = -47 - 37. Let j = d + -1. Factor -3*x**2 - 2 + 3*x - 6*x + 10*x**3 - j*x**3 + 1.
-(x + 1)**3
Factor 16*q - 2*q**4 - 12*q**3 - 29*q - 6*q**2 + 8 + 21*q + 4*q**3.
-2*(q - 1)*(q + 1)*(q + 2)**2
What is r in -12508 + r**4 - 94*r**2 - 26*r**3 - 312*r + 12652 + 287*r**2 = 0?
1, 12
Solve -4/7*d**2 + 2 - 250/21*d = 0 for d.
-21, 1/6
Let r(t) = -5*t**3 + 8*t**2 - 3*t - 3. Let x(h) = -9*h**3 + 14*h**2 - 5*h - 5. Let d(z) = 5*r(z) - 3*x(z). Suppose d(l) = 0. Calculate l.
0, 1
Let b be (128/(-4) + 38)*(2 + 28/(-18)). Find i such that 0 - b*i + 2/3*i**3 - 2*i**2 = 0.
-1, 0, 4
Let z(b) = -65*b - 325. Let s be z(-5). Let g(j) be the third derivative of s - 1/15*j**5 + 0*j + 2/3*j**4 + 3*j**2 - 2*j**3. Factor g(f).
-4*(f - 3)*(f - 1)
Let a(u) = u**2 - 9*u. Let w(l) = 2*l**2 - 43*l. Let r(p) = -7*p**2 + 171*p. Let x(h) = 2*r(h) + 9*w(h). Let n(t) = -11*a(t) + 2*x(t). Factor n(g).
-3*g*(g - 3)
Let g = 744 - 6680/9. Find w such that -2/9 - 2/3*w**4 - g*w**2 - w - 1/9*w**5 - 14/9*w**3 = 0.
-2, -1
Let h(q) = q**3 - 4*q**2 + 4*q - 1. Let r be h(1). Let x(k) be the third derivative of 11/72*k**4 + 0 - 1/60*k**5 - 1/3*k**3 - 5*k**2 + r*k. Factor x(j).
-(j - 3)*(3*j - 2)/3
Factor 30*h - 3/4*h**2 - 300.
-3*(h - 20)**2/4
Let o(p) be the first derivative of -p**7/168 + p**6/40 - 3*p**5/80 + p**4/48 - p + 10. Let k(n) be the first derivative of o(n). Factor k(t).
-t**2*(t - 1)**3/4
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