k(q).
-2*q**3*(q - 2)/9
Let f be (4/(-2))/(7/(-3962)) + -1. Let i = 1134 - f. Factor 2/3*o + 1/3*o**5 - 1/3*o**2 + 1/3*o**4 + 0 - o**i.
o*(o - 1)**2*(o + 1)*(o + 2)/3
Let g(z) = z**3 - 2*z**2 - 7*z - 4. Let j(f) = f**3 - 2*f**2 - 7*f - 4. Let a(h) = -6*g(h) + 7*j(h). Find s, given that a(s) = 0.
-1, 4
Let b be 120/(-120) - (-7 - (-1)/(-1)). Let u be 1/b + (10 - 1990/210). Determine a, given that 4/3*a**4 - 8/3*a - 16/3*a**2 - 2*a**3 + 0 + u*a**5 = 0.
-2, -1, 0, 2
Suppose 4*c - 15 = z, -156 = -5*c + 4*z - 151. Let t(f) be the second derivative of 35/6*f**3 - 5/4*f**4 + 0 + 15*f - c*f**2. What is u in t(u) = 0?
1/3, 2
Let a(h) = 2*h**3 + 11*h**2 - 5*h + 6. Let u be a(-6). Let j be 4 + u + (1 - (-22)/(-5)). Factor 6/5*k - j - 3/5*k**2.
-3*(k - 1)**2/5
Let x be -5*4 + 40176/1953. Solve 18/7*k - 8/7*k**2 - x = 0.
1/4, 2
Let s(t) = 55*t - 73. Let j be s(16). Let i = j + -801. Determine p, given that 15/2*p**3 + i*p**2 + 0 + 3*p**4 + 3/2*p = 0.
-1, -1/2, 0
Let s = -2/686369 - 2983646035/2745476. Let v = s - -1087. Solve -5/4*p + 3/2 - v*p**2 = 0 for p.
-6, 1
Let x(z) be the third derivative of -10985/6*z**3 - 13/4*z**5 - 845/8*z**4 + 0*z - 1/24*z**6 + 76*z**2 + 0. Suppose x(b) = 0. What is b?
-13
Let b(y) be the third derivative of -y**6/480 + 7*y**5/12 - 759*y**4/32 + 1647*y**3/4 - 7612*y**2. Factor b(i).
-(i - 122)*(i - 9)**2/4
Let u(a) = 3002*a**2 - 3016*a + 446. Let s(q) = -3003*q**2 + 3015*q - 372. Let o(w) = -6*s(w) - 5*u(w). Factor o(l).
2*(l - 1)*(1504*l - 1)
Suppose 105*u - 280 = 35*u. Let b(x) be the second derivative of 13*x - 1/75*x**6 + 0*x**2 + 0 + 4/15*x**3 + 0*x**u - 3/50*x**5. Factor b(h).
-2*h*(h - 1)*(h + 2)**2/5
Let h be (-180)/(-189)*(7 - 1). Let i = h + -3/14. Find t such that 2 + 6*t + 7/2*t**4 - 6*t**3 - i*t**2 = 0.
-1, -2/7, 1, 2
Let j(x) be the second derivative of -x**7/56 - 23*x**6/120 - 13*x**5/16 - 85*x**4/48 - 13*x**3/6 - 3*x**2/2 + 1742*x. Determine w, given that j(w) = 0.
-3, -2, -1, -2/3
Let y = -8577 + 60041/7. Suppose 0 = d - 2 - 0. Let y*k**4 + 44/7*k**d - 16/7*k**3 - 48/7*k + 18/7 = 0. What is k?
1, 3
Suppose x - 67 - 8 = 2*l, -294 = -4*x + 5*l. Let d = x - 69. Factor -47*i**3 - 5*i**4 - 2*i + 32*i**3 - 13*i**2 - 3*i - 2*i**d.
-5*i*(i + 1)**3
Let b(m) = 21*m**2 - 5*m**3 + 7*m**3 + 2*m**3 + 12 - 3*m**2 - 34*m + 14*m. Let o(d) = -3*d**3 - 12*d**2 + 13*d - 8. Let z(n) = 5*b(n) + 7*o(n). Factor z(w).
-(w - 4)*(w - 1)**2
Let n = 226 + -222. Let -1104*f + 0 + 24 - n*f**2 + 1084*f = 0. What is f?
-6, 1
Let f(b) be the second derivative of b**5/4 + 325*b**4/6 - 5*b**3/6 - 325*b**2 - 2*b - 2528. Find k, given that f(k) = 0.
-130, -1, 1
Let -890 + 6*d**2 - 2*d**2 + 555*d + 1140 + d**2 - 810 = 0. What is d?
-112, 1
Let u be 1/(540/(-106)) + 9/810*18. Let d(w) be the third derivative of 1/540*w**6 + 5*w**2 + 0 + 0*w**4 + 0*w**3 + 0*w - u*w**5. Suppose d(i) = 0. Calculate i.
0, 1
Suppose 0 = -3*a - 3*q + 75, 1122 = a - q + 1141. Suppose -7/6*k**4 + 23/6*k**2 - 6 - 1/6*k**5 - 20/3*k + 7/2*k**a = 0. Calculate k.
-9, -1, 2
Suppose -59*n + 6 = -57*n. Factor 4*y**3 + 285*y**2 - 17*y + y**5 - 10*y**4 + 4*y**n - 283*y**2 + 8 + 8*y**3.
(y - 8)*(y - 1)**3*(y + 1)
Let s be (6 - 89960/180) + 4/(-18). Let z = 499 + s. Determine p so that 0 - 2/5*p - 2/5*p**2 + 2/5*p**4 + 3/10*p**3 + 1/10*p**z = 0.
-2, -1, 0, 1
Factor 33/4*y**2 - 1/4*y**3 + 0 - 31/2*y.
-y*(y - 31)*(y - 2)/4
Let 0 + 6/11*f**5 - 126/11*f**4 + 342/11*f**3 - 30*f**2 + 108/11*f = 0. Calculate f.
0, 1, 18
Let j(r) = 2*r**3 - 3*r**2 + r. Let n be j(1). Let c be (5 + n/(-4))*(-10)/(-25). Find f, given that 8/3*f**3 - 5*f**c + 16/3*f**4 - 8/3*f - 1/3 = 0.
-1, -1/4, 1
Factor -27/2*z + 5/2*z**2 + 5.
(z - 5)*(5*z - 2)/2
Let t(u) be the third derivative of -u**5/300 - 47*u**4/120 - 528*u**2. Determine z so that t(z) = 0.
-47, 0
Factor 10/3*o**4 - 206/3*o - 196/3*o**2 - 70/3 + 2/3*o**5 - 52/3*o**3.
2*(o - 5)*(o + 1)**3*(o + 7)/3
Let g(r) be the third derivative of -171*r**2 + 0*r + 9/7*r**3 - 2/7*r**4 + 0 - 1/7*r**5 + 1/245*r**7 + 2/35*r**6. Factor g(v).
6*(v - 1)**2*(v + 1)*(v + 9)/7
Suppose 4*n + 4*l = 56, 56 = 5*n - 4*l - 23. Determine d so that -55*d + 113*d + n*d**2 + 72*d + 80 = 0.
-8, -2/3
Factor -6*o**2 + 23*o**2 - 10*o**2 + 42902500 + 16234*o - 3*o**2 + 9966*o.
4*(o + 3275)**2
Suppose 0 = -4*v - 4*d + 216, 2*v - 5*v = 2*d - 163. Factor -6*x + 2*x - 3*x**2 + 52 - 2*x - v.
-3*(x + 1)**2
Let f(j) = 16*j**2 - 1789*j + 399619. Let m(t) = -14*t**2 + t - 1. Let s(n) = -2*f(n) - 2*m(n). Solve s(o) = 0 for o.
447
Let j = 11069 + -11067. Let g(p) be the third derivative of -5/12*p**5 - 25/3*p**3 + 0 + 45/8*p**4 + 0*p - 6*p**j. Solve g(y) = 0.
2/5, 5
Let n = -1603211/5 - -320671. Find w such that -2/5*w**2 + n*w - 2592/5 = 0.
36
Suppose 0 = 14*o - 16*o + 4. Factor 4*m**5 + 942*m**4 - 5*m**5 + o*m**2 - 944*m**4 + m.
-m*(m - 1)*(m + 1)**3
Factor 7/4*a**4 + 0 - 7*a**2 + 3/4*a**3 - 3*a.
a*(a - 2)*(a + 2)*(7*a + 3)/4
Let f be -69*((-42)/105 - 544/(-1410)). Let u = f + -137/188. Factor -u*z**2 + 0 + 0*z + 1/4*z**3.
z**2*(z - 1)/4
Let l(z) be the third derivative of z**8/80640 + z**7/5040 + z**6/960 + 31*z**5/30 - 3*z**2 - 8. Let w(t) be the third derivative of l(t). Factor w(a).
(a + 1)*(a + 3)/4
Let p(k) be the third derivative of -k**5/75 + 11*k**4/10 + 76*k**3/3 + 21*k**2. Solve p(u) = 0 for u.
-5, 38
Suppose g = -3*g + 1724. Solve 28*b + 20*b**2 + 215 - g + 4*b**3 + 228 = 0 for b.
-3, -1
Let n be 650/65 + (-59)/6. Let g(l) be the second derivative of 1/12*l**6 - 9*l + 7/24*l**4 + 0*l**2 - 1/84*l**7 + 0 - 9/40*l**5 - n*l**3. Factor g(d).
-d*(d - 2)*(d - 1)**3/2
Let v be (300 - 299)/((-21)/(-1369))*(-1 + 7). Factor -v - 2/7*g**2 - 148/7*g.
-2*(g + 37)**2/7
Let g(o) = -o**2 + 459*o - 5065. Let n(u) = -152*u + 1689. Suppose -46*d = 11*d - 627. Let p(w) = d*n(w) + 4*g(w). Factor p(l).
-(2*l - 41)**2
Let y(c) be the third derivative of 0*c - 18*c**2 + 1/2*c**3 - 1/60*c**5 + 1/1080*c**6 + 0 + 1/9*c**4. Let n(l) be the first derivative of y(l). Factor n(r).
(r - 4)*(r - 2)/3
Let h(t) be the third derivative of -1 + 0*t**3 + 1/420*t**6 - 1/35*t**5 + t**2 + 2/21*t**4 + 0*t. Solve h(q) = 0 for q.
0, 2, 4
Let d be (2 - 536/(-14)) + 76/(-266). Factor 2*m**3 + 497*m**2 + d*m - 472*m**2 + 3*m**3 + 20.
5*(m + 1)*(m + 2)**2
Let l(p) = p**3 - 10*p**2 + 12*p - 23. Let d be l(9). What is o in 20*o + 11*o - 6 + 3*o**3 - 4*o**3 - 20*o - d*o**2 = 0?
-6, 1
Suppose -32*s + 35*s - 15 = -3*o, 17 = 3*o + 4*s. Let a = 2/383 + 2260/7277. Factor 2/19*x**o + 0*x**2 - 4/19 - a*x.
2*(x - 2)*(x + 1)**2/19
Let m(j) = 60*j - 409. Let q be m(7). Find z, given that 59*z - q*z - 437 + 385 + 4*z**2 = 0.
-13, 1
Let x = -2923 - -2926. Let v(i) be the first derivative of -32/27*i**x - 8/9*i**2 - 6 - 5/9*i**4 - 4/45*i**5 + 0*i. Factor v(r).
-4*r*(r + 1)*(r + 2)**2/9
Let q(i) be the first derivative of i**3/12 + 89*i**2/8 - 69*i - 1142. Find g, given that q(g) = 0.
-92, 3
Let v = -206 + 116. Let n = v + 93. Find o, given that -6/7*o**2 + 0*o + 0 + n*o**3 - 15/7*o**4 = 0.
0, 2/5, 1
Let a be 0/(-1)*(2201/(-213) - (-1 - 9)). Factor a - 8/13*i - 2/13*i**4 - 10/13*i**3 - 16/13*i**2.
-2*i*(i + 1)*(i + 2)**2/13
Let x(a) be the second derivative of a**5/140 - 11*a**4/84 - 20*a**3/21 - 2*a**2 + 688*a. Find l such that x(l) = 0.
-2, -1, 14
Let n(w) = -w**4 + 3*w**2 - w + 1. Let f = 151 - 149. Let h(p) = p**3 + p**2 - p + 1. Let x(r) = f*n(r) - 2*h(r). Determine o, given that x(o) = 0.
-2, 0, 1
Suppose 0 = -8*k + 7*k + 2*p + 7, -4*k + 17 = 3*p. Factor 29*c**3 - 20*c**3 + 2*c**4 - 10*c**3 - c**k.
-c**3*(c - 1)**2
Let c(u) be the first derivative of u**8/840 - u**7/105 + u**6/60 + 2*u**3/3 + u**2 - 9. Let k(y) be the third derivative of c(y). Determine g so that k(g) = 0.
0, 1, 3
Suppose -3*r = -5*p + 5, 25*r - 37 = -3*p + 20*r. Suppose 3*u = 0, -x + u = -u - 2. Determine l, given that 0 - 2/7*l**x + 2/21*l - 2/21*l**p + 2/7*l**3 = 0.
0, 1
Let o(a) be the second derivative of 3*a**5/80 + 173*a**4/8 + 2049*a**3/8 + 2295*a**2/2 - 8*a - 54. Let o(r) = 0. What is r?
-340, -3
Let d(n) = 105*n**2 + 408*n - 144. Let f(i) = -13*i**2 - 51*i + 12. Let a(p) = 1. Let s(l) = -6*a(l) - f(l). Let k(h) = 4*d(h) - 33*s(h). Factor k(r).
-3*(r + 6)*(3*r - 1)
Factor -497*i**2 - 11109*i**2 - 1985 - 6656*i + 98*i**3 + 1033.
2*(i - 119)*(7*i + 2)**2
Factor 4/5*r - 