*k + c*k**2 + 3/4*k**3 + 2 = 0. Calculate k.
-2, 1, 2
Let r be ((-456)/(-180))/(-19) - 2764/(-30). Suppose r = -12*s + 92. Determine t, given that 0*t - 15/8*t**5 - 3/8*t**3 + 3*t**4 - 3/4*t**2 + s = 0.
-2/5, 0, 1
Let i(a) be the third derivative of a**5/40 + 17*a**4/16 + 4*a**3 - a**2 + 517. Find d such that i(d) = 0.
-16, -1
Let v(u) be the third derivative of -u**7/8820 + 31*u**4/12 + 4*u**2 + 2. Let k(n) be the second derivative of v(n). Find x such that k(x) = 0.
0
Let f(w) be the second derivative of -1/6*w**4 + 0*w**2 - 2/3*w**3 + 0 + 1/15*w**6 + 1/5*w**5 - 109*w. Determine y, given that f(y) = 0.
-2, -1, 0, 1
Suppose 9*x = -16*x - 6725. Let o = x + 271. Factor 3/2*z**o + 3/8*z - 3/8*z**3 - 3/2.
-3*(z - 4)*(z - 1)*(z + 1)/8
Let u(q) be the first derivative of -5*q**6/48 - 403*q**5/40 - 2057*q**4/8 - 961*q**3/6 + 1180*q**2 - 800*q + 5464. Let u(n) = 0. Calculate n.
-40, -2, 2/5, 1
Solve 160 - 3079*g + 2711*g + 12*g**5 - 140*g**4 + 76*g**4 + 44*g**3 + 216*g**2 = 0.
-2, 1, 2, 10/3
Let b(l) = 56*l**4 + l**3 + 25*l**2 + 9*l + 13. Let n(t) = -26*t**4 - 12*t**2 - 4*t - 6. Let i(q) = -6*b(q) - 13*n(q). Factor i(o).
2*o*(o - 1)**3
Factor 53*z - 358*z + z**2 - 206 + 107*z - 7*z.
(z - 206)*(z + 1)
Let l be ((-12)/21)/(0 + -7*10/245). Determine x so that 54/7*x**l + 8 + 4/7*x**3 + 104/7*x - 2/7*x**4 = 0.
-2, -1, 7
Let b(c) be the first derivative of -2*c**5/55 - 14*c**4/11 - 180*c**3/11 - 972*c**2/11 - 1458*c/11 - 1276. Factor b(l).
-2*(l + 1)*(l + 9)**3/11
Suppose 31*k = 151 - 27. Let y(m) = m**2 - m - 4. Let l be y(3). Factor -3*u**l + 10*u**2 + k*u**3 - 4*u**2 + u**2.
4*u**2*(u + 1)
Let u = -308 + 248. Let g be ((-20)/24)/(3/(54/u)). Factor 1/4*m**2 + m - m**3 - g.
-(m - 1)*(m + 1)*(4*m - 1)/4
Let j = -169445 - -169511. Factor -726 + j*p - 3/2*p**2.
-3*(p - 22)**2/2
Determine w so that -2*w**2 - 112*w + 337*w - 74*w - w**2 + 416*w = 0.
0, 189
Let u(g) = -23*g**3 + 25*g**2 + 47*g + 29. Let s(a) = 12*a**3 + a**2 + 2*a - 2. Let k(x) = -2*s(x) - u(x). Let k(h) = 0. What is h?
-25, -1
Factor 432/5 + 12/5*q**3 + 188/5*q**2 + 768/5*q.
4*(q + 6)*(q + 9)*(3*q + 2)/5
Suppose -13*b + 9 = -199. Factor b*f**2 + 5*f**3 + 10*f**4 + 14*f**4 - 8*f - 15*f**3 - 22*f**4.
2*f*(f - 2)**2*(f - 1)
Let b be (-80)/96 - (5/(-2) - -1). Let v(a) be the second derivative of 0 - 1/5*a**5 - 28*a - 2/3*a**4 - b*a**3 + 0*a**2. Factor v(z).
-4*z*(z + 1)**2
Let j(f) be the first derivative of -2*f**3 + 32*f - 1/15*f**5 + 16/3*f**2 + 72 - 3/4*f**4. Factor j(w).
-(w - 2)*(w + 3)*(w + 4)**2/3
What is f in 28/5*f**4 - 1/5*f**5 - 244/5*f**3 + 0 + 672/5*f**2 - 576/5*f = 0?
0, 2, 12
Let b be -6*(10/6 - 2). Determine q, given that 140*q - 61*q - 70*q + b*q**2 + 7 = 0.
-7/2, -1
Suppose -2*k = -456 + 450. Factor 0*x**3 + 119*x**2 + 39*x**2 + 102*x**2 - 4*x**k.
-4*x**2*(x - 65)
Let y(h) be the second derivative of -h**4/12 + 155*h**3 - h + 2804. Find o such that y(o) = 0.
0, 930
Let m(j) be the first derivative of -j**4/30 + 56*j**3/45 - 53*j**2/15 + 52*j/15 + 9909. Factor m(a).
-2*(a - 26)*(a - 1)**2/15
Let j(k) = 9*k**2 + 1671*k - 364. Let r(v) = -2*v**2 - 418*v + 84. Let z(i) = 3*j(i) + 13*r(i). Find h such that z(h) = 0.
0, 421
Let t(y) be the second derivative of 0*y**2 + 0 - 1/3*y**3 + 86*y + 1/78*y**4. Factor t(r).
2*r*(r - 13)/13
Let v(y) be the first derivative of 5*y**3 - 9 - 5/12*y**4 + 12*y - 25/2*y**2. Let n(b) be the first derivative of v(b). Factor n(a).
-5*(a - 5)*(a - 1)
Let w(l) be the second derivative of 0 - 1/2*l**2 - 1/12*l**3 - 13*l + 1/24*l**4. Factor w(b).
(b - 2)*(b + 1)/2
Let d(o) be the first derivative of o**4 - 1520*o**3/3 + 73696*o**2 - 565504*o + 9389. Solve d(x) = 0.
4, 188
Let g(b) be the first derivative of -2*b**3/15 - 107*b**2/5 - 212*b/5 + 684. Determine a so that g(a) = 0.
-106, -1
Let b be (-1)/(-5) - 58*(-2)/20. Let x(h) = 18*h**2 - 119*h - 36. Let z(m) = 3*m**2 - 20*m - 6. Let p(u) = b*x(u) - 34*z(u). Determine d, given that p(d) = 0.
-1/3, 6
Let d = 25891/25 - 1035. Let t = d - 11/25. Let 2*z**2 + 9/5*z - t = 0. Calculate z.
-1, 1/10
Let m = 20558/9 + -2282. Suppose -6*h = 3*j + 3, -5*j = 11 + 14. Determine y so that h + m*y + 2/9*y**2 = 0.
-9, -1
Let l = 35 + 182. Let d = l - 1518/7. Factor -d*y**2 + 4/7 + 0*y.
-(y - 2)*(y + 2)/7
Let m(o) be the first derivative of o**6/12 + 31*o**5/5 + 147*o**4/4 + 260*o**3/3 + 401*o**2/4 + 57*o + 1189. Suppose m(p) = 0. What is p?
-57, -2, -1
Let h be -1 - (8 + 17 + (-1918)/70). Suppose -h*o + 1/5*o**2 + 0 = 0. What is o?
0, 7
Suppose 1542*b - 59023 - 55583 = 476*b + 60218. Factor b*z + 495*z**2 - 3375/4*z**4 + 675/4*z**3 + 16.
-(z - 1)*(15*z + 4)**3/4
Let f(h) be the first derivative of -h**4/2 + 24*h**3 + 76*h**2 - 197. Factor f(z).
-2*z*(z - 38)*(z + 2)
Suppose -8*f + 20 = -3*f. Suppose -2*r - 6 = 0, f*c - r - 5 = -6*r. Factor 13*l**2 - 6*l**2 + 23*l**2 + c*l**3.
5*l**2*(l + 6)
Let m = 28997/2 + -13648. Factor 12 - 729/2*x**4 + m*x**3 + 675*x**2 + 158*x.
-(x - 3)*(9*x + 2)**3/2
Let l be 7*60/70 - 6. Let i(r) be the second derivative of -1/3*r**3 + l + 4*r - 1/18*r**4 - 2/3*r**2. Factor i(p).
-2*(p + 1)*(p + 2)/3
Let i = 2246498/1347897 + -1/449299. Suppose 280/3*z - i*z**2 - 3920/3 = 0. What is z?
28
Let m(p) be the second derivative of -3*p**5/20 - 2*p**4/3 + p**3/3 + 3*p**2 + 155*p. Let l(v) = v + 1. Let h(g) = -6*l(g) + m(g). Solve h(r) = 0.
-2, -2/3, 0
Let 0 - 137/7*q - 1/7*q**2 = 0. What is q?
-137, 0
Suppose 315 + 101 = 4*i. Factor 3950*p - 564*p**4 + 560*p**4 - 960*p**2 - 4096 + i*p**3 - 366*p.
-4*(p - 8)**3*(p - 2)
Factor -165/2 + 1/4*m**2 + 23/4*m.
(m - 10)*(m + 33)/4
Let s(n) be the first derivative of 2*n**5/25 - 11*n**4/10 + 16*n**3/3 - 48*n**2/5 - 147. Determine x so that s(x) = 0.
0, 3, 4
Let y(n) be the first derivative of -1/6*n**6 + 0*n**3 + 0*n**5 + 1/2*n**4 + 0*n - 1/2*n**2 - 53. Factor y(f).
-f*(f - 1)**2*(f + 1)**2
Let w = -10586 + 22565/2. Let d = -696 + w. Factor 1/4*c**2 + d*c**3 + 1/4*c**4 + 0*c + 0.
c**2*(c + 1)**2/4
Let c(t) = 6*t. Let u(i) = -i**2 + 90*i. Let z(n) = -9*c(n) + u(n). Factor z(k).
-k*(k - 36)
Suppose 65*y - 111*y = 52 - 144. Let c(x) be the first derivative of -15 + x - 13/4*x**y - 4/3*x**3 + 7/8*x**4. Factor c(z).
(z - 2)*(z + 1)*(7*z - 1)/2
Let t(w) be the second derivative of w**6/70 + 3*w**5/140 - 9*w**4/14 - 26*w**3/7 - 60*w**2/7 + 196*w - 2. Factor t(y).
3*(y - 5)*(y + 2)**3/7
Let r(c) be the first derivative of c**4/20 + c**3/10 - 58*c + 27. Let p(t) be the first derivative of r(t). Factor p(w).
3*w*(w + 1)/5
Let f = -744967/4 - -186242. Factor 1/4*m**2 + f*m - 1/2.
(m - 1)*(m + 2)/4
Let o(g) be the first derivative of -g**3/12 - 15*g**2/4 - 225*g/4 + 2288. Factor o(j).
-(j + 15)**2/4
Let f = 7755 + -7753. Let t(p) be the first derivative of 25 + 5/6*p**3 - 35/4*p**f + 0*p. Factor t(w).
5*w*(w - 7)/2
Let f(k) be the second derivative of 385*k**4/12 - 255*k**3/2 - 5*k**2 - 3557*k. Factor f(m).
5*(m - 2)*(77*m + 1)
Let i(x) be the first derivative of -x**6/45 - x**5/120 + x**4/18 + x**3/36 + 69*x + 82. Let y(t) be the first derivative of i(t). Factor y(w).
-w*(w - 1)*(w + 1)*(4*w + 1)/6
Let k(l) = l**2 - 65 - l + 21 + 21 + 22. Let v(p) = p**3 - 6*p**2 + 5*p + 3. Let x(u) = 12*k(u) + 4*v(u). Determine n so that x(n) = 0.
0, 1, 2
Factor 2 + 13*c**2 - 33*c - 42*c**3 + 21*c**3 - 6*c + 25 + 20*c**3.
-(c - 9)*(c - 3)*(c - 1)
Let p(x) = -10*x**2 - 16*x + 29. Let c be p(5). Let s = c - -304. Let 5/4*r**s + 10*r + 5 + 25/4*r**2 = 0. What is r?
-2, -1
Let l(k) be the second derivative of -k**6/240 + k**5/60 + k**4/48 - k**3/6 + 62*k**2 - 116*k + 2. Let t(d) be the first derivative of l(d). Factor t(f).
-(f - 2)*(f - 1)*(f + 1)/2
Suppose 2*g - 9 = g. Suppose -22 = -g*s - 4. Let 19 + 77 - 11*y**s + 2*y**3 - 5*y**3 - 7*y**2 = 0. What is y?
-4, 2
Let q(n) be the first derivative of 8*n + n**4 + 36 + 16/3*n**3 + 10*n**2. Find d such that q(d) = 0.
-2, -1
Let q be 5*15/(-12)*-4 + -4. Factor 21 - 864*i - 3*i**4 - q - 99*i**3 + 96*i - 864*i**2.
-3*i*(i + 1)*(i + 16)**2
Solve -4/5*i**5 - 4*i**4 + 128/5*i - 16/5*i**3 + 64/5 + 64/5*i**2 = 0.
-2, -1, 2
Suppose -17*x + 65 = -139. Factor 147*g**3 - 11*g - 63*g**2 - x - 66*g + 5*g.
3*(g - 1)*(7*g + 2)**2
Let v(b) be the first derivative of 4*b**3/3 + 700*b**2 - 1582. Find p, given that v(p) = 0.
-350, 0
Let m be -9 - 180/(-162) - -19